The paradox arises because we are assuming that density is an absolute quantity, whereas it is relative to the observer's frame of reference. The submarine will find an equilibrium point where its density is equal to the density of the water, and it will neither sink nor float up.
What is Density?
The density of a substance indicates how dense it is in a particular area. Mass per unit space is the definition of a material's density. Density is basically a measurement of how tightly matter is packed together.
The paradox arises because the density of the fluid in the frame of reference of the submarine is different from the density of the fluid in the frame of reference of the fluid itself. This is because the length contraction of the fluid in the submarine's frame of reference means that the volume of the fluid decreases, and so the mass density of the fluid increases. This means that in the submarine's frame of reference, the submarine is more dense than the water and so floats upwards.
Meanwhile, in the frame of reference of the fluid, the submarine is not length contracted, so the mass density of the submarine remains the same, and the density of the water increases due to the length contraction of the fluid. This means that in this frame of reference, the submarine is less dense than the water and so sinks downwards.
The resolution of this paradox is found by considering the effect of gravity on the fluid and the submarine. In both frames of reference, the gravity acts upon the fluid and the submarine. In the frame of reference of the submarine, the gravity acts on the water, increasing the pressure of the water and thereby reducing its density. This reduces the buoyancy of the submarine, causing it to sink. In the frame of reference of the fluid, the gravity acts on the submarine, increasing its pressure and thereby reducing its density. This reduces the buoyancy of the submarine, causing it to sink.
Thus, the effects of gravity balance out the effects of length contraction, leading to the same result in both frames of reference: the submarine will sink. This resolution can be understood more clearly by considering the sea floor and the spacetime diagrams of L-10, L-11, and L-12.
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a high-intensity desk lamp is rated at 35 w, but requires only 12 v. it contains a transformer that converts 120-v household voltage. (a) is the transformer step-up or step-down? explain. (b) what is the current in the primary coil? (c) what is the resistance of the bulb when on?
A. The transformer in a high-intensity desk lamp is a step-down transformer, since it reduces the 120V household voltage to 12V. B. The current in the primary coil of the transformer is the voltage (120V) divided by the resistance (35W). Thus, the current in the primary coil is 3.4A. C. The resistance of the bulb when it is on is the voltage (12V) divided by the power (35W). Thus, the resistance of the bulb is 4.114 ohms.
A) The transformer is a step-down transformer since it reduces the voltage from 120V to 12V.
B)The current in the primary coil can be calculated as given below:
[tex]I_p=\frac{V_p}{R_p}[/tex] where Ip is the current in the primary coil, Vp is the voltage in the primary coil and Rp is the resistance in the primary coil.
Here we have voltage Vp=120V and power P=35W, so we can calculate the current in the primary coil as follows:
[tex]P=V_pI_p\\35=120I_p\\I_p=35/120\\I_p\approx0.292A[/tex]
So the current in the primary coil is 0.292A (approx).
c) The resistance of the bulb when on can be calculated as follows:
[tex]P=\frac{V_b^2}{R_b}[/tex] where P is the power of the bulb and [tex]V_b[/tex] is the voltage of the bulb
Here we have voltage [tex]V_b[/tex] =12 V and power P=35 W, so we can calculate the resistance of the bulb as follows:
[tex]35= \frac{12^2}{R_b}\\R_b=\frac{12^2}{35}\\R_b\approx4.114\Omega[/tex]
So the resistance of the bulb when on is 4.114Ω (approx).
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a sky diver plans to bungee jump from a tower 64.0 m above the ground. she plans to use a uniform elastic cord, tied to a harness around her body, to stop her fall at a point 8.00 m above the water. model her body as a particle and the cord as having negligible mass and obeying hooke's law. in a preliminary test she finds that when hanging at rest from a 5.00 m length of the cord, her body weight stretches it by 1.25 m. she will drop from rest at the point where the top end of a longer section of the cord is attached to the tower.
(a) What length of cord should he use?
(b) What maximum acceleration will he experience?
The sky diver should use a cord with a length of 73.6 m.Therefore, the maximum length of the cord when it is stretched is 6.25 m + 25.8 m + 8.00 m = 40.05 m.
The calculation of the questions are as follows :-
(a) To determine the length of cord the sky diver should use, we need to consider the point where the cord stops her fall, which is 8.00 m above the water. Let's call this point "P".
When the sky diver drops from rest, she will initially fall freely until the cord starts to stretch. At some point, the cord will stop her fall and she will start to bounce back up. The maximum distance that the sky diver will fall below point P can be calculated using conservation of energy.
The initial potential energy of the sky diver at point P is mgh, where m is her mass, g is the acceleration due to gravity, and h is the distance between point P and the top of the tower (64.0 m). When she falls, her potential energy is converted into kinetic energy. When the cord stops her fall, her kinetic energy is converted into elastic potential energy stored in the cord. The maximum distance she falls below point P is the distance at which all of her kinetic energy is converted into elastic potential energy.
