Question

Calculate the work done by a 2.0 N force (directed at a 30° angle to the vertical) to move a 500-gram box a horizontal distance of 400 cm across a rough floor at a constant speed of 0.5 m/s.

Answer 1

The work done by a 2.0 N force at a 30° angle to the vertical to move a 500-gram box 400 cm across a floor at constant speed is 4.0 J.

Step-by-step explanation:

To calculate the work done by a 2.0 N force that moves a 500-gram box a horizontal distance of 400 cm, you must consider the component of the force that acts along the distance the box moves. Since the force is at a 30° angle to the vertical, you should find the horizontal component of the force. The horizontal component (Fh) can be found using the formula Fh = F × cos(θ), where F is the force and θ is the angle.

In this case, the horizontal component is Fh = 2.0 N × cos(60°) as the angle between the force and the horizontal is 60° (90° - 30°). Thus, Fh = 2.0 N × 0.5 = 1.0 N. The work done (W) is then W = Fh × d, where d is the distance. Hence, W = 1.0 N × 4.0 m = 4.0 J. The force provides enough work to overcome friction and maintain constant speed, indicating that the kinetic energy of the box does not change.