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Chapter 3: Problem 7

If we know that a force of \(5 \mathrm{~N}\) acts on an object while it moves 2 meters, can we calculate how much work was done with no other information? Explain.

Short Answer

Expert verified
Answer: It is impossible to calculate the work done without knowing the angle between the force and the displacement vectors because the formula for work is dependent on this angle. The angle determines the proportion of the force that contributes to the work done in the direction of the displacement. Without knowing the angle, there is a range of possible values for the work, making it impossible to calculate it accurately.

Step by step solution

01

Identify the variables given in the problem

We are given that the force applied on the object is \(5 \mathrm{~N}\), and the object moves for 2 meters.
02

Examine the insufficient information

We need more information to calculate the work done—specifically, we need the angle between the force and the displacement vectors.
03

Explain why it is impossible to find the work done without knowing the angle

The work done depends on the angle between the force and the displacement vectors because the formula for work is dependent on this angle. If the angle between the force and the displacement is \(0^{\circ}\), then all of the force is applied in the same direction as the displacement, resulting in the maximum possible work done. If the angle is \(90^{\circ}\), then the force has no component in the direction of the displacement, resulting in zero work done. Without knowing the angle, there is a range of possible values for the work, making it impossible to calculate it accurately.
04

Conclusion

To calculate the work done using the force and displacement values, we need to know the angle between the force and the displacement vectors. Without this information, it is impossible to determine the work done accurately.

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