Question

51.Shoveling snow can be extremely taxing because the arms have such a low efficiency in this activity. Suppose a person shoveling a footpath metabolizes food at the rate of 800 W. (a) What is her useful power output? (b) How long will it take her to lift 3000 kg of snow 1.20 m? (This could be the amount of heavy snow on 20 m of footpath.) (c) How much waste heat transfer in kilojoules will she generate in the process?

Answer 1

Complete question is;

Shoveling snow can be extremely taxing since the arms have such a low efficiency in this activity. Suppose a person shoveling a sidewalk metabolizes food at the rate of 800 W. (The efficiency of a person shoveling is 3%.)

(a) What is her useful power output? (b) How long will it take her to lift 3000 kg of snow 1.20 m? (This could be the amount of heavy snow on 20 m of footpath.) (c) How much waste heat transfer in kilojoules will she generate in the process?

Answer:

A) P_out = 24 W

B) t = 1470 s

C) Q = 1140.72 KJ

Explanation:

We are given;

Input Power; P_in = 800 W

Efficiency; η = 3% = 0.03

A) Formula for efficiency is;

η = P_out/P_in

Making P_out the subject, we have;

P_out = η•P_in

P_out = 0.03 × 800

P_out = 24 W

B) We know that;

Power = work done/time taken

Thus;

P_out = mgh/t

We are given;

m = 3000 kg

h = 1.20 m

Thus, time is;

t = (3000 × 9.8 × 1.2)/24

t = 1470 s

C) amount of heat wasted is calculated from;

Q = (P_in - P_out)t

Q = (800 - 24) × 1470

Q = 1,140,720 J

Q = 1140.72 KJ