Question

Consider a particle on which a force acts that depends on the position of the particle. This force is given by →F1=(2y)i+(3x)j. Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x-axis.

a) 25 J
b) 50 J
c) 75 J
d) 100 J

Answer 1

The work done by the given force when the particle moves from the origin to a point 5 meters to the right on the x-axis is 0 J.

Step-by-step explanation:

To find the work done by the force, we need to integrate the dot product of the force and displacement vectors.

Given that the force vector is given by F₁ = (2y)i + (3x)j, and the particle moves from the origin to a point 5 meters to the right on the x-axis, we can calculate the work done as follows:

Work = ∫ F · dx, where F is the force vector and dx is the displacement vector.

Let's calculate the work done:

Work = ∫ (2y)i + (3x)j · dx = ∫ (2y)dx + ∫ (3x)dy

Since the particle travels along the x-axis from x = 0 to x = 5, and y remains constant at y = 0, the integral becomes:

Work = ∫₍₀₎₅ (3x)dy = ∫₍₀₎₅ 0 dy = 0

Therefore, the work done by the force is 0 J, option (a).