How to Calculate Impulse and Energy Loss During Ball Collision with Ground
Problem
A ball of mass 50 g is dropped from a height h = 10 m. It rebounds losing 75% of its kinetic energy. If it remains in contact with the ground for Δt = 0.01 s, calculate the impulse of the impact force.
🎯 What You'll Learn
- Understand the relationship between impulse and change in momentum
- Calculate impulse during a brief impact event
- Analyze energy loss during a collision
Prerequisites: Newton's laws of motion, conservation of momentum, kinetic energy calculations
Step-by-Step Explanation
🎾 Let's Tackle This Bouncing Ball Problem Together!
What We're Solving:
We need to find the impulse (change in momentum) when a 50g ball drops 10m, bounces back after losing 75% of its kinetic energy, and stays in contact with the ground for 0.01 seconds.The Approach:
Think of impulse as the "momentum punch" the ground delivers to change the ball's direction! We'll:- 1. Find the ball's velocity just before hitting the ground
- 2. Calculate its velocity just after bouncing (with 75% energy loss)
- 3. Use the impulse-momentum theorem: Impulse = Change in momentum
Step-by-Step Solution:
Step 1: Find velocity just before impact When the ball falls from height h = 10m, it converts potential energy to kinetic energy. Using: v² = u² + 2gh (where u = 0, since dropped from rest)
- v₁ = √(2gh) = √(2 × 9.8 × 10) = √196 = 14 m/s (downward)
- KE₁ = ½mv₁² (before impact)
- KE₂ = 0.25 × KE₁ = 0.25 × ½mv₁² (after impact)
- Therefore: ½mv₂² = 0.25 × ½mv₁²
- Solving: v₂² = 0.25v₁²
- v₂ = 0.5 × v₁ = 0.5 × 14 = 7 m/s (upward)
- Mass = 50g = 0.05 kg
- Initial momentum: p₁ = mv₁ = 0.05 × (-14) = -0.7 kg⋅m/s (taking downward as negative)
- Final momentum: p₂ = mv₂ = 0.05 × (+7) = +0.35 kg⋅m/s (upward is positive)
- Impulse = Δp = p₂ - p₁ = 0.35 - (-0.7) = 1.05 kg⋅m/s
The Answer:
The impulse of the impact force is 1.05 N⋅s (upward).Memory Tip:
Remember "Impulse = Change in momentum" - it's like the ground giving the ball a momentum "makeover" from going down fast to going up slower! The contact time doesn't affect the impulse magnitude, but it would affect the average force (F = Impulse/Δt).Great job working through this! You just connected three major physics concepts: energy conservation, momentum, and impulse. That's some serious physics muscle-building! 💪
⚠️ Common Mistakes to Avoid
- Confusing impulse with impact force
- Neglecting energy loss during the collision
- Forgetting to use the time of contact in impulse calculations
This explanation was generated by AI. While we work hard to be accurate, mistakes can happen! Always double-check important answers with your teacher or textbook.
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📷 Problem detected:
Solve: 2x + 5 = 13
Step 1:
Subtract 5 from both sides...
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