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Answers to Checkups 269

110. A woman exercising on a rowing machine pulls the oars back
once per second. During such a pull, each hand moves 0.50 m
while exerting an average force of 100 N.
(a) What is the work the woman does during each stroke
(with both hands)?
(b) What is the average power the woman delivers to the oars?
111. The world’s tallest staircase, of 2570 steps, is located in the
CN tower in Toronto. It reaches a height of 457 m. Estimate
FIGURE 8.27 Ancient Egyptian wall mural from 1900 B.C.
how long it would take an athlete to climb this staircase. The
athlete has a mass of 75 kg, and his leg muscle can deliver a
power of 200 W.
106. In a braking test, a 990-kg automobile takes 2.1 s to come to a 112. A pump placed on the shore of a pond takes in 0.80 kg of
full stop from an initial speed of 60 km/h. What is the amount water per second and squirts it out of a nozzle at 50 m/s.
of energy dissipated in the brakes? What is the average power What mechanical power does this pump supply to the water?
dissipated in the brakes? Ignore external friction in your calcu- 113. The hydroelectric pumped-storage plant in Northfield,
lation and express the power in horsepower. Massachusetts, has a reservoir holding 2.2 10 m of water
3 3
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107. In a waterfall on the Alto Paraná river (between Brazil and on top of a mountain. The water flows 270 m vertically down
Paraguay), the height of fall is 33 m and the average rate of the mountain in pipes and drives turbines connected to elec-
3
flow is 13000 m of water per second. What is the power dis- tric generators.
sipated by this waterfall? (a) How much electric energy, in kW . h, can this storage plant
108. When jogging at 12 km/h on a level road, a 70-kg man uses generate with the water available in the reservoir?
750 kcal/h. How many kilocalories per hour does he require (b) In order to generate 1000 MW of electric energy, at what
when jogging up a 1:10 incline at the same speed? Assume that rate, in m /s, must this storage plant withdraw water from
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the frictional losses are independent of the value of the slope. the reservoir?
109. Consider a projectile traveling horizontally and slowing down 114. A 50-kg circus clown is launched vertically from a spring-
under the influence of air resistance, as described in Problems loaded cannon using a spring with spring constant 3500 N/m.
47 and 48 of Chapter 2. The mass of this projectile is The clown attains a height of 4.0 m above the initial position
45.36 kg, and the speed as a function of time is (when the spring was compressed).
2
v 655.9 61.1t 3.26t (a) How far was the spring compressed before launch?
where speed is in m/s and time in seconds. (b) What was the maximum acceleration of the clown during
launch?
(a) What is the instantaneous power removed from the pro-
jectile by air resistance? (c) What was the maximum speed of the clown?
(b) What is the kinetic energy at time t 0? At time t 3.00 s?
(c) What is the average power for the time interval from 0
to 3.00 s?

Answers to Checkups the slope of the potential; the negative of a negative is positive,
and so the force is directed along the positive x direction.
Checkup 8.1 3. A force is always conservative if the force is an explicit func-
tion of position x. In that case, a potential-energy function can
1. The force can be obtained from F dU/dx kx. Thus, always be constructed by integration of the force according to
x
the force is positive for positive x and negative for negative x; Eq. (8.14).
that is, the new force is repulsive (it pushes a particle away 4. (D) No; no. The work done is equal to the negative of the
from x 0), whereas the spring force is attractive. change in potential energy only for conservative forces. The
2. The potential energy shown in Fig. 8.5a has a negative slope work done is equal to the change in kinetic energy only for the
as a function of x. By Eq. (8.21), the force is the negative of net force acting on a particle.