The potential energy U of the system of charges when charge 2q is at a very large distance from the other charges is given by [tex]U = \frac{-3k \cdot q^2}{d}[/tex], where k is the Coulomb constant ([tex]U = \frac{-3 \times 9 \times 10^9 \cdot q^2}{d}[/tex], q is the magnitude of the charges, and d is the distance between the charges q and -2q.
The potential energy of a system of charges can be calculated using the formula:
[tex]U = \frac{k \cdot (Q_1 \cdot Q_2)}{r}[/tex]
where k is the Coulomb constant ([tex]U = \frac{9 \times 10^9 \cdot (Q_1 \cdot Q_2)}{r}[/tex]), Q1 and Q2 are the magnitudes of the charges, and r is the distance between them.
Assuming the system of charges consists of three charges q, -2q, and q, and the charge 2q is at a very large distance from the other charges, the potential energy U of the system can be calculated as follows:
[tex]U = k \left[ \frac{q \cdot (-2q)}{d} + \frac{q \cdot 2q}{\infty} + \frac{(-2q) \cdot q}{d} \right][/tex]
where d is the distance between the charges q and -2q, and ∞ represents the distance between the charge 2q and the other charges, which is assumed to be very large.
Simplifying this expression, we get:
[tex]U = \frac{-3k \cdot q^2}{d}[/tex]
Therefore, the potential energy U of the system of charges when charge 2q is at a very large distance from the other charges is given by [tex]U = \frac{-3k \cdot q^2}{d}[/tex] where k is the Coulomb constant ([tex]U = \frac{-3 \times (9 \times 10^9) \cdot q^2}{d}[/tex]), q is the magnitude of the charges, and d is the distance between the charges q and -2q.
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What would be the wavelength of the 21-cm-line if it was coming from a distance of 8,000,000,000 (8*10^9) light-years
21 cm is the wavelength of the 21-cm-line if it was coming from a distance of 8,000,000,000 (8*10^9) light-years
Only when relative velocity changes do wavelength alter. Thus, the wavelength will not change. A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in consecutive cycles.
This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm). The relationship between frequency and wavelength is inversely proportional. The wavelength of the wave with the highest frequency is the shortest. Half the wavelength corresponds to twice the frequency. The wavelength in the red spectrum is the longest.
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Consider the function e(h) = ε h h 2 6 m where m is a bound for the third derivative of a function. Show that e(h) has a minimum at p3 3ε/m
Since , e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum of function.
In mathematics, point at which the value of a function is less than or equal to the value at any nearby point (local minimum) or at any point (absolute minimum) or the minimum value of a function is the lowest point of a vertex
e(h) = ∈ /h +( [tex]h^{2}[/tex]/6) M
e'(h) = - ∈ /[tex]h^{2}[/tex] + (2h/6) M
putting , e'(h) = 0
- ∈ /[tex]h^{2}[/tex] + (2h/6) M = 0
h = [tex](3 /M)^{1/3}[/tex] * (∈^(1/3))
e"(h) = 2∈ / [tex]h^{3}[/tex] + (2M)/6 equation 1
substituting value of h in equation 1, we get
e"(h) = 2∈M / 3∈ + M/3
e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum
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What is the acceleration of a 2-kg mass if a 100-N force acts on it?
SOLUTION:
Acceleration = Force/mass
= 100N / 2 kgs
= 50 m/s
.
.
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Two objects X and Y move directly towards each other. The objects have the same mass.
Object X has a velocity of 5.0 m/s to the right. Object Y has a velocity of 3.0 m/s to the left.
Object X and object Y collide and stick together.
What is their velocity after colliding?
X and Y are two things that travel in the same direction. The mass of the things is the same. 5.0 m/s is the velocity of object x as it moves to the right. The velocity of object y to the left is 3.0 m/s. Objects x and y collide and adhere to one another. Following their collision, they both move at a speed of 1.0 m/s to the right.
Their velocity after colliding is 1.0 m / s to the right.
What is the velocity during the collision?
In a collision, the velocity change is always computed by subtracting the initial value from the final value. If an object is moving in one direction before a collision and rebounds or somehow changes direction, then its velocity after the collision has the opposite direction as before.Inelastic collisions occur when only the momentum is conserved but not the system's kinetic energy. Perfectly inelastic collisions happen when objects stick together and have a common velocity after collision. To solve for the final velocity in perfectly inelastic collisions, use v' = (m1v1 + m2v2)/m1 + m2.The magnitude of the relative velocity is the same before and after the collision.To learn more about velocity, refer to:
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In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of .........rpm for shifting is recommended for gas engines.
