A piece of chocolate cake contains about 400 Calories. A nutritional Calorie is equal to 1000 calories (thermochemical calories), which is equal to 4.184 kJ. How many 7-inch-high steps must a 190 pound man climb to expend the 400 Cal from the piece of cake? Assume that the energy used to climb steps is the same as the energy required to lift a mass against the force of gravity, namely: PE = mgh, where m is the mass of the object lifted in kilograms, g is the gravitational constant (9.8 m/s2), and h is the height the object is lifted in meters.

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Chemistry

9 September, 13:42

A piece of chocolate cake contains about 400 Calories. A nutritional Calorie is equal to 1000 calories (thermochemical calories), which is equal to 4.184 kJ. How many 7-inch-high steps must a 190 pound man climb to expend the 400 Cal from the piece of cake? Assume that the energy used to climb steps is the same as the energy required to lift a mass against the force of gravity, namely: PE = mgh, where m is the mass of the object lifted in kilograms, g is the gravitational constant (9.8 m/s2), and h is the height the object is lifted in meters.

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Houston Holland · Answer 1

11,145 steps

Explanation:

First, let's see how much energy he may expend. If a nutritional calorie has 1000 calories or 4.184 kJ, so

PE = 400*4.184 = 1,673.6 kJ = 1,673,600 J

One pound has 0.4536 kg, then m = 190*0.4536 = 86.184 kg.

PE = mgh

1,673,600 = 86.184*9.8*h

h = 1,981.52 m

1 meter has 39.37 inches, so h = 1,981.52*39.37 = 78,012.53 in

1 step has 7 in, so:

78,012.53/7 = 11,145 steps.