Question

A particle moves under the influence of several forces. One of these forces is constant in time and can be written as F 1=(2i^+1j^)N. As a result, the particle moves along the x-axis in 4s, from x=3m to x=12m. What is the work done by the force F1?

Answer 1

The work done by the force F1 as the particle moves from x=3m to x=12m along the x-axis is 18 J, calculated using the work formula with the x-component of the force and the displacement along the x-axis.

Step-by-step explanation:

The work done by a constant force F1 when a particle moves along a displacement can be calculated using the formula Work = Force × Displacement × cos(θ), where θ is the angle between the force vector and the displacement vector. Since the force given is F1 = (2i + 1j) N and the particle moves along the x-axis from x = 3m to x = 12m, the work done is only due to the component of the force in the direction of the displacement, which is the x-component of F1. The displacement in the x-direction is 12m - 3m = 9m, and θ is 0 degrees as the movement is along the x-axis, the same direction as the x-component of the force. Therefore, the work done by force F1 is W = 2 N × 9m × cos(0°) = 18 J.