In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of 2,500 rpm for shifting is recommended for gas engines.
The maximum thermal efficiency of modern gasoline engines is over 50%, but legal cars on the road are only about 20% to 35% when used to power cars.
Unfortunately, even with regular car maintenance such as tuning and oil changes, the efficiency of today's gasoline engines is about 30-35%. In other words, about 65 cents per dollar spent on gasoline is wasted.
EPA's 2020 Automotive Trend Report preliminary data shows that the average fuel economy of 2020 model light trucks has increased to 25.7 miles per gallon (MPG). If this preliminary data holds, it will mark the highest average fuel economy ever for a new light commercial vehicle.
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what behavior is mostly strongly associated with introversion in a personality.
Answer:
Need quiet to concentrate
Are reflective
Are self-aware
Take time making decisions
Feel comfortable being alone
Don’t like group work
Prefer to write rather than talk
And maybe even feel tired after being in a crowd
Explanation:
Two men standing on the same side of wall and at the same distance from It, such that they are 4oom apart when one fires a gun the other hears the first report in 1.2s and the second in 0.5s after the first. calculate 1) Velocity of sound in air . 2)the perpendicular distance of the men from the wall.
Answer:
1. 571.43m/s
2. 142.9m and 342.9m
Explanation:
1.Take the difference in time.
1.2-0.7=0.7 seconds
Take the distance between them and divide with differnce in time.
400÷0.7=571.43 seconds.
2.Take the time of the two men and divide by two.
0.5÷2= 0.25 secs
1.2÷2= 0.6 secs
multiply each with the velocity.
0.25×571.43=142.9m
0.6×571.43=342.9m
Complete the following nuclear reaction:
Answer choice
a) γ
b) α
c) β–
d) p
The particle that was given off in the reaction beta rays is β–. Option C
What is a nuclear reaction?A nuclear reaction will involve the change in the nucleus of an atom. It often leads to the production of new nucleus. As we can see the equation, there was a transformation from nitrogen nucleus to oxygen atom.
Thus, the particle that was given off in the reaction beta rays is β–. The fact that the mass number remained the same but the atomic number increased by one unit from left to right implies that a beta decay has occurred.
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Two large parallel conducting plates are 9.0 cm apart and carry equal but opposite charges on their facing surfaces. The magnitude of the surface charge density on either of the facing surfaces is 3.7 nC/m 2. Determine the magnitude of the electric potential difference between the plates.
The magnitude of the electric potential difference between the plates is 37.63 V.
Given:
Distance between the plates, d = 9 cm
Surface charge density, ρ = 3.7 nC/m² = 3.7 × 10⁻⁹ C/m²
Calculation:
For two parallel plate conductors, the electric field is given as:
E = ρ/ε₀
where ρ is the charge density
ε₀ is the permeability of free space
Applying values in the above equation we get:
E = ( 3.7 × 10⁻⁹ C/m²)/(8.85 × 10⁻¹² C²/m)
= 418.08 V/m
Now, the potential difference between the plates separated by a distance 'd' is given as:
ΔV = Ed
where E is the electric field
d is the distance of separation between the plates
Applying values in the above equation we get:
ΔV = (418.08 V/m) × (0.09 m)
= 37.63 V
Therefore, the magnitude of the electric potential difference between the plates is 37.63 V.
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An object at rest has no ________ energy, but it may have ________ energy resulting from its location or structure. An object at rest has no ________ energy, but it may have ________ energy resulting from its location or structure. chemical; potential kinetic; potential kinetic; heat potential; kinetic
Answer: An object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.
Explanation: To find the answer, we need to know more about the kinetic and potential energies.
What is kinetic energy of a body?Kinetic energy is a form of mechanical energy possessed by a body by virtue of its motion.Kinetic energy of a body of mass m moving with a velocity v is given by,[tex]KE=\frac{1}{2}mv^2[/tex]
What is potential energy?Potential energy is a form of mechanical energy possessed by a body by virtue of its position in the field or configuration.PE is always associated with a conservative force.There cannot be potential energy due to frictional or viscous forces.Thus, we can conclude that, an object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.
