Shortcut Methods and Tricks for Numericals on Work, Energy, and Impulse Momentum Principles

1. Conservation of Momentum:

• Problem: A 10 kg ball moving at 5 m/s collides elastically with a stationary 15 kg ball. Find the velocities of both balls after the collision.

• Solution:

  • Shortcut: Use the concept of relative velocity. This is the difference in velocities between the two balls before the collision.

  • Formula: Relative velocity = velocity of ball 1 - velocity of ball 2

  • In this case, the relative velocity is 5 m/s - 0 m/s = 5 m/s.

  • After the collision, the relative velocity will remain the same, but the directions of the velocities may change.

  • Therefore, the velocity of ball 1 after the collision will be 5 m/s in the opposite direction, i.e., -5 m/s, and the velocity of ball 2 will be 5 m/s in the forward direction.

2. Work-Energy Theorem:

• Problem: A 5 kg object is lifted vertically through a height of 10 meters. Calculate the work done on the object.

• Solution:

• Shortcut: Use the formula for gravitational potential energy.

• Formula: Gravitational potential energy = mass × acceleration due to gravity × height

• In this case, the gravitational potential energy gained by the object is 5 kg × 9.8 m/s² × 10 m = 490 J.

3. Impulse-Momentum Theorem:

• Problem: A 10 kg ball is moving at 5 m/s when it is struck by a force of 20 N for 0.5 seconds. Determine the ball’s final velocity.

• Solution:

• Shortcut: Use the impulse-momentum theorem.

• Formula: Impulse = change in momentum = final momentum - initial momentum

• In this case, the impulse is 20 N × 0.5 s = 10 Ns.

• The initial momentum is 5 kg × 5 m/s = 25 kg m/s.

• The final momentum is therefore 25 kg m/s + 10 Ns = 35 kg m/s.

• Therefore, the ball’s final velocity is 35 kg m/s / 10 kg = 3.5 m/s.