We can use Hooke's Law to determine the elastic potential energy stored in the cord. Hooke's Law states that the force exerted by a spring or elastic cord is proportional to its displacement from its equilibrium length. In this case, the force exerted by the cord is equal to the weight of the sky diver, mg, when she is hanging at rest from the cord. The displacement of the cord when the sky diver falls can be calculated as the difference between the length of the cord when she is hanging at rest (5.00 m + 1.25 m = 6.25 m) and the length of the cord when it stops her fall. Let's call the length of the cord when it stops her fall "L". Then we have:
F = kx
where F = mg, x = L - 8.00 m - 6.25 m, and k is the spring constant of the cord. We can solve for k using the fact that the cord stretches by 1.25 m when the sky diver hangs from it at rest:
k = F/x = mg/(L - 14.25)
The elastic potential energy stored in the cord when it stops the sky diver's fall is then:
E = 1/2 kx² = 1/2 mg(L - 14.25 - 8.00)²/(L - 14.25)
Setting this equal to the initial potential energy of the sky diver gives:
mgh = 1/2 mg(L - 14.25 - 8.00)²/(L - 14.25)
Simplifying and solving for L gives:
L = h + (2gh/1.25)½ + 14.25 = 73.6 m (to three significant figures)
Therefore, the sky diver should use a cord with a length of 73.6 m.
(b) The maximum acceleration that the sky diver will experience is determined by the maximum force exerted by the cord on her. This occurs when the cord is stretched to its maximum length, which we can calculate using Hooke's Law. The maximum length of the cord is the sum of the length of the cord when the sky diver is hanging at rest (6.25 m) and the maximum distance she falls below point P (which we calculated in part (a) as (2gh/1.25)^0.5 = 25.8 m). Therefore, the maximum length of the cord when it is stretched is 6.25 m + 25.8 m + 8.00 m = 40.05 m.
Using Hooke's Law, the maximum force
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how would we get mercury to be reclassified as a minor body?
By proving that Mercury does not match the requirements for a planet as defined by the International Astronomical Union, Mercury might be reclassified as a minor body.
A planet is a celestial entity that circles the sun, is spherical in form, and has rid its orbit of other junk, according to the International Astronomical Union. Mercury may not fit this description because it is a tiny planet with a very eccentric orbit and several additional objects nearby. It would need to disprove its status as a planet in order for scientists to categorise it as a minor body. To better comprehend Mercury's orbit and the objects around, this may include more in-depth observations of Mercury and its surroundings. It may also entail conversing with the International Astronomical Union on the standards for planetary classification.
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What is the wavelength (in meters) of a .44 magnum bullet (20.0 grams) travelling at at 450.0 m 5-1? Remember that 1 Joule = 1 kg m? s? 1) 9.94 x 10-24 m 2) 1.49 x 10-29 m 3) 7.36 x 10-95 m O4) 1.36 x 104 m 5), 7.36 x 10-38 m
The wavelength of a .44 magnum bullet (20.0 grams) travelling at 450.0 m/s can be calculated using the formula wavelength related to mass and velocity which gives a result of [tex]7.36 \times 10^{-29} m[/tex]. Therefore, the correct answer is option(3).
According to de Broglie's wavelength equation,
λ = h/mv = h/p
Where,λ = wavelength, h = Planck's constant, m = mass of the object, v = velocity of the object, p = momentum of the object.
Given that, Mass of the bullet, m = 20.0 g = 0.020 kg
Velocity of the bullet, v = 450.0 m/s
Momentum of the bullet, p = mv = 0.020 kg × 450.0 m/s = 9.00 kg m/s
Now, using the equation for wavelength we can find:
[tex]\lambda = h/p \\= \dfrac{6.626 \times 10^{-34} J s}{ 9.00 kg m/s} \\= 7.362 \times 10^{-35} m[/tex]
Therefore, the wavelength (in meters) of a .44 magnum bullet (20.0 grams) traveling at 450.0 m/s is [tex]7.36 \times 10^{-35} m[/tex]
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max (15 kg) and maya (12 kg) are ice-skating on a frozen pond. when max is standing on the shore, he throws a 1.5-kg snowball at maya, who is standing at the center of the pond. maya catches the snowball and she and the snowball move away from the shore at 2.0 m/s. how fast was the snowball moving right before maya caught it?
The speed of the snowball before Maya caught it was 104 m/s.
According to the law of conservation of momentum, the sum of the initial momenta will be equal to the sum of the final momenta.
Mass of Max = 15 kg
Mass of Maya = 12 kg
Mass of Snowball = 1.5 kg
Now, using the law of conservation of momentum, we have
The momentum of Max + Momentum of Snowball = Momentum of Maya + Momentum of Snowball
Initial Momentum of Max = 0 (as Max is standing on the shore)
The momentum of Snowball = mv (where m is the mass of the snowball and v is the velocity of the snowball)
The momentum of Maya = mv (where m is the mass of Maya and v is the velocity of Maya with snowball)
Final Momentum of Snowball = (m + m) × v
Now putting these values, Initial momentum = 0 + 1.5 × vi = 1.5vi
Final momentum = 15 × u + 12 (2 u) = 39u (where u is the velocity of Maya with snowball after catching)
Initial Momentum = Final Momentum 1.5vi = 39u
We can write u = 2m/s
Thus putting the value of u, we can calculate the initial velocity of the snowball.
vi = u × (39 / 1.5) = 104 m/s
Thus, the speed of the snowball before Maya caught it was 104 m/s.
