A ball of mass 0.20 kg falls freely from a certain height and rebounds elastically with a speed 10m/s.What is the change in momentum of the ball?

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Adrian Ayala · Accepted Answer

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Amelia Adams · Answer

undefined The change in momentum of the ball is 4 kg·m/s.

HIX Tutor · Answer

undefined Great question! Let's find the change in momentum step by step.

1. **What is momentum?**  
   Momentum is mass times speed. The formula is:  
   $$ \text{Momentum} = \text{mass} \times \text{speed} $$

2. **What is the mass of the ball?**  
   You said the mass is 0.20 kg.

3. **What happens when the ball falls?**  
   When the ball falls, it has a speed before it hits the ground. We can call this speed $ v_i $ (initial speed).

4. **What happens when the ball bounces back?**  
   After bouncing, the speed is 10 m/s upwards. We can call this speed $ v_f $ (final speed).

5. **What is the initial momentum?**  
   The initial momentum just before hitting the ground is:  
   $$ p_i = \text{mass} \times \text{initial speed} $$
   But we don't know that speed yet.

6. **What is the final momentum?**  
   The final momentum after bouncing is:  
   $$ p_f = \text{mass} \times \text{final speed} $$  
   $$ p_f = 0.20 \times 10 = 2 \, \text{kg m/s} $$

7. **How can we find the initial speed?**  
   If it falls and then bounces elastically, the initial speed will have the same value but in the opposite direction. So we can consider the speed just before it hits the ground as $ v_i = -10 \, \text{m/s} $.

8. **What is the initial momentum now?**  
   $$ p_i = \text{mass} \times \text{initial speed} $$  
   $$ p_i = 0.20 \times (-10) = -2 \, \text{kg m/s} $$

9. **Now, let’s find the change in momentum!**  
   The change in momentum is:  
   $$ \Delta p = p_f - p_i $$  
   $$ \Delta p = 2 - (-2) = 2 + 2 = 4 \, \text{kg m/s} $$

10. **What is the change in momentum?**  
   The change in momentum of the ball is $ 4 \, \text{kg m/s} $.

Did you follow all the steps? What do you think?