The reaction to this force is A: "The force of the ball against the bat".
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. When a player hits a ball with a bat, the action force is the impact of the bat against the ball. The reaction to this force is the equal and opposite force of the ball against the bat, meaning the ball will push back against the bat with the same amount of force that the bat hit it with.
So, the force of the ball against the bat is the equal and opposite reaction to the impact of the bat against the ball.
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12. Consider the falling and rolling motion of the 2.0 kg ball in the following two resistance-free
situations. In one situation, the ball falls off the top of the platform to the floor. In the other situation,
the ball rolls from the top of the platform along the staircase-like pathway to the floor. Fill in answer
for each the blanks lettered A-K.
PE=100J
KE=0J
PE= F J
KE- GJ
v=__H_m/s
PE=50J
KE-A J
V= B_m/s
PE=_C_J
KE=D J
v=__E__m/s
Answer the questions using logic and a little bit of arithmetic.
Top & Bottom:
1. What is the PE of the ball at the very top of the diagram above?
2.
What is the KE of the ball at the very top of the diagram above?
3. What is the PE of the ball the location shown as I on the diagram above?
4. What is the KE of the ball the location shown as J on the diagram above?
5.
What is the velocity of the ball the location shown as K on the diagram above?
requires a little mental math - but you can use a calculator if you need it.
6. What is the PE of the ball the location shown as F on the diagram above as the ball hits the ground?
10
PE=IJ
KE J J
v=K_m/s
8. What is the velocity of the ball the location shown as H on the diagram above?
your previous answers-don't solve the velocity equation.
7. What is the KE of the ball the location shown as G on the diagram above as the ball hits the ground?
Rolling down the ramp:
9. What is the KE of the ball the location shown as A on the diagram above?
This one
Use logic &
10. What is the velocity of the ball the location shown as B on the diagram above? Use logic & your previous
answers-don't solve the velocity equation.
11. What is the PE of the ball the location shown as C on the diagram above?
12. What is the KE of the ball the location shown as D on the diagram above?
13. What is the velocity of the ball the location shown as E on the diagram above? Use logic & your previo
answers-don't solve the velocity equation.
Gravity is the only force that is active. The overall mechanical energy is preserved since it is an inner or conservative force. As a result, each location has the 100 J of initial mechanical energy. So, 50 J is the KE for A.
The KE is 50 J because the PE at the exact same stairstep is Fifty J (C) (D).
The PE is 0 J at zero height (F and I). As a result, there is 100 J of velocity just at bottom of the hill (G and J).
The velocity may be calculated as 7.07 m/s for B and E as well as 10 m/s for H and K using the formula KE = 0.5*m*v2.
The answers provided here for the speed numbers are based on the assumption that 100% of the ball's kinetic energy is present as translational kinetic energy. The kinetic energy really would take some of the form of rotating kinetic energy. The real speed figures would thus be a little bit lower than those reported. (Torque and angular velocity is not covered in this tutorial for the physics classroom.)
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T or F: The definition of boundary layer refers to the region of flow in which both the temperature gradients are significant and frictional effects are important.
The statement "The definition of boundary layer refers to the region of flow in which both the temperature gradients are significant and frictional effects are important" is true because when a fluid is in direct contact with a solid surface and its temperatures are different, a thermal boundary layer forms.
As long as the temperatures of the solid surface and the fluid are different, a thermal boundary layer forms when a fluid is in direct contact with the solid surface, according to the classical theory of heat transfer. In fluid mechanics, a boundary layer is a thin layer of a moving gas or liquid in contact with a surface, like the inside of a pipe or the wing of an airplane. Shear forces act on the fluid in the boundary layer.
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Steel ball 1 is released from rest at the same time steel ball 2 is given a horizontal kick. The dots represent the locations of the two balls at t=0,1,2,3 and 4 s. The balls continue to fall after t=4 s. Evaluate each of the following statements.
Considering the motion of the two balls:
The magnitude of the vertical component of the velocity of ball 1 at point A is equal to the magnitude of the vertical component of the velocity of ball 2 at point C.The speed of ball 1 at point E is equal to the speed of ball 2 at point B.The magnitude of the horizontal component of the velocity of ball 2 at point G is greater than the magnitude of the horizontal component of the velocity of ball 2 at point B.The magnitude of the horizontal component of the velocity of ball 1 at point A is less than the magnitude of the horizontal component of the velocity of ball 2 at point C.The magnitude of the vertical component of the velocity of ball 1 at point H is less than the magnitude of the vertical component of the velocity of ball 2 at point B.What are horizontal and vertical velocities?The projectile's displacement horizontally as a result of velocity is shown by the horizontal velocity component (vx).
