A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend spins the front wheel, of radius 0.381 m, and observes that drops of water fly off tangentially in an upward direction when the drops are at the same level as the center of the wheel. She measures the height reached by drops moving vertically (Fig. P10.74 on page 332). A drop that breaks loose from the tire on one turn rises h = 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The height to which the drops rise decreases because the angular speed of the wheel decreases. From this information, determine the magnitude of the average angular acceleration of the wheel.

Review. Consider the system shown in Figure P10.36 with m1 = 20.0 kg, m2 = 12.5 kg, R = 0.200 m, and the mass of the pulley M = 5.00 kg. Object m2 is resting on the floor, and object m1 is 4.00 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light, does not stretch, and does not slip on the pulley. (a) Calculate the time interval required for m1 to hit the floor. (b) How would your answer change if the pulley were massless?

An elevator system in a tall building consists of a 800-kg car and a 950-kg counterweight joined by a light cable of constant length that passers over a pulley of mass 280 kg. The pulley, called a sheave, is a solid cylinder of radius 0.700 m turning on a horizontal axle. The cable does not slip on the sheave. A number n of people, each of mass 80.0 kg, are riding in the elevator car, moving upward at 3.00 m/s and approaching the floor where the car should stop. As an energy-conservation measure, a computer disconnects the elevator motor at just the right moment so that t he sheavecarcounterweight system then coasts freely without friction and comes to rest at the floor desired. There it is caught by a simple latch rather than by a massive brake. (a) Determine the distance d the car coasts upward as a function of n. Evaluate the distance for (b) n = 2, (c) n = 12, and (d) n = 0. (e) For what integer values of n does the expression in part (a) apply? (f) Explain your answer to part (e). (g) If an infinite number of people could fit on the elevator, what is the value of d?

Children playing pirates have suspended a uniform wooden plank with mass 15.0 kg and length 2.50 m as shown in Figure P14.27. What is the tension in each of the three ropes when Sophia, with a mass of 23.0 kg, is made to walk the plank and is 1.50 m from reaching the end of the plank? FIGURE P14.27

The puck in Figure P11.46 has a mass of 0.120 kg. The distance of the puck from the center of rotation is originally 40.0 cm, and the puck is sliding with a speed of 80.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Suggestion: Consider the change of kinetic energy.) Figure P11.46

To develop muscle tone, a woman lifts a 2.00-kg weight held in her hand. She uses her biceps muscle to flex the lower arm through an angle of 60.0°. (a) What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.250kg-m2 and the net force she exerts is 750 N at an effective perpendicular lever arm of 2.00 cm? (b) How much work does she do?

Figure P10.31 shows a claw hammer being used to pull a nail out of a horizontal board. The mass of the hammer is 1.00 kg. A force of 150 N is exerted horizontally as shown, and the nail does not yet move relative to the board. Find (a) the force exerted by the hammer claws on the nail and (b) the force exerted by the surface on the point of contact with the hammer head. Assume the force the hammer exerts on the nail is parallel to the nail. Figure P10.31

Review. The mass of a car is 1 500 kg. The shape of the cars body is such that its aerodynamic drag coefficient is D = 0.330 and its frontal area is 2.50 m2. Assuming the drag force is proportional to 2 and ignoring other sources of friction, calculate the power required to maintain a speed of 100 km/h as the car climbs a long hill sloping at 3.20.

BIO When a gymnast performing on the rings executes the iron cross, he maintains the position at rest shown in Figure P10.85a. In this maneuver, the gymnasts feet (not shown) are off the floor. The primary muscles involved in supporting this position are the latissimus dorsi (lats) and the pectoralis major (pecs). One of the rings exerts an upward fore Fh on a hand as shown in Figure P10.85b. The force Fs is exerted by the shoulder joint on the arm. The latissimus dorsi and pectoralis major muscles exert a total force Fm on the arm. (a) Using the information in the figure, find the magnitude of the force Fm. (b) Suppose an athlete in training cannot perform the iron cross but can hold a position similar to the figure in which the arms make a 45 angle with the horizontal rather than being horizontal. Why is this position easier for the athlete? Figure P10.85