Question

Three forces, F1 = 20.0 N, F2 = 40.0 N, and F3 = 10.0 N act on an object of mass 2.00 kg that can move along a frictionless incline as shown in the figure. The questions refer to the instant the object has moved through a distance of 0.600 m along the surface of the inclined plane in an upward direction. Calculate the work done by

(a) F1
(b)F2
(c)F3
(d) the resultant force.

Answer 1

The work done by F1 is -12.0 J, the work done by F2 is 24.0 J, the work done by F3 is -6.0 J, and the resultant force is 70.0 N.

Step-by-step explanation:

The calculation of work done by individual forces involves employing the equation: Work = Force * Distance * cos(theta).

For force F1, the work is computed as 20.0 N * 0.600 m * cos(180°), resulting in -12.0 J.

Force F2's work is determined as 40.0 N * 0.600 m * cos(0°), yielding 24.0 J.

Similarly, force F3's work is found to be 10.0 N * 0.600 m * cos(180°), amounting to -6.0 J.

To establish the resultant force, the vector sum of F1, F2, and F3 is calculated, resulting in a resultant force of 70.0 N.

Consequently, the work done by the resultant force is expressed as Work = Resultant force * Distance * cos(theta), with the final equation involving the specific value of 70.0 N * 0.600 m * cos(theta).

This comprehensive approach allows for the determination of work done in a system with multiple forces acting in various directions.

Answer 2

The work done by the forces F1, F2, and F3 on the object along the incline are calculated by multiplying the force value by the distance traveled. Without specific direction angles, it is assumed that the forces act parallel to the displacement. The resultant force's work is the sum of the works done by F1, F2, and F3.

Step-by-step explanation:

To calculate the work done by each force, we use the equation work (W) = force (F) × distance (d) × cos(θ), where θ is the angle between the force direction and the displacement direction. Since the question implies that the forces act at different angles to the displacement, the angles must be considered (which are not provided in the question, thus assuming each force is aligned with the displacement for simplicity).

1. Work done by F1: Since no angle is given, assuming it acts along the incline, W1 = F1 × d = 20.0 N × 0.600 m = 12.0 J.
2. Work done by F2: Assuming F2 also acts along the incline, W2 = F2 × d = 40.0 N × 0.600 m = 24.0 J.
3. Work done by F3: If F3 acts along the incline, W3 = F3 × d = 10.0 N × 0.600 m = 6.0 J.
4. Work done by the resultant force: First, we need to find the resultant force (FR) by vector addition of F1, F2, and F3 (assuming they are all parallel, which may not be the case; details are necessary). Assuming they are parallel and act in the same direction for simplicity, FR = F1 + F2 + F3 = 70.0 N. The work done by the resultant force is WR = FR × d = 70.0 N × 0.600 m = 42.0 J.

Without the angles between the forces and the direction of displacement, the calculations above assume that the forces are all parallel to the displacement, which may not be accurate.