Question

1-11)A 48-kg woman cheats on her diet and eats a 670-Calorie (670 kcal) jelly doughnut for breakfast.

(a) How many joules of energy are the equivalent of one jelly doughnut?
J

(b) How many stairs must the woman climb to perform an amount of mechanical work equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is 15 cm.
stairs

(c) If the human body is only 23% efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?
stairs

3)A(n) 8.7-kg copper block is given an initial speed of 4.6 m/s on a rough horizontal surface. Because of friction, the block finally comes to rest.

(a) If the block absorbs 85% of its initial kinetic energy as internal energy, calculate its increase in temperature.
°C

4)A 1.50-kg iron horseshoe initially at 550°C is dropped into a bucket containing 16.0 kg of water at 24.0°C. What is the final temperature of the water–horseshoe system? Ignore the heat capacity of the container and assume a negligible amount of water boils away.

Answer 1

(a) Since 1 cal = 4.184 J

670 kcal = 670,000 cal = 2.8 x 10^6 joules

(b) Height of 1 stair step is 0.15 m

E = mgh = 2.8 x 10^6 joules

m = 48 kg (weight of the woman)
g = 9.82 m/s²

Now solve for h

h = E/mg = (2.8×10^6) /(48×9.8)

h = 5.952x 10^3 m or 3.97x 10^4 stair steps

or 39683 complete stair steps

(c) if the body is only 23% efficient, then

E(mechanical) = 0.23 * 2.8 x 10^6 joules = 644000 joules

h = E(mechanical)/mg = 1369 m or 9127 stair steps

The rest of the energy is converted to heat of course, which the woman sweats away while climbing the steps.

Hope this helps you.

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