The projectile's displacement vertically as a result of velocity is shown by the vertical velocity component (vy).
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a dockworker applies a constant horizontal force of 79.0 n to a block of ice on a smooth horizontal floor. the frictional force is negligible. the block starts from rest and moves a distance 11.0 m in a time of 5.30 s
According to the statement, the mass of the ice block is38.1 kg.
The mass of the block of ice can be calculated using the equation F=ma, where F is the applied force, m is the mass of the block, and a is the acceleration.
Assuming the force is constant, the acceleration can be calculated by dividing the distance moved (11.0 m) by the time taken (5.30 s) to get an acceleration of 2.08 m/s². Then the mass of the block can be calculated by dividing the force by the acceleration, giving a mass of 38.1 kg.
A constant horizontal force is a force that is applied in a straight line parallel to the ground and does not change in magnitude or direction. This type of force is typically applied to an object that is already in motion, such as a rolling ball or a sliding box, and keeps it moving in a straight line.
Complete questions:
A dockworker applies a constant horizontal force of 79.0 n to a block of ice on a smooth horizontal floor. the frictional force is negligible. the block starts from rest and moves a distance 11.0 m in a time of 5.30 s. What is the mass of the block of ice?
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Two spacecraft
and
are traveling directly towards each other, intending to meet to dock together. Mission control on Earth initially sees spacecraft
moving with a speed of 154.5 m/s and spacecraft
moving with a speed of 133.0 m/s. Each spacecraft will need to come to a complete stop when they meet, and each will slow down using its rockets. The rockets on spacecraft
cause it to slow down at a constant rate of 17.1 m/s2, and the rockets on spacecraft
cause it to slow down at a constant rate of 22.2 m/s2. Spacecraft
turns on its rockets first.
At what distance
from spacecraft
should spacecraft
turn on its rockets in order for the two spacecraft to meet, have zero velocity relative to the Earth, and arrive at the same time?
A spaceship is a machine or vehicle built to travel through space.
What is Spacecraft?Spacecraft are a form of artificial satellite used for a wide range of tasks, such as communications, Earth observation, meteorology, navigation, space colonization, planetary exploration, and cargo and person transfer.
A spacecraft that is performing a sub-orbital spaceflight launches into space and then lands without gaining enough momentum or energy to complete a full orbit of the Earth. Spacecraft enter confined orbits around the Earth or other celestial bodies for orbital spaceflights.
Only humans are carried on human spacecraft either as crew or guests from launch or while in orbit (space stations).
Therefore, A spaceship is a machine or vehicle built to travel through space.
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From shortest to longest wavelength, which of the following correctly orders the different categories of electromagnetic radiation?
A.gamma rays, X rays, ultraviolet, visible light, infrared, radio
B. infrared, visible light, ultraviolet, X rays, gamma rays, radio
C. gamma rays, X rays, visible light, ultraviolet, infrared, radio
D. radio, infrared, visible light, ultraviolet, X rays, gamma rays
The following correctly orders the different categories of electromagnetic radiation; Radio, infrared, visible light, ultraviolet, X rays, gamma rays.
What is the ultraviolet?Ultraviolet (UV) radiation is a type of electromagnetic radiation emitted from the sun. It is a form of energy that is invisible to the human eye, but it can cause damage to living organisms. UV radiation is divided into three categories: UVA, UVB, and UVC. UVA radiation has the longest wavelength and is the least hazardous form of UV radiation. UVB radiation has a shorter wavelength and is more dangerous. UVC radiation has the shortest wavelength and is the most dangerous form of UV radiation. Exposure to UV radiation can cause sunburns, premature skin aging, and an increased risk of skin cancer.
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A radiating source at rest with respect to an observer produces a series of wave crests that propagate outward. From this figure, how do the waves detected by Observer A compare to those detected by Observer B?
Based on the given figure, for a radiating source at rest, the way waves detected by Observer A compared to those detected by Observer B is that Observer A detects the same wavelength and the same frequency.
The Doppler effect, also called Doppler shift refers to an apparent change in frequency of a wave in relation to an observer. The principle is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.
In the given case, a radiating source at rest with respect to an observer produces a series of wave crests that propagate outward. The waves spread out evenly in all directions as shown in the figure. The crests are separated by a distance, λ, where λ is the wavelength.
