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 a straight path from a Cartesian coordinate of (0 m, 0 m) to (5 m, 6 m). What is the work done by →F1 ?

a) 25 J
b) 30 J
c) 40 J
d) 50 J

Answer 1

The work done by the constant force F₁ is 39 J.

Step-by-step explanation:

To find the work done by the constant force F₁, we can use the formula:

W = F * d * cos(θ)

where W is the work done, F is the magnitude of the force, d is the displacement, and θ is the angle between the force vector and the displacement vector.

In this case, the force F₁ = (3 N)Î + (4 N)Ĵ is constant and the displacement is from (0 m, 0 m) to (5 m, 6 m). The angle between the force and the displacement is 0° since they are parallel.

Therefore, the work done by F₁ is:

W = F₁ * d * cos(0°) = (3 N * 5 m + 4 N * 6 m) * cos(0°) = 15 N * m + 24 N * m = 39 J

So, the correct answer is 39 J.