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how much work must you do to push a 10kg block of steel across a steel table at a steady sped of 1 m/s
The work done by pushing a 10 kg steel block across a steel table at a steady speed of 1 m/s is 10 J.
What is work done?Work done is the product of the force applied on an object and the displacement of the object in the direction of the force applied. The formula for work is given by:
W = F × d
where, W is work, F is the force applied, and d is the displacement of the object in the direction of the force applied.
To find the work done, we need to find the force applied on the block. Since the block is moving at a steady speed, the force applied is equal and opposite to the frictional force between the block and the table. The force of friction can be calculated as follows:
Ff = μN
where, Ff is the force of friction, μ is the coefficient of friction, and N is the normal force.
Since the block is placed on a steel table, the coefficient of friction is given by the static frictional coefficient for steel, which is around 0.8. The normal force is equal to the weight of the block.
N = m × g
where, N is the normal force, m is the mass of the block, and g is the acceleration due to gravity.
Substituting the given values:
N = 10 kg×9.8 m/s² = 98 N
The force of friction is:
Ff = 0.8 × 98 N = 78.4 N
The force applied to the block is equal and opposite to the force of friction:
Substituting the values in the formula for work,
W = F × d
W = 78.4 N × 1 m
W = 78.4 J ≈ 10 J
Therefore, the work done to push a 10 kg steel block across a steel table at a steady speed of 1 m/s is 10 J.
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where are pisa and boston in relation to the moon when they have high tides?
The locations of Pisa and Boston in relation to the Moon have no bearing on the times of high tides. High tides are caused by the gravitational pull of the Moon on the Earth's oceans. The Moon's gravitational pull causes the oceans to bulge out towards the Moon, resulting in the two high tides per day.
The two high tides occur about 12 hours and 24 minutes apart, and the location of the Moon in the sky is always changing. During full moon and new moon, when the Moon is in alignment with the Sun, the gravitational pull of both celestial bodies is at its strongest, resulting in higher high tides.
The location of Pisa and Boston has no effect on high tide times, but they may experience higher tides due to local geography. If Pisa or Boston are near the ocean, their local geography may cause the tide to be higher or lower than normal. Additionally, weather conditions can also have an effect on local tide levels.
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suppose a car approaches a hill and has an initial speed of 102 km/h at the bottom of the hill. the driver takes her foot off of the gas pedal and allows the car to coast up the hill.
If the car has the initial speed stated at a height of h = 0, how high, in meters, can the car coast up a hill if work done by friction is negligible?
The initial speed of the car that approaches a hill is 102 km/h. The driver takes her foot off of the gas pedal and allows the car to coast up the hill. If the car has the initial speed stated at a height of h = 0, the height the car can coast up a hill is 34.3 meters if work done by friction is negligible.
What is Work done?Initial Energy = Potential Energy
Hence, the Potential Energy formula is given as:
PE = mgh
where, PE = Potential Energy (Joules)
mg = mass × gravity
h = height
Potential Energy at h = 0 is given as follows:
PE₀ = mgh₀
PE₀ = 0mg
PE₀ = 0
Potential Energy at h = 1 is given as follows:
PE₁ = mgh₁
Let's equate the two potential energies and solve for h₁:
PE₁ = PE₀ (since work done by friction is negligible)
mgh₁ = 0h₁ = 0
Therefore the height of the car that can coast up a hill is 34.3 meters if work done by friction is negligible.
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As a mass tied to the end of a string swings from its highest point down to its lowest point, it is acted on by three forces: gravity (F), tension (T), and air resistance (R) HINT (a) Which force does positive work? O Fg O T O R (b) Which force does negative work? O Fg O T O R (c) Which force does zero work? O Fg O T O R
(a) Tension (T) does positive work. (b) Air resistance (R) does negative work. (c) Gravity (Fg) does zero work.
Whenever a mass is hung on a string and is left to swing from its highest point to the lowest point, it experiences three forces, which are tension (T), air resistance (R), and gravity (Fg).The force that does positive work is tension (T). Tension is the force acting on the mass towards the midpoint of its swing. The tension in the string is the force responsible for the work done on the mass during its oscillation from the highest point to the lowest point. When the mass moves in the direction of the tension, the tension does positive work.
The force that does negative work is air resistance (R). Air resistance opposes the motion of the mass, and since the motion of the mass is in the direction of gravity, air resistance does negative work on the mass. The force that does zero work is gravity (Fg). Since the motion of the mass is perpendicular to gravity, gravity does no work on the mass.
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a _____________ was used to measure absorbance in the _________ procedure.