The observer located in the at point A will see the waves coming evenly, one wavelength apart. The observers located anywhere else would see the same thing. Hence, Observer A will detect the same wavelength and frequency as Observer B.
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water displacement is a good method to find the volume of an object that is more dense than water but does not work for objects which float
The volume of an item may be determined simply yet accurately by measuring the displacement of water.
It works by putting the object in a water-filled container and then calculating how much water the object has moved out of the container. The volume of the item may be calculated using the difference in water level before and after it is submerged.
Unfortunately, this approach does not work with floating objects. This is due to the fact that the item does not move the same volume of water as it does while immersed.
Water will be moved by the item, although considerably less water will be moved than by the submerged object.
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What is the kinetic energy of a 22 kg dog that is running at a speed of 8.2 m/s (about 18 mi/h)?
E=1/2 mv^2
E=1/2 22x(8,2)^2
E=739,64
A amusement park ride consists of a large vertical wheel of radies R
An amusement park ride consists of a large vertical wheel of radius R and a horizontal axis through its center that revolves counterclockwise.
What is an amusement ride?Amusement rides, often known as carnival rides, are machines or installations that move people for entertainment and fun.
Many people mistakenly believe that rides are scarier or more dangerous than they actually are. This can be the result of the design, acrophobia, or knowledge of accidents involving similar rides. Some people enjoy the adrenaline rush that comes with riding amusement attractions since it adds to the experience.
amusement rides such as ferris wheels, Enterprise, and Skydiver are examples of vertical rides that typically move their guests in a vertical plane and around a fixed point.
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An astronaut floating alone in outer space throws a baseball. If the ball moves away at 20 m/s, the
astronaut will
a. move in the opposite direction at 20 m/s.
b. move in the opposite direction at a lower speed.
c. move in the opposite direction at a higher speed.
d. none of the above
Throwing a baseball while floating alone in space is an astronaut. The astronaut will move in the opposite direction at a slower speed if the ball is moving away at 20 m/s (option B)
Since there is no gravity in space, the ball is not subject to the effects of gravity. When a ball is hurled upward into space, it rises steadily until it collides with an obstruction in its path.
A thrown ball will travel in a straight line and the person tossing the ball will also travel in a straight line in the opposite direction in deep space, which is far enough away from massive objects like stars and planets that gravity may be disregarded.
There is no longer any force exerted on the thing after it is out of your hand (at least in a vacuum). As a result, the object won't accelerate and will continue moving at the same speed as when it first left your hand.
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Five resistors, each 10 Ω, are connected in parallel to a voltage source. What is the equivalent resistance of the circuit?
A: 5 Ω
B: 50 Ω
C: 2 Ω
D: 20 Ω
Answer:
So the answer is C: 2 Ω.
Explanation:
The equivalent resistance of a parallel circuit is given by the formula:
1/R_equiv = 1/R1 + 1/R2 + ... + 1/Rn
In this case, there are 5 resistors each with a resistance of 10 ohms, so:
1/R_equiv = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10 = 0.5
And the equivalent resistance is:
R_equiv = 1 / 0.5 = 2 ohms
So the answer is C: 2 Ω.
In order to compute a power of two, you can take the next-lower power and double it. For example, if you want to compute 211 and you know that 210 = 1024, then 211 = 2 × 1024 = 2048. Based on this observation, write a recursive function int pow2(int n) where n is the exponent. If the exponent is negative, return -1.
To compute [tex]2^3[/tex], the function first calls itself with [tex]n=2,[/tex] which computes[tex]2^2 = 4[/tex]. Then, the function doubles this result to get [tex]2^3 = 8.[/tex]
Here is the pseudo-code for the pow2 function:
function pow2(n):
if n < 0:
return -1
if n == 0:
return 1
else:
prev_power = pow2(n-1) # Compute 2^(n-1) recursively
return prev_power * 2 # Double the result to get [tex]2^n[/tex]
The base case for the recursion is when n is 0, in which case the function returns 1 since [tex]2^0 = 1.[/tex]
The function recursively calls itself with smaller values of n until it reaches the base case. The recursive calls build up the power of 2 by doubling the previous power.
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A 15-cm X 15-cm circuit board dissipating 15 W of power uniformly is cooled by air,
which approaches the circuit board at 20°C with a velocity of 5 m/s. Disregarding
any heat transfer from the back surface of the board, determine the surface
temperature of the electronic components (a) at the leading edge and (b) at the end
of the board. Assume the flow to be turbulent since the electronic components are
expected to act as turbulators.
