A(n) 80.0-kg student eats a 160-Calorie doughnut. To burn-it-off, he decides to climb the steps of a tall
building. How high (in m) would he have to climb to expend an equivalent amount of work?
To find the height the student would have to climb to expend an equivalent amount of work, we need to calculate the work done by climbing the steps and equate it to the energy gained from eating the doughnut.
Let's break down the problem:
1. Calculate the work done by climbing the steps:
The work done (W) is equal to the force (F) applied in the direction of motion multiplied by the distance (d) over which the force is applied:
W = F × d
In this case, the force applied is equal to the weight of the student due to gravity, which can be calculated using the formula:
F = m × g, where m is the mass of the student and g is the acceleration due to gravity (approximately 9.8 m/s²).
2. Calculate the energy gained from eating the doughnut:
The energy gained is given in calories. One calorie (Calorie with a capital "C") is equal to 4.18 joules of energy.
So, the energy gained is equal to:
Energy = Calories × 4.18
Now, let's put it all together:
1. Calculate the force applied:
F = m × g
F = 80.0 kg × 9.8 m/s²
2. Calculate the work done (distance climbed):
W = F × d
d = W / F
3. Calculate the energy gained:
Energy = Calories × 4.18
4. Equate the work done to the energy gained:
W = Energy
5. Solve for the height (d):
d = (Energy / F)
Let's calculate it:
Step 1:
F = 80.0 kg × 9.8 m/s²
F = 784 N
Step 2:
d = (Energy / F)
Step 3:
Energy = 160 Calories × 4.18
Energy = 668.8 Joules
Step 4:
d = 668.8 Joules / 784 N
Step 5:
d = 0.853 m
Therefore, the student would have to climb approximately 0.853 meters to expend an equivalent amount of work as the energy gained from eating the doughnut.