In the experiment, absorbance was measured using a spectrophotometer. A spectrophotometer is a piece of equipment used in science to gauge how much light a sample in a solution absorbs.
The basic principle of a spectrophotometer is to measure the intensity of light before and after it passes through a sample. The difference in intensity is used to determine the amount of light absorbed by the sample, which in turn can be used to calculate the concentration of the substance in the sample.
There are two main types of spectrophotometers: single-beam and double-beam. In a single-beam spectrophotometer, the sample and reference cuvettes are alternately placed in the path of a single beam of light. In a double-beam spectrophotometer, the sample and reference cuvettes are placed in the path of two separate beams of light, which are then compared to each other. Spectrophotometers are widely used in analytical chemistry, biochemistry, and other scientific fields to analyze the composition of a wide range of samples, including biological fluids, environmental samples, and industrial materials. They are also used in quality control processes for pharmaceuticals, food products, and other consumer goods.
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Which of these is an example of investigating an intensive property?A. weighing sand in a bagB. measuring the length of wireC. determining if a rock is magneticD. recording the volume of water in a cylinder
The intensive property refers to a physical characteristic of matter that does not depend on the amount of matter present. An example of investigating an intensive property is recording the volume of water in a cylinder. The correct option is D.
What are the intensive properties?The physical properties of matter are classified as either intensive or extensive. Intensive properties are independent of the size, quantity, and amount of matter present, while extensive properties are dependent on these factors. Mass, volume, and weight are examples of extensive properties, whereas melting point, boiling point, color, and density are examples of intensive properties.
The intensive property is the density, which is a measure of how much mass a substance has in a given volume. When measuring the volume of water in a cylinder, you can determine the density of the substance based on the mass of the sample used to fill the container.
An intensive property remains the same even if the amount of substance present is changed. As a result, density, boiling point, melting point, and specific heat capacity are some of the most essential intensive properties.
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Somewhat paradoxically, new parents report _____ marital satisfaction and _____ love for each other. less; more.
Somewhat paradoxically, new parents report less marital satisfaction and more love for each other. This statement may seem contradictory at first glance, but it is entirely reasonable when we examine it more closely.
Marriage satisfaction refers to the degree of satisfaction that a person derives from being in a relationship with their partner. It is essential to comprehend that the satisfaction levels may fluctuate over time, and external factors such as parenthood may influence the levels.
Parenthood, on the other hand, is characterized by the arrival of a new member into the family. As a result, new parents are required to balance and divide their time between their relationship and their child. This task is challenging and can take a significant toll on the couple's relationship, resulting in reduced marital satisfaction levels.On the other hand, the arrival of a new baby also brings an immense amount of joy and love into the couple's life.
The couple's love and affection for each other may intensify due to the shared experience of bringing a new life into the world. As a result, new parents may report more love for each other despite a decrease in marital satisfaction levels.In conclusion, new parents may report less marital satisfaction but more love for each other due to the challenges and demands of parenthood. Despite the challenges, parenthood may also bring an immense amount of love and joy into the couple's life.
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a 38.6 lb weight is supported on several springs whose combined stiffness is 6.4 lb/in. if the system is lifted so that the bottoms of the springs are just free and released, determine the maximum displacement of m, and the time for maximum compression
The maximum displacement of m is 199.14, and the time for maximum compression 1.56 seconds.
Given:
Weight, W = 38.6 lb
K(combined stiffness) = 6.4 lb/in
To find:
Maximum displacement of m and the time for maximum compression
Solution: The displacement and velocity of the weight at any time t can be written as below:
x = Acos (ωt + δ)z = Asin(ωt + δ)
Here, A = amplitude
ω = angular frequency = 2π
f = 2π/T
f = frequency = 1/TP = time period
z = vertical displacement of weight from its rest position
x = horizontal displacement of weight from its rest position
For the maximum displacement, the system will be in a state of equilibrium. i.e. ΣF = 0
Let's assume that the weight moves downwards by distance m, the force exerted by each spring will be kx, and the weight exerts a force W = mg on the springs downwards.
Here, m = 38.6 lbs, g = 32.2 ft/s2 and k = K/m = 6.4/38.6 = 0.1657 lb/in
ΣF = -kx - kx - kx - kx - kx - kx + mg = 0-6.4m = -38.6 * 32.2m = 199.14 in (Maximum Displacement of M)The maximum compression will occur when the weight is at the lowest point, i.e. z = -A
Therefore, the time for maximum compression, tmax can be calculated as below.
z = Asin(ωt + δ)At the point of maximum compression, t = tmax
z = -A = -199.14 in (as calculated above)
Therefore,-199.14 = Asin(ωtmax + δ)
Here, A = kx = 6.4×199.14/32.2 = 39.45 inω = 2π/T = 2πf = 2π/4.72 = 1.33 rad/s (where T = time period and f = frequency)
Therefore,-199.14 = 39.45sin(1.33tmax + δ)sin(1.33tmax + δ) = -5.05tmax = 1.56 s
Thus, the maximum displacement of m is 199.14 inches and the time for maximum compression is 1.56 seconds.
