During winter break you are pushing a neighborhood child on a sled on a horizont

Question

During winter break you are pushing a neighborhood child on a sled on a horizontal surface. You are exerting a force of 65 N and the child/sled together have a mass of 38 kg. The child starts at rest relative to the ground and you push for 3 seconds.

(a) What is the average power that you put out over the three seconds?
Average Power =

Watts


(b) What is the instantaneous power that you are putting out at t = 2.0 seconds?
Instantaneous Power (t=2 s) = Watts


(c) If your body is 25% efficient, how many (food) Calories did you use in pushing the child during these three seconds?
Calories =

Explanation / Answer

(a) acceleration = force / mass
a = 65 / 38 =1.71m/s2
s = ut + 0.5 * at^2
s = 0 + 0.5 * 1.71 * 3^2
s = 7.695m
work done
= 65 * 7.695
= 500.175 J
the average power that you put out over the three seconds (in Watts)
= 500.175 / 3
= 166.725 W --answer

(b) v = u +at
v = 0 + 1.71* 2 = 3.42 m/s
the instantaneous power that you are putting out at t = 2.0 seconds (in Watts)
= force * speed
= 65 * 3.42
= 222.3 W --answer

(c) total energy in 3 s
= 500.175 J
If your body is 25% efficient
energy = 500.175 / 0.25 = 2000.7 J
= 2000.7 * 0.239
= 478.16 Cal ---answer

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