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2. A ball is tossed straight upwards with a velocity of 60m/s. Using an estimate of gravity of -10m/s², about how many seconds would it take to reach the peak (top of the flight). A.) 10 seconds B.) 3 seconds C.) 6 seconds D.) 12 seconds
Answer: A
Explanation:
Color is a result of the absorption and reflection of light. A shirt appears a color because it reflects that color of light. A shirt appears black when it absorbs all wavelengths of light. Why does a shirt appear white outside on a sunny day
The clothing seems white because the entire light is reflected.
what is absorption and reflection?Absorption:
This occurs when light is transformed into another type of energy. This happens when light vanishes while travelling through another medium.
reflection:
It is referred to as light reflection when a light ray hits a polished, smooth surface and bounces back. The incident light rays hit the surface and are reflected off of it. The beam that returns is referred to as the reflected ray.
according to the question we know that a shirt appears a color because it reflects that color of light. A shirt appears black when it absorbs all wavelengths of light. In case of white shirt no wavelength is absorbed by the shirt due to which the shirt appears white and in simple words the entire light is reflected back.
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A car approaches a stationary police car at 36 m/s. The frequency of the siren (as heard in the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car
The frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.
Frequency hear by the observerThe frequency heard by the observer is calculated by applying the principle of Doppler effect.
f₀ = f'[(v/v - vs)]
where;
f₀ is the observed frequencyv is speed of sound = 343 m/svs is the speed of the sourcef₀ = 500[(343 / 343 - 36)]
f₀ = 500(343/307)
f₀ = 558.6 Hz
Thus, the frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.
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On what does the magnitude of an applied torque depend?
Answer:
See below
Explanation:
The force applied and the length of the arm
The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.
What is torque?
The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction. A vector quantity is a torque.
Torque is defined as Γ=r×F=rFsin(θ). In other words, torque is the cross product of the force vector, where 'θ' is the angle between r and F, and the distance vector (the distance between the pivot point and the place where force is applied).
The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.
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Consider two copper wires. one has twice the length and twice the cross-sectional area of the other. how do the resistances of these two wires compare?
Answer:
R = ρ L / A where R is the resistance and ρ the resistivity:
R2 / R1 = (L2 / A2) / (L1 / A1) = L2 * A1 / (L1 * A2)
R2 / R1 = (2 L * A) / (L * 2 A) = 1
Their resistances should be the same.
The lion has a kinetic energy of 5000 j. What is the speed of the lion?
The lion has a kinetic energy of 5000 j, the speed of the lion is v = 100 / [tex]\sqrt{M1}[/tex] m/s
What is kinetic energy ?Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy or Kinetic energy is the energy that an object possesses due to its motion. It is basically the energy of mass in motion. Kinetic energy can never be negative and it is a scalar quantity i.e. it provides only the magnitude and not the direction.
given
kinetic energy = 5000 J
speed = ?
since , mass is not given in the question
Let mass of lion will be = M1
kinetic energy = 1/2 * M1 * [tex]v^{2}[/tex]
5000 J = 1/2 * M1 * [tex]v^{2}[/tex]
[tex]v^{2}[/tex] = [tex]\sqrt{10,000 / M1}[/tex] m/s
v = 100 / [tex]\sqrt{M1}[/tex] m/s
The speed of the lion = v = 100 / [tex]\sqrt{M1}[/tex] m/s
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2) Which pattern of organization did Alicia choose for her speech outline?
The pattern of organization Alicia chose for her speech outline is referred to as topical.
What is Topical pattern of organization?
This type of organization involves the arrangement of subtopics within a large or broad topic.
Alicia talked about speech pathology and the different subtopics include challenges, therapy etc which depicts topical pattern.
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Which requires more work, increasing a car's speed from 0 mph to 30 mph or from 50 mph to 60 mph?
Increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.
What is work?Work is a measure of energy expended in moving an object. It is calculated by multiplying the force by the distance.
According to this question, work is required to move a car from one position to another.
The distance moved from 0 - 30mph is more than that moved from 50 - 60mph, therefore, increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.
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When a 3.0 N weight is attached to a vertical coil spring, it stretches 5.0 cm. What weight would be required to stretch the spring 12.5 cm?
Group of answer choices
a. 7.5 N
b. 15 N
c. 4.5 N
d. 1.2 N
The weight required to stretch the spring 12.5 cm is 7.5 N (Option A)
Data obtained from the questionInitial weight (W₁) = 3 N Initial Length (L₁) = 5 cmNew length (L₂) = 12.5 cmNew Weight (W₂) =? How to determine the new weightThe new weight required to stretch the spring can be obtained as follow:
W₁ / L₁ = W₂ / L₂
3 / 5 = W₂ / 12.5
Cross multiply
W₂ × 5 = 3 × 12.5
Divide both sides by 5
W₂ = (3 × 12.5) / 5
W₂ = 7.5 N
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In the pinball game, momentum is transferred from the plunger to the ___
In the pinball game, momentum is transferred from the plunger to the ball.
