Conservation of momentum and energy

[JJBrian]

Homework Statement

a) At t=1 second, a 0.5 kg cart is at x=0.5 m, traveling at 0.5 m/s. At t=3 seconds, the cart is
at 1.4 m, traveling at 0.4 m/s. What is the acceleration due to friction, the frictional force and
the work done by friction? What is the change in kinetic energy of the cart?
b) If a cart of mass 0.6 kg, traveling a 0.5 m/s collides elastically with a cart of mass 0.4 kg,
initially at rest, what is the final velocity of the first cart?
c) If the two carts above stick together after the collision, what is the final velocity of the first
cart?
d) What is the final velocity of the first cart in (b) if the second cart has mass 1.5 kg?
e) What is the final velocity of the first cart in (c) if the second cart has mass 1.5 kg?

Homework Equations

Elastic collison formula
Inelastic collision
Impulse
W=-FD
Change in kinetic energy formula

The Attempt at a Solution

ok here is my attempt. I need someone to check if I am using the right equation for each problem.

part a)
i used vf^2-vi^2 = 2ad
to get an acceleration of .05

To find the firctional force i used
F = -ma F= (.5)(.05)
Ff = -.025N

work done by friction
W = -Fd
W =-(-.025)(.05)
W = 0.0125J

change in ke
Ke =1/2mvf^2-1/2mvi^2
KE=1/2(.5)(0.5)^2-.5(0.5)(0.4)^2
Kef = .0225



part b)
v1f = vi*(m1-m2)/(m1+m2)
0.5*(0.6-0.4)/(0.6+0.4)
v1f=0.1m/s

part c)
v1f = vi*(m1)/(m1+m2)
(0.5)(.6)/(0.6+0.4)
v1f=0.3m/s


part d
v1f = vi*(m1-m2)/(m1+m2)
0.5*(0.6-1.5)/(0.6+1.5)
v1f=0.2143m/s


part e

v1f = vi*(m1)/(m1+m2)
(0.5)(.6)/(0.6+1.5)
v1f=0.143m/s

 

[anathema]

Your solutions for part a) seem to be correct. For part b), you are using the correct formula for elastic collisions, but I believe you made a mistake in your calculation. It should be v1f = vi*(m1-m2)/(m1+m2) = 0.5*(0.6-0.4)/(0.6+0.4) = 0.1 m/s. For part c), your solution is correct. For part d), you have the right formula, but I believe you made a mistake in your calculation. It should be v1f = vi*(m1-m2)/(m1+m2) = 0.5*(0.6-1.5)/(0.6+1.5) = -0.2143 m/s. The negative sign indicates that the first cart is moving in the opposite direction after the collision. For part e), your solution is correct. Good job!

 

[tomcue]

Your attempt is correct. You have used the appropriate equations for each part and your calculations are also correct. Well done!