Question

A block of mass $$m = 2.50 kg$$ is pushed a distance $$d = 2.20 m$$ along a frictionless, horizontal table by a constant applied force of magnitude $$F = 16.0 N$$ directed at an angle $$\theta = 25.0^{0}$$ below the horizontal as shown in above figure. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block.

Answer 1

We apply the definition of work by a constant force in the first three parts, but then in the fourth part we add up the answers. The total (net) work is the sum of the amounts of work done by the individual forces, and is the work done by the total (net) force. This identification is not represented by an equation in the chapter text, but is something you know by thinking about it, without relying on an equation in a list.
The definition of work by a constant force is $$W = FΔr \cosθ$$.
(a) The applied force does work given by
$$W = FΔr \cosθ = (16.0 N)(2.20 m)\cos25.0^{0} = 31.9 J$$
(b), (c) The normal force and the weight are both at $$90^{0}$$ to the displacement in any time interval. Both do $$0$$ work.
(d) $$\sum W = 31.9 J + 0 + 0 = 31.9 J$$