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 first along the x-axis from x=0 to x=5m and then parallel to the y-axis from y=0 to y=6m. 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 force →F1 when the particle moves along the x-axis and y-axis is calculated by summing the work done on each axis. The total work done is 39 J, which is not exactly listed in the provided options, but 40 J is the closest.

Step-by-step explanation:

The work done by a force on an object is given by the scalar product of the force vector and the displacement vector. Since the question specifies that the particle moves first along the x-axis and then parallel to the y-axis, we can calculate the work done in two segments and then sum them up.

For the movement along the x-axis, the displacement is (5 m) î and for the y-axis, it is (6 m) ᴇ. Using the given constant force →F1 = (3 N)î + (4 N)ᴇ, the work done along the x-axis is (3 N) * (5 m) = 15 J and along the y-axis is (4 N) * (6 m) = 24 J.

The total work done by the force →F1 is the sum of the work done along the x-axis and the y-axis, which is 15 J + 24 J = 39 J. However, the options provided in the question (25 J, 30 J, 40 J, and 50 J) do not include 39 J. Thus, since we are required to select an option and 39 J is closest to 40 J, we would normally pick 40 J as the closest answer. Nevertheless, this discrepancy should be noted as none of the provided options exactly match the calculated work done.