Which of the following requires the expenditure of more work? (a) Lifting a 100 newton [N] weight a height of 3 meters [m]. (b) Exerting a force of 60 pounds-force [lb Subscript f] on a sofa to slide it 30 feet [ft] across a room.

More work is done in moving a sofa than lifting a 100 N weight.

Explanation:

When a force is applied on an object and the object changes its position, then there is some work has been done on the object. Its S.I. unit is joule(J). Thus,

Work done, W = F x d       (1)

Here F is force applied on the object and d is displacement.

(a) In this case, force is equal to 100 N and displacement is equal to 3 m.

Substitute the values of F and d in the equation (1). Hence,

W₁ = 100 x 3 = 300 J

(b) In this case, force is equal to 60 pounds-force and displacement is equal to 30 feet. First we have to convert force and displacement in units newton and meter respectively.

As,

1 pound-force = 4.45 N

F = 60 pounds-force = 60 x 4.45 N = 267 N

1 foot = 0.3048 m

d = 30 feet = 30 x 0.3048 m = 9.144 m

Substitute these values in equation (1).

W₂ = 267 x 9.144 = 2441.4 N

Since, W₂ is greater than W₁. Hence, more work is done in moving a sofa than lifting a weight.  

c. magnitude and direction