Newton's Second Law of Motion in terms of momentum

1. Understanding Newton's Second Law and Momentum

• Newton's Second Law states that an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass.
• This can also be expressed in terms of momentum:

where: $F_{\text{net}} = \frac{\Delta p}{\Delta t}$

• $F_{\text{net}} =$ net force $(N)$
• $\Delta p =$ change in momentum $(kg·m/s)$
• $\Delta t =$ time interval $(s)$
• Key relationships:
  • Larger force = greater change in momentum.
  • Longer time = greater change in momentum.
  • The force and momentum change occur in the same direction.

2. Worked Example: High Jumper Landing on Foam

Question:

• Why does landing on foam rubber hurt less than landing on hard ground? Solution:

• The force required to stop the jumper depends on: $F_{\text{net}} = \frac{\Delta p}{\Delta t}$

• Foam increases the stopping time ($\Delta t).$

• A longer time reduces the force experienced.

• Smaller force = less impact and less pain.

4. Activity: Baseball Collision with a Wall

• A 150 g baseball moves at 18 m/s and collides with a wall.
• It rebounds at 12 m/s in the opposite direction.
• Contact time: 0.1 s. Steps to Solve:

1. Calculate initial and final momentum.
2. Find change in momentum.
3. Use $F = \frac{\Delta p}{\Delta t}$ to find force exerted by the wall.
4. Use Newton's Third Law to determine the force on the wall by the ball.
5. Draw a vector diagram to show initial, final, and change in momentum.

5. Key Takeaways

• Newton's Second Law in momentum form: . $F_{\text{net}} = \frac{\Delta p}{\Delta t}$

• Larger force or longer time = greater momentum change.

• Momentum change depends on force and duration.

• Impulse = Change in Momentum.