If the box moves 14 meters, how much work has the constant force done? Keep 4 significant figures.
Understand the Problem
The question is asking for the calculation of the work done by a constant force when a box moves a certain distance at an angle. We will use the formula for work, W = F * d * cos(θ), where F is the force, d is the distance, and θ is the angle of the force with respect to the direction of motion.
Answer
The work done is approximately \( 1483 \, \text{J} \).
Answer for screen readers
The work done is approximately ( 1483 , \text{J} ).
Steps to Solve
- Identify the formula for work done
The formula for work done ( W ) by a constant force is given by
$$ W = F \cdot d \cdot \cos(\theta) $$
where ( F ) is the force applied, ( d ) is the distance moved, and ( \theta ) is the angle between the force and the direction of motion.
- Substitute the known values
Here, ( F = 120 , \text{N} ), ( d = 14 , \text{m} ), and ( \theta = 28^{\circ} ). We can now substitute these values into the work formula.
- Calculate the cosine of the angle
First, calculate ( \cos(28^{\circ}) ):
Using a calculator, we find
$$ \cos(28^{\circ}) \approx 0.8829 $$
- Calculate work done
Substituting the values back into the work formula:
$$ W = 120 \cdot 14 \cdot 0.8829 $$
Now, perform the multiplication:
$$ W = 1680 \cdot 0.8829 \approx 1481.1 $$
- Round to four significant figures
Round ( 1481.1 ) to four significant figures:
The final result is
$$ W \approx 1483 , \text{J} $$
The work done is approximately ( 1483 , \text{J} ).
More Information
The calculation of work involves the application of the cosine function to account for the angle at which the force is applied relative to the direction of motion. This demonstrates how the orientation of the force affects the amount of work done in moving an object.
Tips
- Not using the cosine of the angle when calculating work. Make sure to include ( \cos(\theta) ) in the work formula to get accurate results.
- Forgetting to round to the correct number of significant figures. Always pay attention to significant figures based on the given values.
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