Object is at rest when object collides with it. The collision is one-dimensional andelastic. After the collision object has half the velocity that object had before thecollision. (a) Which object has the greater mass? (b) How much greater? (c) If the velocityof object before the collision was to the right, what is its velocity after the collision

a) M₂ (the object that is stationary) b) 3 times c) the velocity is to the left

Explanation:

let the object in motion = M₁, object stationary = M₂, the initial velocity of the M₁ = U₁, since the second object is at rest U₂ = 0, final velocity of the M₁ = V₁ and final velocity for M₂ = V₂

Using conservation law of momentum:

M₁U₁ = M₁V₁ + M₂V₂ since the second body is at rest

also

V₂ = U₁ / 2 and the collision is elastic meaning

U₁ = V₂ - V₁

U₁ = U₁ / 2 - V₁

V₁ = - U₁/2

substitute V₁ into the first equation

M₁U₁ = M₁V₁ + M₂V₂

M₁U₁ = M₁ (-U₁/2) + M₂ (U₁/2)

collect the like terms

M₁U₁ + M₁ (U₁/2) = M₂ (U₁/2)

3/2 (M₁ U₁) = M₂ (U₁/2)

divide both side by U₁/2

3 M₁ = M₂

b) M₂ = 3 M₁

M₂ is three times M₁

c) V₁ = - U₁/2

since V₁ is negative, the velocity will be to the left