stick collision

Question

A 2500 kg van runs into the back of a 700 kg compact car at rest. They move off together at 8 m/s. Assuming no friction with the ground, find the initial speed of the van.  m/s

Answer 1

Hi Greisy H.!

Step 1: Identify Collision Type

We must first identify which type of collision we are considering so that we know which assumptions we can make.

Because the two objects stick together following the collision, this must be a perfectly inelastic collision.

In perfectly inelastic collisions, momentum is conserved, but kinetic energy is not.

Step 2: Conservation of Momentum

Now that we have identified which collision type we are considering, we are prepared to set up our equation. In elastic, inelastic and perfectly inelastic collisions, we can assume that momentum is conserved. Only in elastic collisions can we assume that kinetic energy is conserved.

Let us start with the conservation of momentum:

m₁v_1o + m₂v_2o = m₁v_1f + m₂v_2f

m₁v_1o = m₁v_1f + m₂v_2f

m₁v_1o = m₁v_f + m₂v_f = v_f(m₁ + m₂) => v_1o = v_f(m₁ + m₂)/m₁

<=> [8 m*s^-1(2500kg + 700kg)]/2500kg

v_1o = 10,2 m*s^-1

Hope this helps!

Cheers