Urgent help with inellastic collision problem: finding mass and impact force

[mmoadi]

Homework Statement

A cart is driving on straight tracks with a velocity of 2 m/s. In the opposite direction, with an angle of 60º according to the tracks, a child with a mass of 2 kg is running with a velocity of 2m/s, he jumps on the cart and stays there.
- Find the mass of the cart, if its velocity is reduced to 1 m/s when the child jumps onto it.
- What is the impact force perpendicular to the tracks?

http://www.slide.com/s/je7VdmRz7z_Q-uRZVAwV1i0YbEZYONjV?referrer=hlnk

Homework Equations

p= mv
F= ma

The Attempt at a Solution

First part: Find the mass of the cart, if its velocity is reduced to 1 m/s when the child jumps onto it.

Conservation of the moment:

m(2)= 20 kg, v(1-initial)= v(2-initial)= 2 m/s, v(3)= 1 m/s, θ= 60º

m(1)v(1) + m(2)v(2)sinθ= (m(1) + m(2))v(3)
2m(1) + 34.64= m(1) + 20
m(1)= 14.64 kg

Are my calculations correct?

Second part: What is the impact force perpendicular to the tracks?

For this part, I know that the formula for impact force is F(impact)=m(Δv/Δt), but I don't know which mass to use and I don't have the time (t).
Any hint what I should do, or is there another equation to find the impact force without knowing the time (t)?

Thank you for helping!

 

[anathema]

Hello! Your calculations for the first part seem to be correct. The mass of the cart is indeed 14.64 kg.

For the second part, you can use the formula F(impact) = Δp/Δt, where Δp is the change in momentum and Δt is the time it takes for the child to jump onto the cart. Since the child's momentum changes from 2kg*2m/s to (2kg+14.64kg)*1m/s, the change in momentum is (16.64kg*m/s). You can estimate the time it takes for the child to jump onto the cart and use that to calculate the impact force. Alternatively, you can use the impulse-momentum theorem, which states that the impulse (change in momentum) is equal to the average force acting on an object multiplied by the time it takes for the force to act. So, you can estimate the average force by dividing the change in momentum by the time it takes for the child to jump onto the cart. I hope this helps!

 

[kerimek]

Dear student,

Thank you for reaching out for help with your inelastic collision problem. Your calculations for the first part, finding the mass of the cart, appear to be correct. However, for the second part, finding the impact force, there are a few things to consider.

Firstly, the formula you mentioned, F(impact)=m(Δv/Δt), is correct. However, in this case, we do not know the time (Δt) over which the impact force is applied. Therefore, we will need to find a different approach to solve for the impact force.

One way to find the impact force is by using the conservation of momentum equation, which you have already used in the first part of your solution. The equation is m(1)v(1) + m(2)v(2) = (m(1) + m(2))v(3). In this case, m(1) represents the mass of the cart before the collision, and m(2) represents the mass of the child. v(1) and v(2) represent the velocities of the cart and the child before the collision, and v(3) represents the velocity of the combined system after the collision.

To find the impact force, we can rearrange this equation to solve for v(3), which represents the final velocity of the combined system after the collision. Once we have v(3), we can use the formula F(impact)=m(Δv/Δt) to find the impact force, where Δv represents the change in velocity of the combined system.

I hope this helps you solve the problem. If you have any further questions, please do not hesitate to ask. Good luck with your homework!