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} $.

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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