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- To get in shape, you head to the local gym to exercise by lifting weights. Using a lat machine (Fig. P5.48), you notice that the wire connected to the bar is run around three different pulleys and is connected to a vertical stack of weights on the other end. The weights move up and down as you pull down on the bar. Suppose you set the machine so that the weight to be lifted is 120.0 lb. When you pull down on the bar, exerting a constant force, the acceleration experienced by the weights is 0.250 m/s2. What tension must exist in the wire connecting the bar and weights under these conditions? Assume the pulleys are massless and frictionless. FIGURE P5.48A rectangular block has a length that is five times its width and a height that is three times its width. The blocks surfaces are all identical except for size. When the block is placed on a horizontal tabletop so that the area in contact with the table is length width, it is found that a horizontal force of 10.0 N applied to the block is just sufficient to overcome the static friction force and cause the block to move. The block is then knocked over so that the area in contact with the table is length height. Now, what minimum horizontal force will cause the block to move? Explain.(a) How much gravitational potential energy (relative to the ground on which it is built) is stored in the Great Pyramid of Cheops, given that its mass is about 7109 kg and its center of mass is 36.5 m above the surrounding ground? (b) How does this energy compare with the daily food intake of a person?
- To give a pet hamster exercise, some people put the hamster in a ventilated ball andallow it roam around the house(Fig. P13.66). When a hamsteris in such a ball, it can cross atypical room in a few minutes.Estimate the total kinetic energyin the ball-hamster system. FIGURE P13.66 Problems 66 and 67The system shown in Figure P5.49 has an acceleration of magnitude 1.50 m/s2. Assume that the coefficient of kinetic friction between block and incline is the same for both inclines. Find (a) the coefficient of kinetic friction and (b) the tension in the string.The mass of a roller-coaster car, including its passengers, is 500 kg. Its speed at the bottom of the track in Figure P6.16 is 19 m/s. The radius of this section of the track is r1 = 25 m. Find the force that a seat in the roller-coaster car exerts on a 50-kg passenger at the lowest point.
- Repeat Exercise 5.18 with the contestant pulling the block of ice with a rope over his shoulder at the same angle above the horizontal as shown in Figure 5.23(b).Jamal and Dayo are lifting a large chest, weighing 207 lb, by using the two rope handles attached to either side. As they lift and hold it up so that it is motionless, each handle makes a different angle with respect to the vertical side of the chest (Fig. P5.76). If the angle between Jamals handle and the vertical side is 25.0 and the angle between Dayos handle and the vertical side of the chest is 30.0, what are the tensions in each handle? FIGURE P5.76A One end of a metal rod of weight Fg and length L presses against a corner between a wall and the floor (Fig. P14.64). A rope is attached to the other end of the rod. Find the magnitude of the tension in the rope if the angle between the rod and the rope is 90.
- Bruce Lee was famous for breaking concrete blocks with a single karate chop. From slow-motion video, the speed of his 1.50-kg hand descending on a block was estimated to be 15.0 m/s, which decreased to a speed of 0.500 m/s in the 2.50 103 s during which his hand made contact with and broke through the block. The maximum shear stress a concrete block can be subjected to before breaking is 9.50 105 N/m2. a. What was the force exerted by Lees hand on the block? b. If a typical concrete block broken by Lee was 3.00 cm thick and 15.2 cm wide, what is the shear stress experienced by the concrete block? c. Will the concrete block succumb to Lees karate chop?If you hold a horizontal metal bar several centimeters above the ground and move it through grass, each leaf of grass bends out of the way. If you increase the speed of the bar, each leaf of grass will bend more quickly. How then does a rotary power lawn mower manage to cut grass? How can it exert enough force on a leaf of grass to shear it off?Scissors are like a double-lever "Stem, Which of the Simple machines in Figure 9.23 and Figure 9.24 is most analogous to scissors? Figure 9.23 A nail puller is a lever with a large mechanical advantage. The external forces on the nail puller are represented by solid arrows. The force that the nail puller applies to the nail ( Fo ) is not a force on the nail puller. The reaction force the nail exerts back on the puller ( Fn ) is an external force and is equal and opposite to Fo. The perpendicular lever arms of the input and output forces are li and l0 Figure 9.24 (a) In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot IS the wheel's axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. (b) In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel's load) is less than the input force (from the hand nearest the load), because the Input is exerted closer to the pivot than is the output