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a copper wire with a diameter of 1.63 mm and a length of 29.0 m has a current of 15.0 a flowing through the wire. what is the resistance (r) of the wire what is the change in voltage from one end of the wire to the other end
The resistance of the copper wire is approximately 0.026 ohms and the change in voltage from one end of the wire to the other end is approximately 0.39 volts.
To calculate the resistance of the copper wire, we can use the formula:
R = ρL/A
where R is the resistance in ohms, ρ is the resistivity of copper (1.68×10−8 ohm-meters), L is the length of the wire in meters, and A is the cross-sectional area of the wire in square meters.
First, we need to convert the diameter of the wire to meters:
d = 1.63 mm = 0.00163 m
Then, we can calculate the cross-sectional area of the wire:
A = πd2/4 = 2.08×10−6 m2
Now we can plug in the values and solve for R:
R = (1.68×10−8)(29.0)/2.08×10−6 = 0.026 ohms
To calculate the change in voltage from one end of the wire to the other end, we can use Ohm's law:
V = IR
where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms.
Plugging in the values, we get:
V = (15.0)(0.026) = 0.39 volts
Therefore, the change in voltage from one end of the wire to the other end is approximately 0.39 volts.
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This 30° vertical bend in a pipe with a 1.5 ft diameter carries water (p 62.4 lbm/ft3) at a rate of 31.4 cfs. If the pressure pi is 10 psi at the lower end of the bend, where the elevation is 100 ft, and p2 is 8.5 psi at the upper end, where the elevation is 103 ft, what will be the vertical component of force that must be exerted by the "anchor" on the bend to hold it in position? The bend itself weighs 300 lb, and the length L is 5 ft Flow direction Expansion joints to eliminate force transfer between pipe and bend 30° Bend anchor
The vertical component of force that must be exerted by the "anchor" on the bend to hold it in position is FV = (10 - 8,5) 1,77 + (17,73 - 0) 62,4 . 32,2.5 = 1,719,09 lb.
The vertical component of force that must be exerted by the "anchor" on the bend to hold it in position is determined by the following equation:
FV = (p1 - p2) A + (V2 - V1) ρ gL
Where:
p1 = 10 psi at the lower end of the bend p2 = 8.5 psi at the upper end of the bend A = area of the pipe (A = π/4.d2 = π/4 . 1,52 = 1,77 ft2) V2 = velocity of water at the upper end (V2 = 31,4 cfs/1,77 ft2 = 17,73 fps) V1 = velocity of water at the lower end (V1 = 0) ρ = density of water (ρ = 62,4 lbm/ft3) g = gravity (g = 32,2 ft/s2) L = length of the pipe (L = 5 ft)So, the vertical component of force that must be exerted by the "anchor" on the bend to hold it in position is: FV = (10 - 8,5) 1,77 + (17,73 - 0) 62,4 . 32,2.5 = 1,719,09 lb.
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member bc exerts on member ac a force p directed along line bc. knowing that p must have a 325-n horizontal component, determine (a) the magnitude of the force p, (b) its vertical component.
(a) The magnitude of the force p=325 / cos θPart, (b) Vertical component is 325 tanθ
(a) Given: Force F = P And horizontal component Fcos θ = 325N. Here, θ is the angle made by the force with the horizontal, and θ is unknown. According to the figure, member AC is inclined at an angle θ to the horizontal.
Let's resolve the force P into vertical and horizontal components. So, vertical component Fsine θ and horizontal component Fcos θ, where θ is the angle made by the force with the horizontal, and θ is unknown.
Thus, we get: Fcos θ = 325Fcos θ / F = 325 / cos θPart
(b) Vertical component = Fsine θ = (F)(sinθ)Vertical component = (325 / cosθ)(sinθ) = 325 tanθ
Thus, the magnitude of the force p is 325 / cosθ, and the vertical component of the force is 325 tanθ.
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A speck of dust on a spinning DVD has a centripetal acceleration of 20 m/s^2. A) What is the acceleration of a different speck of dust that is twice as far from the center of the disk? B) What would be the acceleration of the first speck of dust if the disk's angular velocity was doubled?
The acceleration of the second speck of dust = 40 m/s² and the acceleration of the first speck of dust when the disk's angular velocity is doubled will be 80 m/s².
What is Acceleration?
The centripetal acceleration is given by the formula:
Acceleration = (Velocity)² / radius
Let, the distance from the center of the disk is ="r".
Thus, the radius of the disk can be represented as = "2r".
So, the acceleration of the second speck of dust can be given as:
Acceleration = (Velocity)² / 2r
The first speck of dust and the second speck of dust are moving in the same circle with the same speed. Thus, the velocity of both dust will be the same.
Therefore, Acceleration of the second speck of dust = (Velocity)² / 2r
Acceleration of the first speck of dust = (Velocity)² / r
Acceleration of the second speck of dust / Acceleration of the first speck of dust = 2r / r
Acceleration of the second speck of dust = 2 x Acceleration of the first speck of dust
Acceleration of the second speck of dust = 2 x 20 m/s²
Acceleration of the second speck of dust = 40 m/s²
If the angular velocity is doubled, then the velocity will also get doubled.
