Question

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% and the useful power output is 24 W)

a.) How long (in s) will it take her to lift 2,800 kg of snow 1.20 m? (This could be the amount of heavy snow on 60.0 ft of sidewalk.)

Answer 1

Power = Work / time

In this case, we're looking at the useful power output because that's how much power is actually used to do the work
The rest of it is inefficient being used up in making heat etc

So power = 24 W

we're obviously solving for time

and to calculate work, we're lifting up 2,800 kg of snow by 1.2 m

and in this case, the work would be equal to the potential energy since it's now 1.2 m in the air

and PE = mgh
you know m is 2,800 kg
g is 9.8 m/s^2
h = 1.2 m

can you calculate the work done?

and then you should be able to calculate the time

Answer 2

So the Eg would be 33,600, correct? (If the force of the gravitational field is 10 rather than 9.8)
Then the Work would be 33600 x 60?? divided by the power, 24, which would equal 84,000? Is this right? When I put it in to check it was wrong. Although I was given the following hint: What is the relationship between power output, work output and the time needed to do the work? Can you express the power output in terms of the efficiency and the power input? Can you express the work output in term of the change in gravitational potential energy of the snow?

Answer 3

Your hint basically tells you the formula that I gave you earlier

power output = work output / time

and you should know how to calculate the power output as well since they gave you the power input and the efficiency

power output = power input * efficiency
power output = 800 W * 0.03
power output = 24 W

That's how they told you the useful power output was 24 W

Answer 4

Now I'm not sure what you're referring to by Eg

We know the power output and we can calculate the work output

work output = mgh

m is 2,800 kg
g is 9.8 or 10 m/s^2
h is 1.2 meters

so what is

2800 * 9.8 * 1.2 = ??

Answer 5

Work output would be 33600 as I stated before since we have been told to use 10 as the g instead, correct?

Answer 6

Oh yes

and the units are kg * m^2/s^2

and 1 Watt is equivalent to 1 kg * m^2/s^(-3)

So now that we have the power output and the work output, we can calculate the time. You'll also notice that the units will cancel out giving us the time in seconds

24 = (33600) / t

t = ??

Answer 7

Nvm. Apparently, they did want 9.8 as the gravitational field strength (tried it in the end and got it right) but didn't decide to gosh darn specify. Thanks a lot though! Really appreciate your help!!!

Answer 8

Haha, it's always safer to use 9.8 unless specifically mentioned but of course! It was my pleasure!! :)