A person is pushing a box of mass 50 kg across a flat, horizontal surface. Takin

Question

A person is pushing a box of mass 50 kg across a flat, horizontal surface. Taking into account all possible forces, the displacement magnitude of the box is modeled mathematically as

(a) Calculate the work done on the box, using the definition of work from the beginning of the chapter, during the first two seconds of its motion.

(b) Calculate the work done on the box, using the work-energy theorem, during the first two seconds of its motion.

(c) Calculate the average power delivered to the box during the first two seconds of its motion.

Explanation / Answer

Given distance equation r = 1.9/2 t^2 + 0.55 t

average speed = x(1.1)/1.1 = (1.9/2*2 ^2+1.5*2 )/ 2 = 3.4 m/s

distance = (1.9/2* 2^2+1.5*2)= 6.8 m

so at that time v = 1.9*2+1.5= 5.3 m/s

accleration a = d^2r/dt^2 = 3.8m/s^2

Work Done W = m a s

W = 50 * 3.8 * 6.8

W = 1292 J

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using Work energy theorem

WNet = change in KE

Wnet = 0.5 * 50* (5.3^2 - 3.4^2)

Wnet = 413.25 J

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C> power P = W/t

P = 1292/2

P = 646 Watts

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