The temperature change at the two conditions will be at the leading edge will be 20°C and at the end of the board will be 45.64°C.
What is Heat transfer?The movement of heat across the border of the system due to a difference in the temperature between the system and the surroundings.
Board size = 15 cm × 15cm,
Power = 15W,
Temperature of cooled Air: 20°C, and velocity is 5 m/sec.
Firstly, take some value from Standard Air table, at pressure. Suppose That The film Temperature of the is 35°, at this temperature. and pressure.
K = 0.0265 w/m²c (Thermal conductivity)
V = 1.655 × 10⁻⁵ m²/sec (kinematic viscosity)
and Pr = 0.7668 ( pr and t' Number)
According To The Nusselt. Number Equation,
NVx = hxX / k
Here, x = heat transfer from the edge distance which is 0, 30
hx = ∞
So, express the Surface Temperature at the end board by using the equation
Q = hx. Ax (Ts, T∞)
Q/ hx. As = (Ts-T∞)
Ts = Q/hx. As + T∞
Put all the values in this equation, like, P = 15W, T= 20°C, hx = ∞
So,
Ts = 15/∞As + 20
Ts = 20°C
The Temperature of surface at the leading edge = 20°C
At the end of the board. Assume The flow to be turbulent since the electronic components. turbulators.
So, firstly determine The Reynolds Number equation, and
Rex = Vx/ u
Re = 5 × 0.15/ 1.655 × 10⁻⁵
Re = 45317.22
which is less than 3x 10⁵, so The flow is laminar flow at the surface.
again from The Relation of pr and t' Number, Reynolds. Nusselt number.
NVx = [tex]0.030s (Re)^(0.8)[/tex] [tex](pr)^(1/3)[/tex]
Put all the values in this equation
NVx = 0.0308 × 5308.97 × 0.90005
NVx = 147.1728
So, determine equation the heat transfer coefficient by using Relation.
here, x = 0.15m, consider.
hx = NVxK/ x
hx = 147.1728 × 0.0265/ 0.15
hx = 26.00
Area = 0.0225 m²
Q = hx. As (Ts - T∞)
Put all the values in equation,
Ts - 20 = 25.64
Ts = 45.64°C
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Two pans of a balance are 33.6 cm apart. The fulcrum of the balance has been shifted 1.35 cm away from the center by a dishonest shopkeeper. By what percentage is the true weight of the goods being marked up by the shopkeeper? Assume the balance has negligible mass. Answer in units of %.
The true weight of the goods being marked up by 8.3% by the shopkeeper.
What is bending moment?A bending moment is the reaction that occurs in a structural element as a result of an external force or moment that causes the element to bend, as defined by solid mechanics. The beam is the most prevalent or most basic structural component that experiences bending moments.
Calculated the bending moment about the balance:
P₁(33.6 + 1.35) = P₂ ( 33.6 - 1.35)
P₂ = 1.083 P₁
Hence, percentage change = (P₂-P₁)/P₁ × 100% = 8.3 %
So, the true weight of the goods being marked up by 8.3% by the shopkeeper.
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What is the value of the electric potential at the center of the triangle if q1 = 4.1 μC , q2 = 3.4 μC , q3 = -3.5 μC ?
Answer:
triangle if q1 = 4.1 μC , q2 = 3.4 μC , q3 = -3.5 μC ?
The water in a tank is pressurized by air,and the pressure is measured by a multifluid manometer as shown in the Fig. The tank is located on a mountain at an altitude of 1400 m where the atmospheric pressure is 85.6 kPa. Determine the air pressure in the tank if â„Ž1 = 0.1 m, â„Ž2 =0.2 m, and â„Ž3 = 0.35 m. Take the densities of water, oil, and mercury to be1000 kg/m3, 850 kg/m3, and 13,600 kg/m3
, respectively?
Air is used to pressurize water in a tank, and the pressure is then measured. by a multifluid manometer so Consequently, the air pressure in the tank is 129.45KPa.
