College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
2. Calculate the impulse imparted to a 0.2 kg tennis ball traveling in the air at 15 m/s when the ball is stopped over a period of 0.1 seconds.
---
In this problem, we need to determine the impulse given to a tennis ball. The key parameters given are the mass of the ball, its initial velocity, and the time over which it is brought to a stop.
**Mathematical Relationship:**
Impulse (\( J \)) can be calculated using the formula:
\[ J = \Delta p = m \cdot \Delta v = m \cdot (v_f - v_i) \]
Where:
- \( J \) is the impulse.
- \( \Delta p \) is the change in momentum.
- \( m \) is the mass of the object (0.2 kg).
- \( v_f \) is the final velocity (0 m/s, as the ball is stopped).
- \( v_i \) is the initial velocity (15 m/s).
Since the ball is stopped, \( v_f = 0 \).
**Solution Approach:**
1. Calculate the change in velocity (\( \Delta v \)):
- \( \Delta v = v_f - v_i = 0 - 15 = -15 \, \text{m/s} \)
2. Use the impulse formula:
- \( J = 0.2 \, \text{kg} \times (-15 \, \text{m/s}) = -3 \, \text{kg m/s} \)
**Explanation:**
The negative sign indicates the direction of the impulse is opposite to the direction of the initial velocity of the ball. The ball experiences an impulse of \( 3 \, \text{kg m/s} \) in the direction opposite to its motion to bring it to a stop.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c8c5c21-75ec-43df-a11c-eaf8dc741c9d%2F79967991-e958-4f6e-980c-1596fd797241%2Ftt4b1qn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
2. Calculate the impulse imparted to a 0.2 kg tennis ball traveling in the air at 15 m/s when the ball is stopped over a period of 0.1 seconds.
---
In this problem, we need to determine the impulse given to a tennis ball. The key parameters given are the mass of the ball, its initial velocity, and the time over which it is brought to a stop.
**Mathematical Relationship:**
Impulse (\( J \)) can be calculated using the formula:
\[ J = \Delta p = m \cdot \Delta v = m \cdot (v_f - v_i) \]
Where:
- \( J \) is the impulse.
- \( \Delta p \) is the change in momentum.
- \( m \) is the mass of the object (0.2 kg).
- \( v_f \) is the final velocity (0 m/s, as the ball is stopped).
- \( v_i \) is the initial velocity (15 m/s).
Since the ball is stopped, \( v_f = 0 \).
**Solution Approach:**
1. Calculate the change in velocity (\( \Delta v \)):
- \( \Delta v = v_f - v_i = 0 - 15 = -15 \, \text{m/s} \)
2. Use the impulse formula:
- \( J = 0.2 \, \text{kg} \times (-15 \, \text{m/s}) = -3 \, \text{kg m/s} \)
**Explanation:**
The negative sign indicates the direction of the impulse is opposite to the direction of the initial velocity of the ball. The ball experiences an impulse of \( 3 \, \text{kg m/s} \) in the direction opposite to its motion to bring it to a stop.
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