A box is dragged horizontally across a floor by a 100 N force acting parallel to the floor. What is the work done by the force in moving it through a distance of 8 m
F = 100 N
S = 8 m
Since F and S are in the same direction,
θ = 0, where θ is the angle of the force to the direction of movement.
W = F Cos θ
= 100 x 8 x Cos 0
= 100 J (Cos 0 = 1)Example 2
A box is dragged across a floor by a 100N force directed 60o above the horizontal. How much work does the force do in pulling the object 8m?
F = 100N
θ = 60o
S = 8m
W = (F Cos θ) S
=(100 Cos 60o) 8
= 100x1/2x 8 = 400 JExample 3
A horizontal force F pulls a 10 kg carton across the floor at constant speed. If the coefficient of sliding friction between the carton and the floor is 0.30, how much work is done by F in moving the carton by 5m?
The carton moves with constant speed. Thus, the carton is in horizontal equilibrium.
We look at all the forces acting on the carton:
F is the applied force to the right.
P is the frictional force to the left.
W is the weight of the carton acting downwards.
N is the normal reaction by the floor on the carton acting upwards.
Since there is no movement in the vertical direction W = N = mg
Also since the carton is moving with constant speed,
F = f = μN = μmg.
Thus F = 0.3 x 10 x 9.8
= 29.4 N
Therefore work done W = FS
=(29.4 Cos 0o)