In the physical sciences, pressure is defined as either the stress at a place within a confined fluid or the perpendicular force per unit area. The weight of the atm is atmospheric pressure, which is approximately 15 pounds per square inch at sea level. Each square meter of the Earth's surface is under pressure from the atmosphere.
atmospheric pressure ([tex]P_{atm[/tex])=85.6kPa
[tex]P_{atm[/tex]=85600Pa
density of water=[tex]\rho =[/tex]1000 kg/[tex]m^3[/tex]
density of oil([tex]\rho_0[/tex])=850kg/[tex]m^3[/tex]
density of mercury([tex]\rho_{m[/tex])=13600 kg/[tex]m^3[/tex]
height of water column([tex]h_1[/tex])= 0.1m
height of oil column from water level([tex]h_2[/tex])=0.2m
height of mercury column ([tex]h_3[/tex])=0.35m
pressure at point B
[tex]P_B=P_{air} +\:\rho_0gh_1\: +\rho_wgh_2 \: \rightarrow(1)[/tex]
[tex]P_B=P_{atm} +\:\rho_mgh_3\: \rightarrow(2)[/tex]
[tex]P_{air} +\:\rho_0gh_1\: +\rho_wgh_2 \:=P_{atm} +\:\rho_mgh_3\:[/tex]
[tex]P_{air} =\:-\rho_0gh_1\: -\rho_wgh_2 \:+P_{atm} +\:\rho_mgh_3\:\rightarrow(3)[/tex]
[tex]\rho _mgh_3[/tex]=13600x9.8x0.35=46648 Pa
[tex]\rho _0gh_1[/tex] =850x9.8x0.1=833 Pa
[tex]\rho _wgh_2[/tex] =1000x9.8x0.2=1960 Pa
By putting the value in eq.3
[tex]P_{air[/tex]=85600+46648−833−1960 = 129455Pa
therefore pressure of air in the tank is 129.45KPa
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An earthquake 25 km from a city produces P and
S waves that travel outwards at 5000 and
3000 m/s, respectively.
The time taken before S-wave arrives is 3.33 seconds.
What time before the S wave arrives?
The time taken before S wave arrives is calculated by applying the following equation.
Let the time taken for P-wave = t₁
Let the time taken for S-wave = t₂
The time taken for P-wave, t₁ = ( 25,000 m ) / ( 5000 m/s )
t₁ = 5 s
The time taken for S-wave, t₂ = ( 25,000 m ) / ( 3,000 m/s )
t₂ = 8.33 s
The time taken before S-wave arrives = 8.33 s - 5 s = 3.33 s
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The complete question is below:
An earthquake 25 km from a city produces P and
S waves that travel outwards at 5000 and
3000 m/s, respectively. how much time do they have before the S wave arrives?
True/Falsethe moisture content of the air in different locations of the country must be taken into account when selecting air conditioning equipment.
The statement "the moisture content of the air in different locations of the country must be taken into account when selecting air conditioning equipment" is true because moisture affects the performance.
The selection of the conditioning equipment must take into account the differences in humidity between the two locations (different sections of the country). The conventional copper tube-aluminum fin coil transfers heat more slowly than the all-aluminum coil.
The general rule of thumb is that for every 20°F increase in temperature, saturated air's ability to store twice as much moisture increases. The moisture retention capacity of air at 50°F is 0.0077 lb H2O/lb dry air, which is a little over twice as much as that of air at 30°F, which is 0.0035 lb H2O/lb dry air.
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suppose that a ball is dropped from the upper observation deck of a building, 300 m above the ground. (a) what is the velocity of the ball after 2 seconds? (b) how fast is the ball traveling when it hits the ground? solution we will need to find the velocity both when t
The velocity of the ball is 19.6 m/s and when the ball lands, it is moving at a speed of 77.134 m/s.
What is gravity?All objects with mass are subject to gravity, which is a fundamental force of nature. It is the force that pulls everything toward the core of a planet or other entity.
How do you determine it?(a) The equation can be used to determine the velocity of a dropped ball.
v = v0 + a * t
where a is the acceleration caused by gravity (9.8 m/s2), v0 is the beginning velocity (0 in this case because the ball is dropped from rest), and t is the amount of time that has passed.
Therefore, if t = 2 seconds, the ball's velocity at that time would be:
v = 0 + 9.8 * 2 = 19.6 m/s
(b) The ball's final velocity is identical to its velocity when it lands. The following equation can be used to determine how long it takes the ball to touch the ground:
t = √(2h / a)
where a is the acceleration brought on by gravity (9.8 m/s2) and h is the height (in this case, 300 m) from which the ball is dropped.
Thus, the duration of time required for the ball to touch the ground is:
t = √(2 * 300 / 9.8) = √(600 / 9.8) = √(61.22) = 7.83 s
The formula: can be used to determine the ball's velocity when it lands.
v=v0 + a*t = 0 + 9.8 * 7.83 = 77.134 m/s
So, when the ball lands, it is moving at a speed of 77.134 m/s.
