Question

Consider a particle on which several forces act, one of which is known to be constant in time: →F1=(3N)ˆi+(4N)ˆj. As a result, the particle moves along the x-axis from x=0 to x=5m in some time interval. What is the work done by →F1 ?

a) 15 J
b) 25 J
c) 30 J
d) 40 J

Answer 1

The work done by the constant force →F1 on the particle as it moves along the x-axis from 0 to 5 m is 15 J, considering only the x-component of the force since the displacement is solely in the x-direction.

Step-by-step explanation:

The question asks about the work done by a constant force on a particle that moves along the x-axis from x = 0 to x = 5m. The given force →F1 is (3 N)î + (4 N)ï.

Since work done is the dot product of force and displacement, and the displacement is along the x-axis only, we only consider the x-component of the force (3 N) in calculating the work done. Therefore, the work done by →F1 is:

Work = Force × Displacement × cos(θ)
Since the force in the y-direction (4 Nï) is perpendicular to the displacement (which is along the x-axis), it does no work. The angle (θ) between the force along the x-axis (3 Nî) and the displacement (5 m along the x-axis) is 0 degrees, and cos(0 degrees) is 1. Hence, the work done by →F1 is:

Work = 3 N × 5 m × 1 = 15 J