What is momentum?
Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity.
The formula of the momentum is: p = m*v
Here a pinball game machine is given.
We know that,
A plunger in a pinball is a spring loaded rod used to shoot the ball out into the playing field.When the plunger tugged all the way back and released, the plunger will send the ball flying around the playfield. so here elastic potential energy is converted to kinetic energy.That is how the momentum is transferred to the pinball from the plunger.Hence,
In the pinball game, momentum is transferred from the plunger to the ball.
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A proton exits the cyclotron 1. 0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1. 0 ms ?.
(a) The diameter of the largest orbit just before the protons exit the cyclotron is 39 cm.
(b) The number of orbits completed by the proton during this 1.0 ms is 14000 revolutions.
What is kinetic energy?
The kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Formula of KE:
K.E = 1/2mv²
mv² = 2 K.E
v = sqrt( 2*KE / M)
Here,
(a)
The KE of the medical isotopes = 6.5 MeV
substituting the values,
v = sqrt( 2* 6.5* 1.6* 10^-13 / 1.67* 10^-27 )
v = 3.53 × 10⁷ m/s
Now the centripetal force:
mv² / R = qvB
r = q*v / mv²
r = ( 1.67* 10^-27 * 3.53 × 10⁷ ) / ( 1.9* 1.6* 10^-19 )
r = 0.19415 m
diameter d = 2r,
d= 2(0.19415 m)
d= 0.39 m ≅ 39 cm
(b)
The time period to complete a revolution around the spiral trajectory is:
T = 2πr / v
T = 2*3.14* 0.1941 / 3.53*10^7
T = 0.7 × 10⁻⁷ s
Thus, the number of orbits that the proton does to complete the revolution in 1 ms is:
n = t / T
n = 10^-3 / (0.7*10^-7)
n = 14285.71 ≅ 14000 revolutions
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Your question is incomplete, but most probably full question was:
A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 T.
(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d = 57 cm Previous
(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?
A ball of mass 4 kg is initially traveling at 2 m/s and has a 5 N force applied to it for 3 s. What is the final velocity of the ball?
A. 4 m/s
B. 12 m/s
C. 5.75 m/s
D. 3.25 m/s
Answer:
the answer to your question will be D
Explanation:
5 N* 3S =3.25
(a) A certain parallel-plate capacitor has plates of area 4.00m2 , separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage
The applied voltage is 1.41* 10⁴ kV.
Calculation of applied voltage-
The capacitance of parallel plates in the absence of a dielectric is:
C = ∈₀A/d
where, "d" = the spacing between the plates = 0.01 * 10⁻³ m
"A" = the area of the plates = 4 m²
"∈₀" = the constant = 8.85419*10⁻¹² C²/Nm²
So, C₀ = [tex]\frac{8.85419*10^{-12}*4 }{0.0100*10^{-3} }[/tex]
= 3541.67 *10⁻⁹ F
The dielectric constant, κ= 3.4, is defined as:
κ = C/C₀
The effective capacitance (with the dielectric) is denoted by "C", whereas the original capacitance is denoted by "C₀". (without the dielectric).
As a result, the new capacitance is:
C = κC₀
However, capacitance is connected to a voltage by:
C = Q/V
utilizing the increased capacitance and accounting for "V":
κC₀ = Q/V
V = Q/κC₀ = [tex]\frac{0.170}{3.4 * 3541.67 *10^{-9} }[/tex] = 1.41* 10⁴ kV
Therefore the applied voltage is 1.41* 10⁴ kV.
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If a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver __________________.
If a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver is making a mistake or he is not conscious of his driving
What is traffic light?Traffic light can simply be defined as a set of automatically operated coloured lights such as red, amber, and green, for controlling traffic at road junctions, pedestrian crossings and roundabouts.
Below are the meaning of some traffic light colours:
Red means stop or dangerGreen means go. I.e it is safe to proceedYellow means move with caution or get ready to stopSo therefore, if a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver is making a mistake
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If a car increases its velocity from zero to 60 km/h in 10 seconds, its acceleration is______.
Answer:
1.66m/s
Explanation:
here
initial velocity(u): 0m/s
final velocity (v):60km= 60×1000/60×60
:16.6m/s
time taken(t): 10s
now
acceleration:v-u/t
or a: 16.6-0/10
:16.6/10
acceleration: 1.66 m/s
In physics, acceleration is the rate at which the velocity of an object changes in relation to time. The sum of all forces exerted on an object results in its acceleration. The acceleration is 1.66 m/s².