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a trian traveling at 20kmph is accelerated at the rate of 0.5meters squared . what is the distance travelled by the train in 12 second's
Answer:
The distance traveled by train in 12 seconds is 66.72 meters.
Explanation:
The acceleration rate given is in meters per second squared, so we need to convert the velocity of the train to meters per second.
20 km/hr = (20 x 1000)/(60 x 60) = 5.56 m/s
Now we can use the formula for displacement with constant acceleration:
d = v₀t + 0.5at²
where
v₀ = initial velocity = 5.56 m/s
t = time = 12 s
a = acceleration = 0.5 m/s²
Substituting the values, we get:
d = 5.56 x 12 + 0.5 x 0.5 x 12²
d = 66.72 m
Cell phone conversations are transmitted by high-frequency radio waves. Suppose the signal has wavelength 36.5cm while traveling through air.
What is the frequency as the signal travels through 3 mm thick window glass into your room?
in MHz please
What is the wavelength as the signal travels through 3 mm thick window glass into your room?
in cm please
show work please I really need to understand this stuff
I will rate good
The frequency of a signal traveling through a window with a thickness of 3 mm is 12270 MHz and the wavelength is 24.33 cm.
What is wavelength?The distance between two successive peaks or troughs of a wave is referred to as its wavelength.
How do you determine it?The formula f = c /λ, where f is the frequency, c is the speed of light, and λ is the wavelength, relates a wave's frequency to both its wavelength and speed.
When a signal enters glass, its speed slows and its wavelength lengthens because glass has a slower rate of light propagation than air. We require knowledge about the glass's refractive index in order to compute the new wavelength and frequency. The new speed of light in the glass would be c/1.5 assuming that the refractive index of the glass is 1.5.
The new wavelength in the glass is given by= λ' = λ * (c / c') = λ * (c / (c / 1.5)) = λ / 1.5
The formula for the new frequency in the glass is: f' = c / λ' = c / (λ / 1.5) = 1.5 * f
As a result, the frequency of a signal traveling through a window with a thickness of 3 mm would be 1.5 * (8.18 x 109 Hz) = 12.27 x 109 Hz = 12.27 GHz *1000 = 12270 MHz.
The wavelength of the signal would be (λ/1.5) = (36.5 cm) / 1.5 = 24.33 cm as it passes through the 3 mm thick window glass into your room.
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A boat with initial speed v0 is launched on a lake. The boat is slowed by the water by a force F = −αeβv. (a) Find an expression for the speed v(t). (b) Find the time and (c) distance for the boat to stop.
The gap the boat travels earlier than slowing down is 2.303m/[tex]αe^2[/tex] v0 ln(10)
How to find an expression for the speed v(t)?The equation of movement for the boat is given through:
m dv/dt = -[tex]αe^2v[/tex]
in which m is the mass of the boat, v is the rate of the boat, and α is a steady that relies upon at the residences of the water.
To resolve for the rate of the boat as a feature of time, we are able to separate the variables and combine each facets of the equation:
[tex]m \int\limits v0^v dv / (v*√(1/v)) = -αe^2 ∫ zero^t dt[/tex]
Simplifying the left-hand aspect the usage of the substitution u = 1/v and [tex]du = -dv/v^2[/tex], we get:
[tex]-m ∫ 1/v0^1/v du = -αe^2 t\\-m ln(v/v0) = -αe^2 t\\ln(v/v0) = αe^2 t / m\\v(t) = v0 * e^(-αe^2 t / m)[/tex]
To discover the time at which the boat stops, we are able to set v(t) identical to 0 and resolve for t:
[tex]v(t) = v0 * e^(-αe^2 t / m) = zero\\e^(-αe^2 t / m) = zero\\-αe^2 t / m = -∞\\t = ∞[/tex]
v = zero.1v0 We can resolve for t in this example through putting v(t) = zero.1v0:
[tex]v(t) = v0 * e^(-αe^2 t / m) = zero.1v0\\e^(-αe^2 t / m) = zero.1\\-αe^2 t / m = ln(zero.1)\\t = -m/αe^2 ln(zero.1)[/tex]
Finally, to discover the gap the boat travels earlier than it slows down, we are able to combine the rate equation from v0 to zero.1v0:
∫ [tex]x0^x dt = ∫ zero^t v(t) dt[/tex]
in which x0 is the preliminary function of the boat. Substituting for v(t), we get: ∫[tex]x0^x dx / v(x) = -m/αe^2 ln(zero.1)[/tex]
Using the substitution u = v/v0, we get: ∫ [tex]1^zero.1 du / u = -m/αe^2[/tex]ln(zero.1)
[tex]ln(10) = -m/αe^2 ln(zero.1)\\x - x0 = -m/αe^2 ln(zero.1) * ln(10) / v0\\x - x0 = 2.303m/αe^2 v0 ln(10)[/tex]
Therefore, the gap the boat travels earlier than slowing down is 2.303m/[tex]αe^2[/tex] v0 ln(10).
