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# Examples on Work Done

Example 1

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

= 800 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 J

Example 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)

=147 J