A body of mass 2.1 kg makes an elastic collision with another body at rest and...

A body of mass 2.1 kg makes an elastic collision with another body at rest and continues to move in the original direction but with 1/6 of its original speed. (a) What is the mass of the other body? (b) What is the speed of the two-body center of mass if the initial speed of the 2.1 kg body was 3.1 m/s?

Solutions

Expert Solution

Let particles 1 and 2 have masses m₁, m₂, and velocities u₁, u₂ before collision, v₁, v₂ after collision.

By conservation of momentum before and after the collision

By the conservation of the kinetic energy

These equations may be solved directly to find

m₁ = 2.1 kg, v₁ = 1/6 u₁, u₂ = 0

from first equation

(b) If there is no external force on the system then the motion of the center of mass of the system remains unchanged,

The velocity of com of two bodies before collision = (m₁u₁ + m₂u₂)/(m₁+m₂)

= (2.1 x 3.1 + 1,5 x0 ) / (2.1+1.5)

= 1.8 m/s

There is no external force, hence the velocity of the center of mass will remain same after Collison i.e. 1.8 m/s

genius_generous answered 1 year ago

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