Question

Two balls are suspended on parallel threads of the same length so that they touch each other. The mass of the first ball is m1 = 0.2 kg, and that of the second m2 = 100 g. The first ball is deflected so that its center of gravity rises to a height of 4.5 cm and is then released. At what height will the balls rise to after the collision if: (i) the impact is elastic, (ii) the impact is inelastic?

a) Please calculate the final height for an elastic collision.
b) Please calculate the final height for an inelastic collision.
c) Determine the velocity of each ball after the collision.
d) Find the kinetic energy before and after the collision.

Answer 1

The final heights and velocities of two balls after a collision can be calculated by applying the principles of conservation of momentum and conservation of energy. In an elastic collision, both balls will rise to the initial height, while in an inelastic collision, they will rise to a lower height because kinetic energy is lost.

Step-by-step explanation:

To determine the outcomes after a collision between two balls suspended on parallel threads, we must use concepts from physics such as the conservation of momentum and the conservation of energy. Elastic and inelastic collisions are governed by different principles, which affect the final velocities and heights reached by the two balls after the collision.

Elastic Collision

For an elastic collision, both kinetic energy and momentum are conserved. The balls will exchange their velocities due to having the same mass (assuming 100 g to be 0.1 kg to match the mass unit of the first ball), and both will rise to the original height of 4.5 cm that the first ball was raised, since kinetic energy is conserved and they have the same mass.

Inelastic Collision

In an inelastic collision, momentum is conserved, but kinetic energy is not; part of it is lost as heat or deformation. For a completely inelastic collision, the two balls would stick together and move with a common velocity after the collision. Because kinetic energy is not conserved, they will rise to a lower height than in the elastic case. To calculate the velocity and the height after the collision, conservation of momentum would be used, and then potential energy at the height would be set equal to the combined kinetic energy of the masses just after the collision.

Kinetic Energy and Velocity Calculations

The velocity of each ball after the collision would need to be determined using the conservation of momentum equation for both elastic and inelastic collisions. Kinetic energy, before and after the collision, would be calculated using the formula KE = 1/2 mv2, where m is the mass and v is the velocity of the ball.