A man drinks a bottle of beer and proposes to work off it's 460 kj by exercising with a 20-kg barbell. If each lift of the barbell from chest height to over his head is through 60 cm and the efficiceny of his body is 10 percent under these circumstances, how many times must he left the barbell?

I'm not going to do all of your homework for you. Show some work of your own and someone will critique it.

(460 kJ)(x) = (20kg)(9.8 m/s2)(.6 m)

460,000 J (x) = 117.6
460,000/117.6 = x
3912 times of lifting the barbell

But, here is where I lose it,

if it is 10% efficient, then wouldn't he have to do 10 times as much?

39120 lifts?

Please show me where I am going wrong.

To find out how many times the man must lift the barbell, we need to calculate the total energy expended by lifting the barbell.

First, we need to determine the amount of energy in the beer bottle, which is given as 460 kJ (kilojoules).

Next, we need to calculate the energy required to lift the barbell. The formula for gravitational potential energy is:

E = m * g * h

where:
E = Energy (in joules)
m = Mass (in kilograms)
g = Acceleration due to gravity (approx. 9.8 m/s^2)
h = Height (in meters)

The given height is 60 cm, so we need to convert it to meters by dividing by 100. Therefore, h = 0.6 meters.

The mass of the barbell is given as 20 kg, so m = 20 kg.

Now, let's calculate the energy required to lift the barbell:

E = (20 kg) * (9.8 m/s^2) * (0.6 m)
E ≈ 117.6 joules

Since the man's body is only 10 percent efficient in converting energy, we need to divide the energy required by 0.1 (or multiply by 10).

Energy required by the man = 117.6 joules / 0.1
Energy required by the man ≈ 1176 joules

Finally, to find the number of times he must lift the barbell, we divide the energy in the beer bottle by the energy required per lift:

Number of lifts = 460 kJ / 1176 joules
Number of lifts ≈ 391.5

Since it's not possible to perform a fraction of a lift, we round up the number of lifts to the nearest whole number.

Answer: The man must lift the barbell approximately 392 times to work off the energy from the beer.