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(a) The roof of a large arena, with a weight of 430 kN, is lifted by 15 cm so that it can be centered. How much work is done on the roof by the forces making the lift? (b) In 1960 a Tampa, Florida, mother reportedly raised one end of a car that had fallen onto her son when a jack failed. If her panic lift effectively raised 4000 N (about 1/4 of the car's weight) by 5 cm, how much work did her force do on the car?

Respuesta :

Answer:

(a) 64.5 kJ

(b) 800 J

Solution:

As per the question:

Weight, w = 430 kN = [tex]430\times 10^{3}\ N[/tex]

Displacement, d = 15 cm = 0.15 m

Force, F = 4000 N

Displacement, d' = 5 cm = 0.05 m

Now,

(a) We know that work done in the given case equals the potential energy:

Work done, W = PE = mgd = wd = [tex]430\times 10^{3}\times 0.15= 64500\ J[/tex]

W = 64.5 kJ

(b) We know that work done is the product of force and displacement and is given by:

W' = Fd' = [tex]4000\times 0.05 = 800\ J[/tex]

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