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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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Most popular questions from this chapter

A certain tractor is capable of pulling with a steady force of \(14 \mathrm{kN}\) while moving at a speed of \(3.0 \mathrm{~m} / \mathrm{s}\). How much power in kilowatts and in horsepower is the tractor delivering under these conditions?

Two railroad cars, each of mass \(7000 . \mathrm{kg}\) and traveling at \(90.0 \mathrm{~km} / \mathrm{h},\) collide head on and come to rest. How much mechanical energy is lost in this collision?

An ideal spring has the spring constant \(k=440 \mathrm{~N} / \mathrm{m}\) Calculate the distance this spring must be stretched from its equilibrium position for 25 J of work to be done.

A \(65-\mathrm{kg}\) hiker climbs to the second base camp on Nanga Parbat in Pakistan, at an altitude of \(3900 \mathrm{~m}\), starting from the first base camp at \(2200 \mathrm{~m}\). The climb is made in \(5.0 \mathrm{~h}\). Calculate (a) the work done against gravity, (b) the average power output, and (c) the rate of energy input required, assuming the energy conversion efficiency of the human body is \(15 \%\)

Two cars are moving. The first car has twice the mass of the second car but only half as much kinetic energy. When both cars increase their speed by \(5.0 \mathrm{~m} / \mathrm{s}\), they then have the same kinetic energy, Calculate the original speeds of the two cars.
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