What is the horizontal acceleration of the pillow?
Understand the Problem
The question involves analyzing forces acting on a pillow with a given mass and determining its horizontal acceleration based on those forces. It requires the application of Newton's second law.
Answer
The horizontal acceleration of the pillow is $3.33 \, \text{m/s}^2$.
Answer for screen readers
The horizontal acceleration of the pillow is approximately $3.33 , \text{m/s}^2$.
Steps to Solve
- Identify the Known Values We have the following information:
- Mass of the pillow: $m = 0.30 , \text{kg}$
- Force exerted by Anuja on the pillow: $F_{\text{Anuja}} = 11.0 , \text{N}$
- Force exerted by Sarah on the pillow: $F_{\text{Sarah}} = 10.0 , \text{N}$
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Calculate the Net Force Acting on the Pillow The net force is calculated by subtracting the force exerted by Sarah from the force exerted by Anuja, since they are in opposite directions: $$ F_{\text{net}} = F_{\text{Anuja}} - F_{\text{Sarah}} $$ Substituting in the known values: $$ F_{\text{net}} = 11.0 , \text{N} - 10.0 , \text{N} = 1.0 , \text{N} $$
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Apply Newton's Second Law Using Newton's second law, which states that the acceleration is the net force divided by the mass: $$ a = \frac{F_{\text{net}}}{m} $$ Substituting the known values: $$ a = \frac{1.0 , \text{N}}{0.30 , \text{kg}} $$
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Calculate the Acceleration Now, perform the division: $$ a = \frac{1.0 , \text{N}}{0.30 , \text{kg}} \approx 3.33 , \text{m/s}^2 $$
The horizontal acceleration of the pillow is approximately $3.33 , \text{m/s}^2$.
More Information
The result indicates that the pillow is accelerating toward Anuja, who is pulling it with a greater force than Sarah. This scenario effectively demonstrates Newton's second law, which links force, mass, and acceleration.
Tips
- Forgetting Direction of Forces: It's crucial to recognize the direction of each force when calculating the net force.
- Sign Errors: Ensure that the direction assigned to positive and negative forces is consistent throughout the calculation.
- Incorrectly Using Units: Ensure that units are consistent, particularly when converting forces and mass—N (Newton) and kg (kilogram) must be used correctly.
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