The rate at which velocity, either in terms of speed or direction or both, varies over time is known as acceleration. A circle's motion accelerates despite its constant speed because its direction is continually shifting.
Here
initial velocity(u) = 0m/s
final velocity (v) = 60km
v = 60 × 1000 / 60 × 60
v = 16.6 m/s
Time taken(t) = 10s
Now.
acceleration = v-u / t
a = 16.6-0/10
a = 16.6/10
a = 1.66 m/s²
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A solenoid 6.00 cm in diameter and 10.0 cm long has 750 turns and carries a current of 15.0 A. Calculate the magnetic flux through the circular cross-sectional area of the solenoid.
The magnetic flux through the circular cross-sectional area of the solenoid is 0.00066 Weber or (Tm²).
What is a solenoid?A wire tightly twisted in a lengthy, thin coil is a solenoid. Due to its design, the solenoid will have an electromagnet inside of it and a weak magnetic field surrounding it if we pass a current through it.
Equation of solenoid's magnetic field:
The simplest solenoid to describe is one with unlimited length. An infinite solenoid's magnetic field has a constant within and a precise zero value outside. If we can accept that the magnetic field near the ends will be different from what is calculated for just an infinite solenoid, the unlimited solenoid is frequently a rough estimate of an actual, finite-length solenoid.By utilizing the convolution operation as well as right hand rule, the magnetic field within a large solenoid is appropriately computed, but all of that can be condensed into:
B = (µ₀ × N × I )/ L
where
B = magnetic field (Tesla)
µ₀ = [tex]\pi[/tex]× 10^-7 (Tm/A ) is the vacuum permeability,
N = number of turns on solenoid,
I = electric current (Ampere)
L = length of the solenoid (m)
According to the question;
A diameter of solenoid 6.00 cm.
A radius of solenoid is 3 cm = 0.03m
Number of turns = 750
The length of solenoid is 10cm = 0.1m
Substitute all the values in equation to fine mangetic filed.
B = ([tex]\pi[/tex]×[tex]10^{-7}[/tex] × 750× 15 )/ 0.1
B = 0.035 Tesla
The formula for magnetic flux is
Ф = B×A
= B×([tex]\pi[/tex][tex]r^{2}[/tex])
= 0.035×[tex]\pi[/tex]×[tex].03^{2}[/tex]
Ф = 0.000099
Ф = 99×[tex]10^{-6}[/tex] Weber
Therefore, the magnetic flux through the circular cross-sectional area of the solenoid. is 99×[tex]10^{-6}[/tex] Weber.
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Normal human body temperature is 98.6°F. What is this temperature expressed in Celsius (°C) and in Kelvin (K)?
Answer: 37 Celsius and 310.15 K
Explanation:
C/5 = (F-32)/9 = (98.6-32)/9 = 66.6/9 = 7.4
C = 7.4 * 5 = 37 so the temperature is 37 Celsius
K = C + 273.15 = 37 + 273.15 = 310.15 K
Car A is traveling with a constant speed of 80 km>h due north, while car B is traveling with a constant speed of 100 km>h due east. Determine the velocity of car B relative to car A
Answer:
80J
Explanation:
K.E = ½ mv²
k.e = ½ * 80*
100²
ke= 4*20
ke= 80 J
Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force must an 85.0-kg grouper exert to stay submerged in salt water if its body density is
The force require to keep grouper submerged is 8.207N.
According to Archimedes principle buoyant force of any object must equal to weight of fluid it displaced.
The expression for the force exerted to stay submerged in salt water is
F = F(b) - w(fish)
where F(b) = buoyant force
w(fish) = weight
now substitute w(b) for F(b)
→ F = Vρg - w(fish)
where V = volume of sea water
ρ = density of sea water
Now by Archimedes principle V = m(fish) / ρ(fish)
→ F = (m(fish) / ρ (fish) ) ρg - m(fish)g
F = (85 kg/1015 kg-m^-3) (1.025× 10³ kg-m^-3) (9.8 m/s^2)
- (85kg) × 9.8 m/s^2
F = 841.207N - 833N
F = 8.207 N
Hence, the force require to keep grouper submerged is 8.207N.
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useful and inconvenience of frictional force of a soccor player running with soccer boots
They are useful in providing larger frictional force.
The force produced by two surfaces coming into contact and sliding against one another is referred to as frictional force.
The following variables impact the frictional force: Surface roughness and the amount of force pressing them together have the biggest impact on these forces.
Football shoes have spikes or studs because they offer more frictional force when running on grass than regular shoes do.
The studs make it easier for players to move faster and change directions rapidly without slipping while also preventing them from slipping on the grass.
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