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Chapter 5: Problem 6

How much work is done when a \(75-\mathrm{kg}\) person climbs a flight of stairs \(10 \mathrm{~m}\) high at constant speed? a) \(7.35 \cdot 10^{5}\) J c) 75 e) 7350 J b) 750 J d) 7500 J

Short Answer

Expert verified
a) \(7.35 \cdot 10^{5}\) J c) 75 J e) 7350 J b) 750 J d) 7500 J

Step by step solution

01

Identify the Mass and Height

Given in the problem, we know that the mass of the person (m) is \(75 \mathrm{kg}\), and the height of the stairs (h) is \(10\mathrm{~m}\).
02

Calculate the Force Exerted

To calculate the force exerted, we use the formula for gravitational force, \(F = mg\). Here, \(g = 9.81 \mathrm{m/s^2}\) is the gravitational acceleration. So, \(F = (75 \mathrm{kg})(9.81 \mathrm{m/s^2})\). Calculate this product to get the force exerted in climbing the stairs.
03

Calculate Work Done

Now, we know the distance is equal to the height of the stairs, \(d = h = 10\mathrm{~ m}\). We can calculate the work done (W) using the formula \(W = Fd\): \(W = F \times d\). Using the values obtained in Step 2 and the height of the stairs, calculate the work done.
04

Choose the Correct Answer

Compare the calculated work done value from Step 3 to the options given in the exercise: a) \(7.35 \cdot 10^{5}\) J c) 75 J e) 7350 J b) 750 J d) 7500 J Determine which option matches the calculated value for the work done while climbing the stairs.

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