A machine has an 700 g steel shuttle that is pulled along a square steel rail by an elastic cord. The shuttle is released when the elastic cord has 15.0 N tension at a 45° angle. (Figure 1) Figure 45° 1 of 1 Elastic cord Fixed steel rail Part A What is the initial acceleration of the shuttle? Express your answer with the appropriate units. Value Submit μᾶ Provide Feedback Units Request Answer ?
A machine has an 700 g steel shuttle that is pulled along a square steel rail by an elastic cord. The shuttle is released when the elastic cord has 15.0 N tension at a 45° angle. (Figure 1) Figure 45° 1 of 1 Elastic cord Fixed steel rail Part A What is the initial acceleration of the shuttle? Express your answer with the appropriate units. Value Submit μᾶ Provide Feedback Units Request Answer ?
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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![### Problem Description
A machine has a 700 g steel shuttle that is pulled along a square steel rail by an elastic cord. The shuttle is released when the elastic cord has a tension of 15.0 N at a 45° angle.
#### Question:
What is the initial acceleration of the shuttle?
**Express your answer with the appropriate units.**
### Diagram Explanation
- **Figure 1:** The diagram depicts a steel shuttle connected to an elastic cord. The cord is pulled at a 45° angle, creating tension.
- The tension in the elastic cord is labeled as 15.0 N.
- The shuttle sits on a fixed steel rail, suggesting linear motion upon release.
### Solution Steps
The task involves calculating the initial acceleration of the shuttle using the given tension and angle:
1. Convert the mass of the shuttle from grams to kilograms:
\[
700 \, \text{g} = 0.7 \, \text{kg}
\]
2. Decompose the tension into horizontal and vertical components:
- \( T_x = 15.0 \, \text{N} \times \cos(45^\circ) \)
- \( T_y = 15.0 \, \text{N} \times \sin(45^\circ) \)
3. Use Newton’s second law to find the horizontal acceleration:
\[
a = \frac{T_x}{m} = \frac{15.0 \, \text{N} \times \cos(45^\circ)}{0.7 \, \text{kg}}
\]
4. Calculate the numeric value, keeping in mind to express the acceleration with the appropriate units of \( \text{m/s}^2 \).
### Answer Submission
Fill in your calculated values for the acceleration’s magnitude and units:
- **Value:** (Calculated value)
- **Units:** m/s²
Press **Submit** to record your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc676ab97-b3d8-47fc-b3e9-1fc3fb529310%2F9c0ce652-d301-4447-a5b1-5be8039845f5%2Fkucrqx_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description
A machine has a 700 g steel shuttle that is pulled along a square steel rail by an elastic cord. The shuttle is released when the elastic cord has a tension of 15.0 N at a 45° angle.
#### Question:
What is the initial acceleration of the shuttle?
**Express your answer with the appropriate units.**
### Diagram Explanation
- **Figure 1:** The diagram depicts a steel shuttle connected to an elastic cord. The cord is pulled at a 45° angle, creating tension.
- The tension in the elastic cord is labeled as 15.0 N.
- The shuttle sits on a fixed steel rail, suggesting linear motion upon release.
### Solution Steps
The task involves calculating the initial acceleration of the shuttle using the given tension and angle:
1. Convert the mass of the shuttle from grams to kilograms:
\[
700 \, \text{g} = 0.7 \, \text{kg}
\]
2. Decompose the tension into horizontal and vertical components:
- \( T_x = 15.0 \, \text{N} \times \cos(45^\circ) \)
- \( T_y = 15.0 \, \text{N} \times \sin(45^\circ) \)
3. Use Newton’s second law to find the horizontal acceleration:
\[
a = \frac{T_x}{m} = \frac{15.0 \, \text{N} \times \cos(45^\circ)}{0.7 \, \text{kg}}
\]
4. Calculate the numeric value, keeping in mind to express the acceleration with the appropriate units of \( \text{m/s}^2 \).
### Answer Submission
Fill in your calculated values for the acceleration’s magnitude and units:
- **Value:** (Calculated value)
- **Units:** m/s²
Press **Submit** to record your answer.
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