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When you leap down from a high perch, you have a gentler landing with less force if you bend your knees as you land. Use the principles of impulse and momentum to explain why this approach reduces the force on you.
It is better to land with the knees bent while leaping from a substantial height since it prolongs the time it takes to halt, lessens the impact, and causes less pain.
The equation for impulse-momentum:
Δp = F Δt
Where,
Δp = momentum
F = force
t = time
The equation is referred to as the impulse-momentum theorem. The impulse is defined as the average net external force multiplied by the time it takes for that force to act. It is comparable to the shift in momentum. The strength, duration, and length of action of a force all have an impact on how it affects an object. The idea of impulse is useful since it measures the effect of a force. A strong force operating quickly, as the force of a tennis racket striking the ball, can have a considerable impact on an object's momentum.
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Current is defined (mathematically) by the equation I is equal to start fraction delta Q over delta t end fraction (for average current) or I is equal to start fraction dQ over dt end fraction (for instantaneous current, using calculus). using whichever definition you are confortable with, when considering current in a wire, this can be stated (conceptually) as which of the following?
Current is the rate at which charge passes a certain place in the wire.
Thus option D is correct.
What does the term "electric current" mean?
The rate of electron passage in a conductor is known as electric current. The ampere is the electric current's SI unit. Electrons are little particles that are part of a substance's molecular structure. These electrons can be held loosely or securely depending on the situation.
Electric current in a wire, where electrons serve as the charge carriers, is a measurement of the amount of charge that moves through any point of the wire in a given amount of time. Electric charge motion is occasionally reversed in alternating current but not in direct current.
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Complete question:
Current is defined (mathematically) by the equation I is equal to start fraction delta Q over delta t end fraction (for average current) or I is equal to start fraction dQ over dt end fraction (for instantaneous current, using calculus). Using whichever definition you are comfortable with, when considering current in a wire, this can be stated (conceptually) as which of the following?
A. Current is distance times charge (d times Q) divided by distance times time (d times t).
B. Current is the amount of charge in a wire, divided by the time it takes to fill the wire with charge.
C. Current is the rate at which the total charge within the wire is changing.
D. Current is the rate at which charge passes a certain place in the wire.
Work done by the gravitational force on a body of mass m moving on a smooth horizontal surface through a distance s is: (Given acceleration due to gravity =g):A) mgsB) -mgsC) 0D) 2mgs
The work done by gravity will be 0 since the gravitational force is perpendicular to the distance travelled by the body.
What is gravitational force?
Any two bodies will be attracted to one another by the force of gravity. There is an attraction between every thing in the cosmos, but most of the time it is too faint to be noticed due to the extreme distance between the objects. Furthermore, although the influence of gravity is weaker as objects are moved away, its range is infinite.
The gravitational force is a central force that always acts along the line connecting the centers of the two masses and only depends on the distance between the test mass and the source mass.
Only when displacement is in the direction of the force is work accomplished.
When a force is perpendicular to a displacement, no work is done.
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Use the approximation that vavg = pf/m for each time step.
A paddle ball toy consists of a flat wooden paddle and a small rubber ball that are attached to each other by an elastic band (figure). You have a paddle ball toy for which the mass of the ball is 0.011 kg, the stiffness of the elastic band is 0.925 N/m, and the relaxed length of the elastic band is 0.255 m. You are holding the paddle so the ball hangs suspended under it, when your cat comes along and bats the ball around, setting it in motion. At a particular instant the momentum of the ball is <−0.02, −0.01, −0.02> kg · m/s, and the moving ball is at location <−0.2, −0.61, 0> m relative to an origin located at the point where the elastic band is attached to the paddle. Define this instant as t = 0.
(a) Determine the position of the ball 0.1 s later, using a Δt of 0.1 s. (Express your answer in vector form.)
