# Force exerted from car on trailer question

## Homework Statement

A 1480(k)g car pulls a 300(k)g trailer. The car exerts a horizontal force of 3900(N) against the ground in order to accelerate.

What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.

## Homework Equations

My question really is how to solve this problem correctly, but more so, correcting the mistakes I have made in my attempt in gathering a correct solution. I will just put all my work that way anyone who looks at this can easily follow my path and be able to correct my work.

## The Attempt at a Solution

Normal force on car = 1480(kg) * 9.81(m/s^2) = 14518.8(N)
Friction on car = 14518.8(N) * 0.15 = 2177.82(N)

Normal force on trailer = 300(kg) * 9.81(m/s^2) = 2943(N)
Friction on trailer = 2943(N) * 0.15 = 441.45(N)

3900(N) in my problem will be working in the positive direction as the other forces are resisting movement due to friction:

F = 3900(N) - 2177.82(N) - 441.45(N) => 1280.73(N)

Now, using Newton's 2nd law of F = m * a, I have rearranged to solve for acceleration:
a = F / m

a = 1280.73(N) / [1480(kg) + 300(kg)] =>0.7195(m/s^2)

F(trailer)=m(trailer) * a(trailer) + any other additional forces acting on the trailer?

F(trailer) = 300(kg) * 0.7195(m/s^2) + 441.45(N) => 657.3(N)

660(N) is my solution.

Would anyone be kind enough to help correct my mistakes? I appreciate you taking the time to take a look!

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It is said in the problem statement that 0.15 is for the trailer only so does that mean 3900N is a net force so kinetic friction on the car can be neglected?

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This was copied directly from masteringphysics so I really cant answer that question...I just attempted to solve it as best I could, but my answer is not what it is looking for.

That would change the answer significantly.

The new F would be 3458.55(N)

acceleration would change to 1.94(m/s^2)

The new F(trailer) would be 300(kg) * 1.94(m/s^2) + 441.45 => 1024.35(N)?

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This was copied directly from masteringphysics so I really cant answer that question...I just attempted to solve it as best I could, but my answer is not what it is looking for.
What is it looking for, then?

What is it looking for, then?

I believe the question is looking for the amount of force that is exerted onto the trailer by the car. It wants the answer in 2 significant digits, and with my experience thus far, I don't imagine an answer would be 1.0E3(N)

I believe the question is looking for the amount of force that is exerted onto the trailer by the car.
Yes, but do you know what the answer should be? I got T≈1024N

Draw free-body diagrams for the car and trailer

Newton second
for Car F-T=mcar*a
for Trailer T-Fμ=mtrailer*a
they have equal acceleration a and T is the force the car exerts on the trailer or vice versa(Newton III) You don't even have to calculate a, just solve for T and substitute it into car equation.

Awesome, now I understand it all. Thanks so much for your help! By the way, I put in 1000 for the solution and it accepted it, even though it was asking for 2 sig figs.