Chapter 8: Q42P (page 240)
Make an order-of-magnitude estimate of your power output as you climb stairs. In your solution, state the physical quantities you take as data and the values you measure or estimate for them. Do you consider your peak power or your sustainable power?
The peak power is , the sustainable power is.
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A wind turbine on a wind farm turns in response to a force of high-speed air resistance, . The power available is, where v is the wind speed and we have assumed a circular face for the wind turbine of radius r. Take the drag coefficient as D = 1.00 and the density of air from the front endpaper. For a wind turbine having r = 1.50 m, calculate the power available with (a) v = 8.00 m/s and (b) v = 24.0 m/s. The power delivered to the generator is limited by the efficiency of the system, about 25%. For comparison, a large American home uses about 2 kW of electric power.
A roller-coaster car shown in Figure P8.72 is released from rest from a height h and then moves freely with negligible friction. The roller-coaster track includes a circular loop of radius R in a vertical plane. (a) First suppose the car barely makes it around the loop; at the top of the loop, the riders are upside down and feel weightless. Find the required height h of the release point above the bottom of the loop in terms of R. (b) Now assume the release point is at or above the minimum required height. Show that the normal force on the car at the bottom of the loop exceeds the normal force at the top of the loop by six times the car’s weight. The normal force on each rider follows the same rule. Such a large normal force is dangerous and very uncomfortable for the riders. Roller coasters are therefore not built with circular loops in vertical planes. Figure P6.17 (page 170) shows an actual design.
A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P8.65). the force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point A, the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The block’s speed at the bottom of the track is , and the block experiences an average friction force of 7.00 N while sliding up the track. (a) What is x? (b) If the block were to reach the top of the track, what would be its speed at that point? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top?
Consider the popgun in Example 8.3. Suppose the projectile mass, compression distance, and spring constant remain the same as given or calculated in the example. Suppose, however, there is a friction force of magnitude 2.00 N acting on the projectile as it rubs against the interior of the barrel. The vertical length from point A to the end of the barrel is 0.600 m. (a) After the spring is compressed and the popgun fired, to what height does the projectile rise above point B? (b) Draw four energy bar charts for this situation, analogous to those in Figures 8.6c–d.
An energy-efficient light bulb, taking in 28.0 W of power, can produce the same level of brightness as a conventional light bulb operating at power 100 W. The lifetime of the energy-efficient bulb is 10000 h and its purchase price is \(4.50, whereas the conventional bulb has a lifetime of 750 h and costs \)0.42. Determine the total savings obtained by using one energy-efficient bulb over its lifetime as opposed to using conventional bulbs over the same time interval. Assume an energy cost of $0.200 per kilowatt-hour.
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