Calculating Average Force on a Ball hitting a Wall

Problem Statement

• Calculate the average force a 2 kg ball imparts to a wall.
• Initial velocity of the ball: 10 m/s.
• Final velocity after bouncing back: -8 m/s (negative sign indicates opposite direction).
• Time of contact with the wall: 20 milliseconds (ms).

Key Concepts

• Impulse-Momentum Theorem: Used to relate force, time, and change in momentum.
• Newton's Laws:
  • Second law relates force to change in momentum.
  • Third law discusses action-reaction forces.

Conversions

• Time conversion: 20 ms = 20 × 10⁻³ s.

Calculations

Change in Momentum

• Formula: ( \Delta p = m(v_2 - v_1) )
  • ( m ) = 2 kg (mass of the ball)
  • ( v_1 ) = 10 m/s (initial velocity)
  • ( v_2 ) = -8 m/s (final velocity)
• Calculate:
  • ( \Delta p = 2 \times (-8) - 2 \times 10 )
  • ( \Delta p = -36 ) kg·m/s
  • Negative sign indicates direction along negative x-axis.

Average Force

• Formula: ( F = \frac{\Delta p}{\Delta t} )
• ( \Delta t ) = 20 × 10⁻³ s
• Calculate:
  • ( F = \frac{-36}{20 \times 10^{-3}} )
  • ( F = -1800 ) N
• Negative sign indicates force by wall onto the ball.

Forces on Wall and Ball

• Newton's Third Law:
  • Force exerted by wall on ball: -1800 N
  • Force exerted by ball on wall: 1800 N (opposite direction, equal magnitude)

Concept of Elasticity

• When the ball hits the wall, it compresses and stores potential energy.
• This potential energy converts back to kinetic energy when the ball bounces back.

Additional Notes

• For further understanding, review energy transformations (kinetic to potential and vice versa).
• Contact instructor if there are any questions or confusions.

Conclusion

• The calculations demonstrate how forces work in collisions and are an example of how Newton's laws apply in everyday situations.

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