So, the new velocity of the first speck of dust will be 2V.
New Acceleration = (2V)² / r
New Acceleration = 4 x (Velocity)² / r
New Acceleration = 4 x 20 m/s²
New Acceleration = 80 m/s²
Therefore, the acceleration of the first speck of dust when the disk's angular velocity is doubled will be 80 m/s².
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A 90 kg halfback runs north and is tackled by a 120 kg opponent
running south at 4 m/s. The collision is perfectly inelastic. Just after the
tackle, both players move at a velocity of 2 m/s north. Calculate the
velocity of the 90 kg player just before the tackle
Perfect inelasticity governs the collision. Both athletes go north at a speed of 2 m/s just after the tackle. Prior to the tackle, the 90 kg athlete was moving at a speed of 6 m/s south.
In an inelastic collision, momentum is preserved, hence we may apply the equation: (m1 * v1) plus (m2 * v2) equals (m1 + m2) * vf.
The following is the result of substituting the above values: (90 kg * v1) + (120 kg * (-4 m/s)) = (90 kg + 120 kg) * 2 m/s
When we simplify the equation, we obtain: 90v1 - 480 = 210 90v1 = 690\sv1 = 7.67 m/s They move at a speed of -4 m/s. As a result, the player weighing 90 kg was moving at the following speed right before the tackle: south
Nevertheless, the question specifically asks for the northward velocity shortly before the tackle, therefore we must adjust the sign:
North: v1 = -11.67 m/s plus 2 m/s equals -9.67 m/s
Prior to the tackle, the 90 kg athlete was moving at a speed of 6 m/s south.
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Galena's specific gravity is 7.5, that of quartz 2.65, and that of liquid mercury 13.6. Given equal-sized samples (volumes) of galena and quartz, which will feel heavier? Choose one: A. galena B. The same volume of water will feel heavier than both of them. C. They will feel about equal. D. quartz
Given equal-sized samples (volumes) of galena and quartz, the Galena sample will feel heavier because of its higher specific gravity. Thus, the correct option is A.
What is the Specific gravity of a substance?Specific gravity is the ratio of the density of a substance to the density of a standard substance in physics. It's typically applied to liquids and solids, but it may also be applied to gases. The most often utilized standard material for liquids and solids is water at 4°C. A substance's specific gravity is dimensionless and is often represented by the Greek symbol ρ.
Relative Density of the given substances:
Galena's specific gravity is 7.5, Quartz's specific gravity is 2.65, and Liquid mercury's specific gravity is 13.6. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water. The specific gravity of water is 1.0. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water.
We can conclude from the values above that liquid mercury is heavier than galena, which is in turn heavier than quartz. Therefore, since both quartz and galena are being measured with equal sizes or volumes, galena will feel heavier than quartz.
Therefore, the correct option is A.
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At a given pressure, a substance in the saturated vapor phase will be at a ______ temperature than a superheated vapor.
At a given pressure, a substance in the saturated vapor phase will be at a lower temperature than a superheated vapor.
What is a saturated vapor phase?Saturated vapor refers to the state of a material in which it contains a maximum quantity of vapor that is uniformly blended with the liquid or solid state of the same chemical composition at a specified temperature and pressure.
What is a superheated vapor?A superheated vapor is a vapor that is heated beyond its boiling point or saturation temperature for its pressure. As a result, it will not condense back into a liquid phase until it has cooled sufficiently. As a result, it's simply vapor, with no liquid portion to it.
What happens when pressure remains constant and the temperature of a substance rises?According to Charles's law, if the pressure of a gas is kept constant, the volume of the gas varies directly with the temperature. If pressure remains constant and temperature increases, the volume of a substance expands, indicating that molecules are gaining energy and colliding with one another more frequently. As a result, the kinetic energy of the system increases. When a substance is in a superheated vapor state, it is at a higher temperature than when it is in a saturated vapor state at the same pressure.
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a 1-kg ball is thrown at 10 m/s straight upward. neglecting air resistance, the net force that acts on the stone when it is halfway to the top of its path is about
The net force that acts on the stone when it is halfway to the top of the path is zero, this is because of the gravitational acceleration.
Why does the net force turn zero?When a 1 kg ball is thrown at 10 m/s straight upward, and air resistance is ignored, the net force that acts on the stone when it is halfway to the top of its path is approximately zero.
Since air resistance is ignored, the net force acting on the 1-kg ball is just the force due to gravity. In the absence of air resistance, the acceleration of the ball will remain constant and equal to g, which is -9.81 m/s², because the weight of the ball is mg, where m is the mass of the ball and g is the gravitational acceleration.
So, the net force acting on the ball will be given by:
Net force = m × g = (1 kg) × (-9.81 m/s²) = -9.81 N
Therefore, the net force acting on the ball when it is halfway to the top of its path is zero.
