A roller coaster car of mass 400kg starts from rest at point A and passes the point B with a speed of 3m/s.if the distance from A to B along the tracks is 20m,how large is the average friction force retarding the motion of the car

Question

A roller coaster car of mass 400kg starts from rest at point A and passes the point B with a speed of 3m/s.if the distance from A to B along the tracks is 20m,how large is the average friction force retarding the motion of the car

Answer 1

Well, the average friction force can be calculated using the work-energy principle. But to make things a bit more entertaining, let's imagine the roller coaster as a really big, clumsy clown trying to reach point B.

So, this clown, let's call him Roller-Roni, starts at point A with his giant roller-skates. As he clumsily glides along the tracks, he gains speed and eventually reaches point B with a speed of 3 m/s. Quite impressive for a clown, I must say! 🤡

Now, let's get back to the question at hand. The average friction force can be determined by calculating the work done by friction. And since Roller-Roni is not the brightest clown out there, we can assume that his efficiency in converting work to kinetic energy is about as good as juggling chainsaws blindfolded.

So, the work done by friction is equal to the change in kinetic energy. The initial kinetic energy at point A is zero because the clown starts from rest. At point B, the kinetic energy is given by 1/2 mv^2, where m is the mass of the roller coaster car (400 kg) and v is its final velocity (3 m/s).

Therefore, the work done by friction is equal to the final kinetic energy:
Work = 1/2 mv^2 = 1/2 * 400 kg * (3 m/s)^2 = 1800 J

Now, the distance from point A to point B is 20 meters. Since friction acts in opposition to motion, we know that the work done by friction is negative:
Work = -Force * Distance

Rearranging this equation, we can find the force:
Force = Work / Distance = -1800 J / 20 m

So, the average friction force retarding the motion of the car, or in other words, the force slowing down Roller-Roni's roller-coaster ride, is -90 Newtons.

And there you have it, the average friction force is -90 N. But hey, let's give Roller-Roni a round of applause for making it to point B, despite all the clumsiness and friction! 🎉

Answer 2

To find the average friction force retarding the motion of the car, we first need to calculate the change in kinetic energy of the car from point A to point B.

The change in kinetic energy (ΔKE) is given by the formula:

ΔKE = (1/2) * m * (v^2)

where m is the mass of the car and v is the final velocity.

Given:
Mass of the car (m) = 400 kg
Final velocity (v) = 3 m/s

ΔKE = (1/2) * 400 kg * (3 m/s)^2
= (1/2) * 400 kg * 9 m^2/s^2
= 1800 kg * m^2/s^2

Next, we need to calculate the work done by friction (W) using the formula:

W = force * distance

The work done by friction is equal to the change in kinetic energy, so:

W = ΔKE
force * distance = ΔKE
force = ΔKE / distance

Given:
Distance (d) = 20 m

force = (1800 kg * m^2/s^2) / 20 m
= 90 kg * m/s^2

Therefore, the average friction force retarding the motion of the car is 90 kg * m/s^2.

Answer 3

To determine the average friction force retarding the motion of the roller coaster car, we need to consider the concept of work and energy.

1. Identify the initial and final conditions:
- Initial condition: The roller coaster car starts from rest at point A.
- Final condition: The car passes point B with a speed of 3 m/s.

2. Calculate the initial kinetic energy (KE₁) of the car at point A:
- The initial kinetic energy can be obtained using the formula KE = 0.5 * mass * velocity².
- KE₁ = 0.5 * 400 kg * (0 m/s)²
= 0 J (as the car starts from rest)

3. Calculate the final kinetic energy (KE₂) of the car at point B:
- KE₂ = 0.5 * 400 kg * (3 m/s)²
= 1800 J

4. Determine the loss of kinetic energy (ΔKE):
- ΔKE = KE₁ - KE₂
= 0 J - 1800 J
= -1800 J (as the car slows down)

5. Calculate the work done by the friction force (W) along the distance from A to B:
- The work done is equal to the loss of kinetic energy, W = ΔKE.
- W = -1800 J

6. Determine the magnitude of the average friction force (F_friction):
- The work done by the friction force is given by the equation W = F_friction * displacement.
- In this case, the displacement is 20 m.
- Therefore, F_friction = W / displacement.
- F_friction = -1800 J / 20 m
= -90 N (Note: The negative sign indicates that the force is acting in the opposite direction of motion)

So, the magnitude of the average friction force retarding the motion of the car is 90 N.

Answer 4

if it is a horizontal track

vf^2=vi^2+2ad remembering a=Forcefriction/mass