Can work ever be negative? If so, give an example of a force that produces negative work. I Instructions square

Work can indeed be negative. Work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. Mathematically, work \( W \) is given by:<br /><br />\[ W = F \cdot d \cdot \cos(\theta) \]<br /><br />where:<br />- \( F \) is the magnitude of the force,<br />- \( d \) is the displacement of the object,<br />- \( \theta \) is the angle between the force and the displacement.<br /><br />When the force and displacement are in opposite directions, the angle \( \theta \) is 180 degrees, and the cosine of 180 degrees is -1. This results in negative work.<br /><br />### Example of Negative Work<br /><br />Consider a person pushing against a wall. The force exerted by the person on the wall is directed towards the wall, while the displacement of the person's hand is away from the wall. Since the force and displacement are in opposite directions, the angle \( \theta \) between them is 180 degrees, and the cosine of 180 degrees is -1. Therefore, the work done by the person's force on the wall is negative.<br /><br />In this scenario:<br />- The force \( F \) is the force exerted by the person on the wall.<br />- The displacement \( d \) is the distance the person's hand moves away from the wall.<br />- The angle \( \theta \) is 180 degrees.<br /><br />Thus, the work done \( W \) is:<br /><br />\[ W = F \cdot d \cdot \cos(180^\circ) = F \cdot d \cdot (-1) = -F \cdot d \]<br /><br />This negative work indicates that the force exerted by the person on the wall does not contribute to moving the wall but instead opposes the displacement of the hand.