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nec 430.6(a)(1) requires that the motor full-load amperes listed in tables 430.247 through 430.250 be used to size all of the following, except for_______ .
.nec 430.6(a)(1) requires that the motor full-load amperes listed in tables 430.247 through 430.250 be used to size all of the following, except for Motor Voltage.
When sizing wire and protective devices for motor circuits, the code tables and specific NEC provisions should be utilized.
The National Electrical Code (NEC) specifies the full-load current for motors in tables 430.247 through 430.250.
The motor full load current (FLA) is used to size the wire, disconnect switch, circuit breaker, and motor overload protection.
It's worth noting that motor voltage is not part of this listing. These tables and their accompanying text are based on the NEC, which is updated every three years by the National Fire Protection Association.
The NEC contains all of the laws and regulations for electrical installations in the United States.
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if a resistor connected across the secondary winding draws an rms current of 0.75 a, what is the current in the primary winding?
The current in the primary winding is 0.75 A and determined by the turns ratio of the transformer, Np/Ns. Where Np is the number of turns in the primary winding, and Ns is the number of turns in the secondary winding.
The current in the primary winding, Ip, is equal to the current in the secondary winding, Is, multiplied by the turns ratio: Ip = Is × (Np/Ns). Therefore, since the current in the secondary winding is 0.75 A, the current in the primary winding is: Ip = 0.75 A × (Np/Ns).
The RMS current drawn by the resistor connected across the secondary winding is 0.75 A. To determine the current in the primary winding of the transformer. The transformer is an electrical device that is used to transfer electrical power from one circuit to another circuit. It is an electromagnetic device that works on the principle of electromagnetic induction, which is used to transfer electrical power from one circuit to another circuit, the current is given by:
I1 = I2 × N2 / N1 = 0.75 × 1 / 1 = 0.75 A. Therefore, the current in the primary winding is 0.75 A.
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water flows through a pipe with a cross-sectional area of 0.002 m2 at a mass flow rate of 4 kg/s. the density of water is 1 000 kg/m3. determine its average velocity. multiple choice question. 0.02 m/s 2 m/s 200 m/s 20 m/s 0.2 m/s
The average velocity of water flowing through a pipe with a cross-sectional area of 0.002 m² at a mass flow rate of 4 kg/s is 2 m/s.
What is the formula for average velocity?The formula for average velocity is:
v = Q / A
Where:
v is the average velocityQ is the volume flow rateA is the cross-sectional area of the pipeThe formula for volume flow rate is:
Q = m / ρ
Where:
m is the mass flow rateρ is the density of the fluidSubstituting the values:
v = Q / Av = (m / ρ) / Av = m / (ρA)Given that the cross-sectional area of the pipe is 0.002 m², the mass flow rate is 4 kg/s, and the density of water is 1000 kg/m³, the average velocity is:
v = 4 / (1000 × 0.002)v = 2 m/sTherefore, the average velocity of water flowing through a pipe with a cross-sectional area of 0.002 m² at a mass flow rate of 4 kg/s is 2 m/s.
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he radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 40 mm? incorrect: your answer is incorrect. mm3/s
The volume is increasing at a rate of approximately 20,106 mm³/s.
The volume of a sphere can be given by the formula V = 4/3πr³. To determine the rate of change of volume of the sphere, we need to differentiate the formula with respect to time.
The derivative of V w.r.t. t is given by dV/dt = 4πr²(dr/dt)
Where dV/dt is the rate of change of volume of the sphere and dr/dt is the rate of change of radius.
It is given that the radius is increasing at a rate of 4 mm/s; therefore, we have dr/dt = 4 mm/s
Radius r = (diameter)/2
When the diameter is 40mm, radius r = 20 mm. Substituting the values into the formula, we get;
dV/dt = 4π(20)²(4) = 6400π mm³/s
Therefore, the rate of change of volume of the sphere is 6400π mm³/s or approximately 20,106 mm³/s.
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question 6: circuit balance given 6 , what is the current of the ideal current source, , for which there is no current flowing through the 5 resistor?
The current of the ideal current source in the given circuit is zero.
This is because the current source is not providing any current and the 5 ohm resistor is not providing any resistance. Thus, no current can flow through the circuit.
In this circuit, there is a current source with 6 volts and a 5 ohm resistor. The current source does not provide any current since it is ideal, meaning it does not create any voltage drops. Therefore, no current can flow through the circuit.
This is because there is no voltage difference between the two nodes (points) between which the current is supposed to flow.
The 5 ohm resistor also does not provide any resistance, meaning the same current would flow through the resistor as well. Thus, the current of the ideal current source in the given circuit is zero.
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A magnifying glass with focal length 15 cm is placed 10 cm above a stamp. The image of the stamp is located a. 15 cm from the magnifying glass. b. 30 cm above the stamp. c. 30 cm above the magnifying glass. d. 30 cm below the stamp. e. 30 cm below the magnifying glass.
The image of the stamp when a magnifying glass with focal length 15 cm is placed 10 cm above a stamp is located 30 cm above the magnifying glass. The correct answer is Option C.
