A 2000 kg car traveling down a hill from a height of h=1.5 m collides with a 3000 kg car at the bottom of the hill initially at rest.

Question

A 2000 kg car traveling down a hill from a height of h=1.5 m collides with a 3000 kg car at the bottom of the hill initially at rest. The cars stick together and move 400m before friction causes them to stop. Calculate the coefficient of kinetic friction between the cars and the road.

Answer 1

Use energy balance to get the final speed of the first cart: potential energy before --> kinetic energy after

mgh = 1/2 mv² and solve for v

Next, you have an inelastic collision: momentum is conserved:

m₁v₁ = (m₁+m₂) v₁₂ where v₁₂ is the velocity of the two carts stuck together.(solve for v₁₂)

Finally, all of the kinetic energy of of the two carts is dissipated by "frictional work."

1/2(m₁ + m₂)v₁₂² = F_fd = (m₁ + m₂)gμd Solve for μ and note that the masses cancel.

good luck!