To calculate the work done by both the applied force and the frictional force, let's break down the information given and apply the work formula.

Given Data

1. Applied Force (F): $2.4 \times 10^2 \, \text{N} = 240 \, \text{N}$
2. Angle of Applied Force (θ): $20^\circ$ above the horizontal
3. Mass of Refrigerator (m): $85.8 \, \text{kg}$ (though mass is not required to calculate work in this case)
4. Frictional Force (f): $1.67 \times 10^2 \, \text{N} = 167 \, \text{N}$
5. Distance (d): $8 \, \text{m}$

1. Work Done by the Applied Force

The work done by the applied force ($W_{\text{applied}}$) is calculated using the formula: $W_{\text{applied}} = F \cdot d \cdot \cos \theta$ Substitute the given values: $W_{\text{applied}} = 240 \, \text{N} \times 8 \, \text{m} \times \cos(20^\circ)$

Now, let's calculate $\cos(20^\circ)$: $\cos(20^\circ) \approx 0.9397$ Substituting back in: $W_{\text{applied}} = 240 \times 8 \times 0.9397 \approx 1804.4 \, \text{J}$ So, the work done by the applied force is approximately 1804.4 J.

2. Work Done by the Frictional Force

The work done by friction ($W_{\text{friction}}$) is calculated as: $W_{\text{friction}} = -f \cdot d$ The frictional force opposes the direction of motion, so the work done by friction will be negative.

Substitute the values: $W_{\text{friction}} = -167 \, \text{N} \times 8 \, \text{m} = -1336 \, \text{J}$ So, the work done by the frictional force is -1336 J.

Summary of Results

• Work done by the applied force: $1804.4 \, \text{J}$
• Work done by the frictional force: $-1336 \, \text{J}$

Would you like more detailed steps or have questions about any part?

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Relative Questions:

1. What is the net work done on the refrigerator?
2. How would the work change if the angle of the applied force increased?
3. What if the frictional force were reduced; how would that affect the net work?
4. How does the angle of force application impact the work done?
5. What if the distance moved was doubled? How would it affect the work done?

Tip: Always consider the direction of forces when calculating work, as opposing forces contribute negatively to the net work done.