- #1
Specter
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Homework Statement
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In an elastic head-on collision, a 0.60 kg cart moving at 5.0 m/s [W] collides with a 0.80 kg cart moving at 2.0 m/s [E]. The collision is cushioned by a spring (k=1200 N/m).
a) Find the velocity of each cart after the collision
b) Find the maximum compression of the spring.
Homework Equations
Conservation of energy
1/2 mv^2
The Attempt at a Solution
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I'm not sure if this question is correct so any help would be great.
a) Find the velocity of each cart after the collision.
Let east be positive.
Drawing the carts in different frames of reference
https://i.imgur.com/56uRFk8.png
Cart 1 (.80kg) is the moving mass and cart 2 is stationary.
v1f=m1-m2/m1+m2 v1o
= 0.80-0.60 / 0.80+0.60 (7.0)
= 1.0
Switch back to Earth's frame of reference by adding (-5.0).
1.0 + (-5.0)= -4.0
Cart 1 is moving at 4.0 m/s [W] after the collision
Cart #2:
v2f=2m1/m1+m2v1o
=2(0.80)/0.80+0.60 (7.0)
= 8.0
Switch back to Earth's frame of reference by adding (-5.0).
8.0 + (-5.0) = 3.0
Cart 2 is moving at 3.0 m/s [E] after the collision.
b) Find the maximum compression of the spring.
This is where I am having the most trouble. I have seen different answers online than what I arrive at.
To find the maximum compression of the spring I need to know fast the carts are moving when the spring is at max compression.
PTO=PTF
m1v1o+m2v2o=(m1+m2)vf
(0.80)(2.0)+(0.60)(0)=(0.80+0.60)vf
1.6=1.4
=1.14 m/s
At max compression the two carts are moving at 1.14 m/s.
Now use conservation of energy to find the maximum compression.
1/2 m2v1o2+1/2 m2v2o2=1/2(m1+m2)v2f2+1/2 kx2
1/2 (0.8)(2.0)2+1/2 (0.6)(-5)2=1/2 (0.8+0.6)(3.0)2+1/2 (1200)x2
9.1 = 6.3+600x2
9.1 = √606.3
9.1 = 24.62315
2.17 m
I don't know what I did wrong but the answers I have seen online are around 0.12m. Where did I go wrong? I've looked it over many times and I can't figure it out.
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