Two objects with masses of 2.30 kg and 4.85 kg are connected by a light string that passes over a light frictionless pulley to form an Atwood machine, as in Figure 5.14a. ↑ M Į Figure 5.14a (a) Determine the tension in the string. N (b) Determine the acceleration of each object. m/s² upwards (2.30 kg mass) m/s2 downwards (4.85 kg mass) (c) Determine the distance each object will move in the first second of motion if they start from rest. m (2.30 kg mass) m (4.85 kg mass)

A baseball catcher is performing a stunt for a television commercial. He will catch a baseball (mass 145 g) dropped from a height of 60.0 m above his glove. His glove stops the ball in 0.0100 s. What is the force exerted by his glove on the ball?

A makeshift sign hangs by a wire that is extended over an ideal pulley and is wrapped around a large potted plant on the roof as shown in Figure P6.10. When first set up by the shopkeeper on a sunny and dry day, the sign and the pot are in equilibrium. Is it possible that the sign falls to the ground during a rainstorm while still remaining connected to the pot? What would have to be true for that to be possible? FIGURE P6.10 Problems 10 and 11.

A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 30.0 kg by a massless string that passes over a light, frictionless pulley. The 30.0-kg block is connected to a spring that has negligible mass and a force constant of k = 250 N/m as shown in Figure P7.73. The spring is un-stretched when the system is as shown in the figure, and the incline is frictionless. The 20.0-kg block is pulled a distance h = 20.0 cm down the incline of angle = 40.0 (so that the 30.0-kg block is 40.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0-kg block is 20.0 cm above the floor (that is, when the spring is unstretched). Figure P7.73

In building a house, carpenters use nails from a large box. The box is suspended from a spring twice dining the day to measure the usage of nails. At the beginning of the day, the spring stretches 50 cm. At the end of the day, the spring stretches 30 cm. What fraction or percentages of the nails have been used?

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 P5.48

In the situation described in Problem 45 and Figure P4.45, the masses of the rope, spring balance, and pulley are negligible. Nicks feet are not touching the ground. (a) Assume Nick is momentarily at rest when he stops pulling down on the rope and passes the end of the rope to another child, of weight 440 N, who is standing on the ground next to him. The rope does not break. Describe the ensuing motion. (b) Instead, assume Nick is momentarily at rest when he ties the end of the rope to a strong hook projecting from the tree trunk. Explain why this action can make the rope break. Figure P4.45 Problems 45 and 46.

An aluminum block of mass m1 = 2.00 kg and a copper block of mass m2 = 6.00 kg are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in Figure P5.46, where = 30.0. (a) When they are released from rest, will they start to move? If they do, determine (b) their acceleration and (c) the tension in the string. If they do not move, determine (d) the sum of the magnitudes of the forces of friction acting on the blocks. Figure P5.46

Figure P5.47 shows a photo of a swing ride at an amusement park. The structure consists of a horizontal, rotating, circular platform of diameter D from which seats of mass m are suspended at the end of massless chains of length d. When the system rotates at constant speed, the chains swing outward and make an angle with the vertical. Consider such a ride with the following parameters: D = 8.00 m, d = 2.50 m, m = 10.0 kg, and = 28.0. (a) What is the speed of each seat? (b) Draw a diagram of forces acting on a 40.0-kg child riding in a seat and (c) find the tension in the chain. Figure P5.47

What can you say about the velocity of a moving body that in dynamic equilibrium? Draw a sketch of such a body using clearly labeled arrows to represent all external forces on the body.