Work and Power Relationship.

Question

A block of mass 4.43kg4.43kg is moving horizontally as a force of 263N, directed at 30.0∘30.0∘ above the horizontal, is exerted on it. When its speed is 7.76ms , what is the rate at which the force is doing work?

Answer 1

Power by definition is the rate of work being done per unit time (P = W/t). Also, work is defined as force applied for a certain displacement (W = F⋅d) Using these concepts, power can be defined as the scalar (dot) product of force and velocity. This is derived from the general power equation which is that power is work per unit time:

P = W/t

Knowing Work is the force times displacement vectors, we can rearrange the equation to get displacement over time, which is the same as velocity:

P = (F⋅d)/t = F⋅v

For the general, instantaneous, case, the resulting equation is:

P_inst = F⋅v = Fv_instcosθ; where θ is the angle between the force and velocity vectors.

Once you have this equation, it is a simple mathematical calculation.

Note: I made an assumption that, since the force is constant, your instructor did not intend for you to use calculus for this problem. If the force is NOT constant, or if the angle is changing, then you will need to use calculus principles.