Which of the following requires the expenditure of more work

Which of the following requires the expenditure of more work?

(a) Lifting a 110 newton weight a height of 55 meters

(b) Exerting a force of 55 pounds-force on a sofa to slide it 25 feet across a room.

Select all that apply

A. Lifting a 110 newton weight a height of 55 meters

B. Exerting a force of 55 pounds-force on a sofa to slide it 25 feet across a room.

Prove you answer by specifying each work in the same units, for example, in joules. (Round your answers to three significant places.)

The work done by lifting a 110 newton weight at a height of 5 meters is ________ J.

The work done by sliding a sofa 25 feet across a room is __________J.

Solution

Soln) a) We know tha

Work done in moving an object against the gravity = mgh

Work done in lifting 110N weight a height of 55m = 110 x 55

= 6050 N-m = 6050 Joule

b) Given: F= 55 pounds-force ( 1 pound- force= 4.448 N)

= 55 x 4.448 = 244.64 N

Displacement (d)= 25 feet

= 25 x 0.3048 (1 feet = 30.48 cm = 0.304 m)

= 7.62 m

Work Done on sofa = F x d

= 244.64 x 7.62

= 1864.156 N-m = 1864.156 Joule

Therefore, Lifting a 110 newton weight a height of 55 meters reqired more work.

work done by lifting a 110 newton weight at a height of 5 meters = mgh

= 110 x 5

= 550 N-m

= 550 Joule

work done by sliding a sofa 25 feet across a room = F x d

= (55 x 4.448) x (25 x 0.304)

= 1859.264 N-m

= 1859.264 Joule