A horse pulls a 300 kg sled for 50 m over level ground at constant speed, exerting a force of 3000 N at 30° above horizontal. How much work is done by the horse on the sled? 150 kJ 2940 J 130 kJ
A horse pulls a 300 kg sled for 50 m over level ground at constant speed, exerting a force of 3000 N at 30° above horizontal. How much work is done by the horse on the sled? 150 kJ 2940 J 130 kJ
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:**
A horse pulls a 300 kg sled for 50 m over level ground at constant speed, exerting a force of 3000 N at 30° above the horizontal. How much work is done by the horse on the sled?
**Options:**
- 150 kJ
- 2940 J
- 130 kJ
- 0 J
**Explanation:**
To find the work done by the horse, we can use the formula:
\[ \text{Work} = F \cdot d \cdot \cos(\theta) \]
Where:
- \( F = 3000 \, \text{N} \) (the force exerted by the horse)
- \( d = 50 \, \text{m} \) (the distance over which the force is applied)
- \( \theta = 30^\circ \) (the angle above the horizontal)
Calculating the component of the force in the direction of the movement:
\[ \text{Work} = 3000 \, \text{N} \times 50 \, \text{m} \times \cos(30^\circ) \]
\[ \text{Work} = 3000 \, \text{N} \times 50 \, \text{m} \times \frac{\sqrt{3}}{2} \]
\[ \text{Work} = 3000 \times 50 \times 0.866 \]
\[ \text{Work} = 129900 \, \text{J} \]
Since 1 kJ = 1000 J:
\[ \text{Work} = 129.9 \, \text{kJ} \]
Therefore, the closest option is 130 kJ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F946f068e-22bb-4068-a00a-e22f7e79f207%2Fd3c877a9-c9cf-4fe6-8e8b-cba5b5e04bfd%2Fy2t1s2f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A horse pulls a 300 kg sled for 50 m over level ground at constant speed, exerting a force of 3000 N at 30° above the horizontal. How much work is done by the horse on the sled?
**Options:**
- 150 kJ
- 2940 J
- 130 kJ
- 0 J
**Explanation:**
To find the work done by the horse, we can use the formula:
\[ \text{Work} = F \cdot d \cdot \cos(\theta) \]
Where:
- \( F = 3000 \, \text{N} \) (the force exerted by the horse)
- \( d = 50 \, \text{m} \) (the distance over which the force is applied)
- \( \theta = 30^\circ \) (the angle above the horizontal)
Calculating the component of the force in the direction of the movement:
\[ \text{Work} = 3000 \, \text{N} \times 50 \, \text{m} \times \cos(30^\circ) \]
\[ \text{Work} = 3000 \, \text{N} \times 50 \, \text{m} \times \frac{\sqrt{3}}{2} \]
\[ \text{Work} = 3000 \times 50 \times 0.866 \]
\[ \text{Work} = 129900 \, \text{J} \]
Since 1 kJ = 1000 J:
\[ \text{Work} = 129.9 \, \text{kJ} \]
Therefore, the closest option is 130 kJ.
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