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- A cat plays with a toy mouse suspended from a light string of length 1.25 m, rapidly batting the mouse so that it acquires a speed of 2.75 m/s while the string is still vertical. Use energy conservation to find the mouses maximum height above its original position. (Assume the string always remains taut.)A block is connected to a spring that is suspended from the ceiling. Assuming air resistance is ignored, describe the energy transformations that occur within die system consisting of the block, the Earth, and the spring when the block is set into vertical motion.Explain why it is easier to climb a mountain on a zigzag path rather than one straight up the side. Is your increase in gravitational potential energy the same in both cases? Is your energy consumption the same in both?
- A small block of mass m = 200 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P8.43). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point relative to point . (b) the kinetic energy of the block at point . (c) its speed at point B, and (d) its kinetic energy and the potential energy when the block is at point . Figure P8.43 Problems 43 and 44.A block of mass m = 5.00 kg is released from point and slides on the frictionless track shown in Figure P8.3. Determine (a) the blocks speed at points and and (b) the net work done by the gravitational force on the block as it moves from point to point . Figure P8.3Answer yes or no to each of the following questions. (a) Can an objectEarth system have kinetic energy and not gravitational potential energy? (b) Can it have gravitational potential energy and not kinetic energy? (c) Can it have both types of energy at the same moment? (d) Can it have neither?
- The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5.39a. If the spring is compressed a distance of 0.120 m and the gun fired vertically as shown, the gun can launch a 20.0-g projectile from rest to a maximum height of 20.0 m above the starting point of the projectile. Neglecting all resistive forces, (a) describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height, (b) determine the spring constant, and (c) find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure P5.39b. Figure P5.39A particle of mass m = 1.18 kg is attached between two identical springs on a frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in Figure P7.50. Show that the force exerted by the springs on the particle is F=2kx(1Lx2+L2)i (b) Show that the potential energy of the system is U(x)=kx2+2kL(Lx2+L2) (c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/m. (d) If the panicle is pulled 0.500 m to the right and then released, what is its speed when it reaches x = 0? Figure P7.50A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0 N directed at ail angle = 25 below the horizontal as shown in Figure P7.5. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block.
- A 5.00-kg block is set into motion up an inclined plane with an initial speed of i = 8.00 m/s (Fig. P7.21). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of = 30.0 to the horizontal. For this motion, determine (a) the change in the blocks kinetic energy, (b) the change in the potential energy of the block-Earth system, and (c) the friction force exerted on the block (assumed to be constant), (d) What is the coefficient of kinetic friction? Figure P7.21A roller-coaster car of mass 1.50 103 kg is initially at the top of a rise at point . It then moves 35.0 m at an angle of 50.0 below the horizontal to a lower point . (a) Find both the potential energy of the system when the car is at points and and the change in potential energy as the car moves from point to point , assuming y = 0 at point . (b) Repeat part (a), this time choosing y = 0 at point , which is another 15.0 m down the same slope from point .A small particle of mass m is pulled to the top of a friction less half-cylinder (of radius R) by a light cord that passes over the top of the cylinder as illustrated in Figure P7.15. (a) Assuming the particle moves at a constant speed, show that F = mg cos . Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times. (b) By directly integrating W=Fdr, find the work done in moving the particle at constant speed from the bottom to the top of the hall-cylinder. Figure P7.15