Two carts on a track have the same mass m = 1.60 kg. They collide elastically wi

Question

Two carts on a track have the same mass m = 1.60 kg. They collide elastically with Cart 1 initially traveling at v1i = 1.26 m/s to the right and Cart 2 initially at rest (v2i = 0 m/s). The collision is monitored by two motion sensors. The time over which the collision lasts is ?t = 0.17 s.

What is the final velocity of Cart 1?v1f =

What is the final velocity of Cart 2? v2f =

What is the change in kinetic energy of each Cart? ?K1 = ?K2 =

What is the impulse delivered to cart 2? ?p2 =

What is the average force of Cart 1 on Cart 2 during the collision? Average F12 =

What is the average force of Cart 2 on Cart 1 during the collision? Average F21 =

Explanation / Answer

This being a case of inelastic collision both bodies will stick to each other.so v1f=v2f
conservation of linear momentum
mv1i+m.0=mv1f+mv1f
This gives v1f=v1i/2=v2f=0.375m/s to the right
cart 1:ΔK1 =0.5.m1.(v1i2-v1f2)=3/8m1.v1i2=0.2109J

cart 2:ΔK2 =0.5.m2.(v1f2)=1/8m1.v1i2=0.0703J

Impulse delivered to cart 2 = m2.v2f=0.5625kg.m/s

Average force =I/t=3.75N

F12 will act towards right and F21 will act towards left.both will be same in magnitude

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