Question

Two objects of masses m₁=m and m₂=4xm undergo a completely inelastic collision in one dimension. if the two objects remain at rest after the collision, and the heavier object (that of mass m₂) had an initial velocity of 2 m/s, what was the initial velocity of the lighter object (that of mass m₁)? be careful about the sign.

Answer 1

To find the initial velocity of the lighter object (mass m₁) in an inelastic collision where the two objects remain at rest after the collision, we can use the principle of conservation of momentum.

Step-by-step explanation:

In an inelastic collision, the two objects stick together and move as a single combined object after the collision. To solve this problem, we can use the principle of conservation of momentum.

Let's denote the initial velocity of the lighter object (mass m₁) as v₁ and the initial velocity of the heavier object (mass m₂) as v₂. Since the two objects remain at rest after the collision, the final velocity of the combined object will be 0 m/s.

Using the principle of conservation of momentum, we can write:

m₁ * v₁ + m₂ * v₂ = 0

Since the velocity of the heavier object (m₂) is given as 2 m/s in the opposite direction, we have:

m₁ * v₁ + 4m₂ * (-2 m/s) = 0

Solving this equation, we can find the initial velocity of the lighter object, m₁:

m₁ * v₁ - 8m₂ = 0

v₁ = 8m₂ / m₁