How much time is spent ??

Question

A man pushes a lawn mower on a level lawn with a force of 200 N. If 48% of this force is directed downward, and 66 W of power is expended in pushing the mower 5.0 m, how much time is spent in pushing the mower this distance?

____ s 

Answer 1

First, determine the amount of force directed in the direction the mower is moving. Since 48% is downward, then 52% is horizontal.

 

52% of 200 N = .52*200N = 104 N.

Next, think about power.

Power is work/time. 

Work is force*distance.

So P = (f*d)/t. This can also be written as P = f*(d/t). d/t is velocity, so another equation for power is P = force * velocity or P = F*V

Divide both sides by F to get P/F = V. Now plug in the values for power and force

66W/104N = .63 m/s. Since velocity = distance/time or v = d/t, solve this equation for t: t = d/v. Plug is the values for d and v.

t = 5m/.63m/s = 7.9 s.   Yay!!!!!