You pull a sled across a horizontal frictionless patch of snow. If your pulling force is in the same direction as the sled's displacement and increases the kinetic energy of the sled by 27%, by what percentage would the sled's kinetic energy increase if the pulling force acted at an angle of 42° above the horizontal?
You pull a sled across a horizontal frictionless patch of snow. If your pulling force is in the same direction as the sled's displacement and increases the kinetic energy of the sled by 27%, by what percentage would the sled's kinetic energy increase if the pulling force acted at an angle of 42° above the horizontal?
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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![**Question:**
You pull a sled across a horizontal frictionless patch of snow. If your pulling force is in the same direction as the sled's displacement and increases the kinetic energy of the sled by 27%, by what percentage would the sled's kinetic energy increase if the pulling force acted at an angle of 42° above the horizontal?
**Answer:**
[ ]%
---
**Explanation:**
This question involves the concepts of work and energy in physics. When a force acts along the direction of displacement, it fully contributes to the increase in kinetic energy. However, if the force is at an angle, only the horizontal component contributes to the kinetic energy increase.
To solve this problem, consider the horizontal component of the force:
1. **Initial Scenario**: Force is aligned with displacement; hence, the kinetic energy increase is 27%.
2. **New Scenario**: Force acts at 42° above the horizontal. Only the cosine component of the force contributes to the kinetic energy increase.
3. **Calculate the Horizontal Component**:
\[
\text{Horizontal Component} = \cos(42°)
\]
4. **Percentage Increase Calculation**:
\[
\text{New KE Increase} = 27\% \times \cos(42°)
\]
Fill in the correct numerical value once the calculation is completed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48deb947-3d41-43de-ac43-bef03e01cc59%2F03b0ef15-5143-4890-a3b9-1d257c344bdf%2Fri1zfq_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
You pull a sled across a horizontal frictionless patch of snow. If your pulling force is in the same direction as the sled's displacement and increases the kinetic energy of the sled by 27%, by what percentage would the sled's kinetic energy increase if the pulling force acted at an angle of 42° above the horizontal?
**Answer:**
[ ]%
---
**Explanation:**
This question involves the concepts of work and energy in physics. When a force acts along the direction of displacement, it fully contributes to the increase in kinetic energy. However, if the force is at an angle, only the horizontal component contributes to the kinetic energy increase.
To solve this problem, consider the horizontal component of the force:
1. **Initial Scenario**: Force is aligned with displacement; hence, the kinetic energy increase is 27%.
2. **New Scenario**: Force acts at 42° above the horizontal. Only the cosine component of the force contributes to the kinetic energy increase.
3. **Calculate the Horizontal Component**:
\[
\text{Horizontal Component} = \cos(42°)
\]
4. **Percentage Increase Calculation**:
\[
\text{New KE Increase} = 27\% \times \cos(42°)
\]
Fill in the correct numerical value once the calculation is completed.
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