Question

A air glider of mass 1.0 kg that is equipped with a spring bumper travels at a speed of 2.5 m/s toward a second stationary glider of mass 0.75 kg. What is the final speed of the 0.75 kg cart

Answer 1

Answer:

the final speed of the 0.75 kg cart is 2.86 m/s

Explanation:

Given;

mass of the air glider, m₁ = 1.0 kg

initial speed of the air glider, u₁ = 2.5 m/s

mass of the stationary cart, m₂ = 0.75 kg

initial speed of the stationary cart, u₂ = 0

Let the final speed of the stationary cart = v₂

Also, let the final speed of the air glider = v₁

Since the air glider has a spring bumper, the collision will be elastic.

Apply the following principle of conservation of linear momentum for elastic collision.

m₁u₁  +  m₂u₂  = m₁v₁   +   m₂v₂

(1 x 2.5)  + 0.75(0)  =  v₁   +  0.75v₂

2.5 = v₁  +  0.75v₂

v₁ = 2.5 - 0.75v₂ ----------- (1)

Apply one-dimensional velocity concept since the collision occured in one direction;

u₁ + v₁  = u₂  +  v₂

2.5  +  v₁   = 0   +  v₂

v₁ = v₂  - 2.5 ----- (2)

solve (1) and (2) together;

v₂  - 2.5 = 2.5 - 0.75v₂

v₂ + 0.75v₂ = 2.5  +  2.5

1.75v₂ = 5

v₂ = 5 / 1.75

v₂ = 2.86 m/s

Therefore, the final speed of the 0.75 kg cart is 2.86 m/s