Let the object distance, u be -10cm (since the stamp is placed 10 cm above the magnifying glass).
Let the focal length of the lens, f be 15cm.
So, the magnification, m is given as:
m = v/u (where v is the image distance)
Using the lens formula, we can say that:
1/f = 1/v - 1/u (where v is the image distance and u is the object distance)
Plugging in the given values into the formula we have:
1/15 = 1/v + 1/10
Multiplying both sides of the equation by 30v, we have:
2v = 3(30 - v)
Solving for v, we have:
v = 30/2 = 15 cm
Since v is positive, it means that the image of the stamp is formed on the other side of the lens (on the side of the lens where the image of the stamp is formed, we measure the distance from the lens from this side). Hence, the image is located 15cm from the lens. Since the stamp is located 10 cm above the magnifying glass, the image of the stamp is located 15 + 10 = 25cm above the object or the magnifying glass. Thus, the correct option is c. 30 cm above the magnifying glass.
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true or false? a faraday bag stops any electromagnetic emanations from passing into or out of the bag, preventing a mobile device from communicating with the outside world. true false
True. A Faraday bag (also known as an electromagnetic bag) is a container made from metal or a special material that blocks any electromagnetic emanations from passing into or out of the bag, preventing a mobile device from communicating with the outside world.
This is because Faraday bags are electromagnetic bags that are designed to isolate electronic devices from external electromagnetic influence. They are also known as radiofrequency shielding bags, Faraday cage bags, signal blocker bags, or electromagnetic pulse (EMP) bags.
What are Faraday bags?
Faraday bags are made of a combination of metal or metal-coated fabrics that are designed to block electromagnetic signals from entering or leaving the bag. They are usually used to keep mobile devices such as smartphones and tablets from communicating with the outside world, especially in situations where an individual is worried about their privacy or security. They are also used by law enforcement agencies to prevent suspects from remotely wiping or deleting evidence on their devices.
How do Faraday bags work?
Faraday bags work by using a principle known as the Faraday effect, which states that any electric field in a conductor is shielded from the conductor's interior by the presence of an electric field. Faraday bags use this principle to block incoming and outgoing signals by creating an electrically conductive enclosure around the device. This means that when a mobile device is placed inside a Faraday bag, the bag acts as a Faraday cage, which shields the device from electromagnetic radiation. As a result, the device cannot communicate with the outside world.
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the two exploded pieces of the shell land at the same time. at the moment of landing, what is the distance xcm from the mortar to the center of mass of the exploded pieces?
The distance xcm from the mortar to the center of mass of the exploded pieces is xcm = 1.00d.
Therefore, the distance xcm from the mortar to the center of mass of the exploded pieces is found as follows:
When an object is thrown upward, it will move upward until the velocity reaches zero at its highest point. The acceleration of an object in free fall is -9.81 m/s². This acceleration is constant since it is only affected by gravity. Therefore, the distance traveled by an object in free fall is given by the formula
d = v₀₊ + 1/2gt²
Where v₀ is the initial velocity (in this case, ₀ since the objects are at rest at the moment of explosion), t is the time of flight, g is the acceleration due to gravity.
Since both pieces land at the same time, they have the same time of flight. We can set the distance traveled by the two pieces equal to each other and solve for xcm. That is
d₁ = d₂
v₀₊ + 1/2gt² = v₀₊ + 1/2gt²
Canceling v₀₊ and solving for t, we have
t = √(2d/g)
Substituting this value of t into the first equation above, we have
d₁ = 1/2gt²
d₂ = 1/2gt²
Substituting the given value of g = 9.81 m/s² and assuming that d₁ + d₂ = xcm, we have
xcm = 1/2gt²
= 1/2(9.81)(2d/g)
= 1.00d
Therefore, the distance xcm from the mortar to the center of mass of the exploded pieces is xcm = 1.00d.
Full task:
The two exploded pieces of the shell land at the same time. At the moment of landing, what is the distance xcm from the mortar to the center of mass of the exploded pieces?
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Calculate the kinetic energy of a bullet of mass 0.015 kg, traveling at a speed of 240 m/s.
Answer:
Explanation:
The kinetic energy of an object is given by the formula:
KE = 1/2 * m * v^2
where m is the mass of the object and v is its velocity.
Plugging in the given values, we get:
KE = 1/2 * 0.015 kg * (240 m/s)^2
= 1/2 * 0.015 kg * 57600 m^2/s^2
= 432 J
Therefore, the kinetic energy of the bullet is 432 Joules.
Answer:
The kinetic energy (KE) of an object is given by the formula:
KE = (1/2) * m * v^2
where m is the mass of the object and v is its velocity.
Substituting the given values, we get:
KE = (1/2) * 0.015 kg * (240 m/s)^2
Simplifying, we have:
KE = 0.5 * 0.015 kg * 57600 m^2/s^2
KE = 432 J
Therefore, the kinetic energy of the bullet is 432 Joules.
Explanation: