Mass m1 slides from rest down a frictionless ramp from a height h=2.5m and then

Question

Mass m1 slides from rest down a frictionless ramp from a height h=2.5m and then collides with a stationary mass m2 where m2=2m1. The collision is elastic. After the collision, m2 slides into a region where the coefficient of kinetic friction µk=0.5 and comes to stop a distance d within that region. Determine both the distance d for m2 and the height m1 travels back up the ramp.

Will be asking more questions after this is answered and answers will be rated. Thank you! (hint, use conservation of mech. energy, conservation of momentum, thermal and total energy, and force due to friction to solve)

Explanation / Answer

Conservation of energy for m1 m1gh=m1u^2/2 u=sqrt(2*9.81*2.5)=7.0 m/s elastic impact v2-v1/(u1-u2)=1 v2-v1=u1 m2 at rest u2=0 conservation of momentum m1u1+m2u2=m1v1+m2v2 m1*7+2m1*0=m1v1+2m1(u1+v1) 7=v1+2*7+2v1 3v1=-7 v1=-2.33 m/s v2=v1+u1=4.67 m/s v^2-u^2=2as v=0 u=v2 a=k*g s=v^2-u^2/2a=4.67^2/2*0.5*9.81 =2.223 m for m1 mv^2/2=mgh v=v1 h=v^2/2g=2.33*2.33/2*9.81=0.277 m

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