(b) Starting with the same initial position <−0.2, −0.61, 0> m and momentum <−0.02, −0.01, −0.02> kg · m/s, determine the position of the ball 0.05 s later. (Express your answer in vector form.)
(c) Using the position and momentum at t= 0.05 s, determine the position of the ball at t= 0.1 s. (Express your answer in vector form.)
Thank you.
Answer:(a) For the first time step, using Δt = 0.1s:
pf = m * vavg
vavg = pf/m
vavg = (<−0.02, −0.01, −0.02> kg · m/s) / 0.011 kg
To find the position at t = 0.1 s, we need to find the average velocity over the time interval, and multiply it by the time interval:
position = initial position + vavg * Δt
position = <−0.2, −0.61, 0> m + vavg * 0.1 s
(b) To find the position at t = 0.05s, repeat the same steps as in (a) but with Δt = 0.05s.
(c) To find the position at t = 0.1s, starting from the position and momentum at t=0.05s, repeat the same steps as in (a) and (b) with the new initial position and momentum value
Explanation:
A hydraulic jack uses hydrostatic pressure forces to leverage a small applied force to generate a large resulting force (alternatively you can think of it as a type of manometer). A force of magnitude, Fapp = 25 lb is applied to the left side of the jack (which has a square cross-section of side d=2.5 in). The right side of the jack also has a square cross-section but each of side D=10 in. The specific gravity of the oil in the jack is soil = 0.8. The weights of the bearing blocks can be neglected. Note that the surfaces of the bearing blocks on both sides of the jack are horizontala. What is the magnitude of the weight, W, that can be supported by the right side of the jack for the given difference in elevation, 2.4 ft as shown?b. The vertical right side of the right side of the jack is a total height of Htot =2.6 ft (and length into the page of D=10 in ). What is the magnitude of the force due to the hydrostatic pressure on that vertical side? Note that this vertical surface is rectangular in geometry and is of height Htot and length, D, into the page.
92.16 lb is the magnitude of the weight that can be supported by the right side of the jack.
Hydraulic jacks are devices that leverage applied force to generate a larger force. In this case, a 25 lb force is applied to the left side of the jack with a square cross-section of side d = 2.5 in.
The right side of the jack is also square with a cross-section of side D = 10 in and has a difference in elevation of 2.4 ft.
To calculate the magnitude of weight, W, that can be supported by the right side of the jack, we need to calculate the pressure due to the hydrostatic force on the vertical side of the jack.
This vertical side is a rectangular shape of height Htot = 2.6 ft and length D = 10 in. Taking into account the specific gravity of the oil in the jack as soil = 0.8, the hydrostatic pressure on the vertical side is equal to the difference in elevation multiplied by the weight of the oil.
W = 2.4 ft x 0.8 x 62.4 lb/ft³ = 92.16 lb. This is the magnitude of the weight that can be supported by the right side of the jack.
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In which one of the following situations does the car have an acceleration that is directed due north? a) A car travels northward with a constant speed of 12 ms. b) A car is traveling southward as its speed increases from 12 ms to 23 m/s c) A car is traveling southward as its speed decreases from 18 ms to 12 m/s d) A car is traveling northward as its speed decreases from 24 ms to 12 m/s e) A car travels southward with a constant speed of 24 mis.
A car is traveling southward as its speed decreases from 18 m/s to 12 m/s have an acceleration that is directed due north.
What is acceleration?
If an object's velocity changes, it is said to have been accelerated. An object's velocity can alter depending on whether it moves faster or slower or in a different direction. A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration. Through these illustrations, we can see that acceleration happens whenever a moving object changes its direction or speed, or both.
Since the speed is decreasing, the acceleration will be in the opposite direction hence option c.
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if the expression for the electric potential due to a small sphere of charge q at point p that is a distance d from the center of a small sphere is kqd , then the electric potential at a point o that is a distance 2d from the center of the small sphere is?
The potential at P is now if twice as much of this charge is uniformly distributed on the surface of a hollow sphere with a radius of 4r and a centre at point A.
What is the electric potential due to a small sphere?Sphere, The collection of points in three dimensions that are all the same distance from the centre (the radius) or the outcome of rotating a circle around one of its diameters.
Because there is no field inside the shell, the potential there is always the same as the potential outside the shell.
They are round, just like the Earth, which is why they are called spheres. The four spheres are the atmosphere, which contains all the gases that surround Earth, the hydrosphere, Which contains all the water on Earth.
Therefore, A sphere's parts and characteristics are comparable to those of a circle.
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