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Chapter 7: Q7.1-2 PE (page 260)

A \(75.0 - {\rm{kg}}\) person climbs stairs, gaining \(2.50{\rm{ meters}}\) in height. Find the work done to accomplish this task.

Short Answer

Expert verified

The work done is \(1837.5{\rm{ J}}\).

Step by step solution

01

Definition of Concept

Potential Energy: The work done against is stored in body as a form of potential energy.

The potential energy is expressed as follows:

\[\begin{aligned}W = {\rm{PE}}\\ = mgh\end{aligned}\]

Here, \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

02

Calculating the work done

Putting\(75.0{\rm{ kg}}\)for\(m\),\(9.8{\rm{ m}}/{{\rm{s}}^2}\)for\(g\), and\(2.50{\rm{ m}}\)for\(h\)into equation (1.1),

\(\begin{aligned}{}W &= \left( {75.0{\rm{ kg}}} \right) \times \left( {9.8{\rm{ m}}/{{\rm{s}}^2}} \right) \times \left( {2.50{\rm{ m}}} \right)\\ &= 1837.5{\rm{ J}}\end{aligned}\)

Hence, the work done to accomplish this task is \(1837.5{\rm{ J}}\).

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Most popular questions from this chapter

(a) What is the power output in watts and horsepower of a 70.0-kg sprinter who accelerates from rest to 10.0 m/s in 3.00 s?

(b) Considering the amount of power generated, do you think a well-trained athlete could do this repetitively for long periods of time?

(a) How long can you rapidly climb stairs\(\left( {116/{\rm{min}}} \right)\)on the\(93.0{\rm{ kcal}}\)of energy in a\(10.0 - {\rm{g}}\)pat of butter?

(b) How many flights is this if each flight has\(16\)stairs?

Kanellos Kanellopoulos flew 119 km from Crete to Santorini, Greece, on April 23, 1988, in the Daedalus 88, an aircraft powered by a bicycle-type drive mechanism (see Figure 7.42). His useful power output for the 234-min trip was about 350 W. Using the efficiency for cycling from Table 7.2, calculate the food energy in kilojoules he metabolized during the flight.

Energy that is not utilized for work or heat transfer is converted to the chemical energy of body fat containing about \(39{\rm{ kJ}}/{\rm{g}}\). How many grams of fat will you gain if you eat \(10,000{\rm{ kJ}}\) (about \(2500{\rm{ kcal}}\)) one day and do nothing but sit relaxed for \(16.0{\rm{ hr}}\) and sleep for the other \(8.00{\rm{ h}}\)? Use data from Table 7.5 for the energy consumption rates of these activities.

Boxing gloves are padded to lessen the force of a blow.

(a) Calculate the force exerted by a boxing glove on an opponent’s face, if the glove and face compress 7.50 cm during a blow in which the 7.00-kg arm and glove are brought to rest from an initial speed of 10.0 m/s.

(b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm.

(c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?
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