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You are attending a county fair with your friend from your physics class. While walking around the fairgrounds, you discover a new game of skill. A thin rod of mass M = 0.500 kg and length ℓ = 2.00 m hangs from a friction-free pivot at its upper end as shown in Figure P11.43. The front surface of the rod is covered with Velcro. You are to throw a Velcro-covered ball of mass m = 1.0 kg at the rod in an attempt to make it swing backward and rotate all the way across the top. The ball must stick to the rod at all times after striking it. If you cause the rod to rotate over the top position, you win a stuffed animal. Your friend volunteers to try his luck. He feels that the most torque would be applied to the rod by striking it at its lowest end. While he prepares to aim at the lowest point on the rod, you calculate how fast he must throw the ball to win the stuffed animal with this technique.
Figure P11.43
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Chapter 11 Solutions
Physics for Scientists and Engineers with Modern Physics
- You are attending a county fair with your friend from your physics class. While walking around the fairgrounds, you discover a new game of skill. A thin rod of mass M = 0.500 kg and length = 2.00 m hangs from a friction-free pivot at its upper end as shown in Figure P11.43. The front surface of the rod is covered with Velcro. You are to throw a Velcro-covered ball of mass m = 1.0 kg at the rod in an attempt to make it swing backward and rotate all the way across the top. The ball must stick to the rod at all times after striking it. If you cause the rod to rotate over the top position, you win a stuffed animal. Your friend volunteers to try his luck. He feels that the most torque would be applied to the rod by striking it at its lowest end. While he prepares to aim at the lowest point on the rod, you calculate how fast he must throw the ball to win the stuffed animal with this technique. Figure P11.43arrow_forwardFigure OQ10.8 shows a system of four particles joined by light, rigid rods. Assume a = b and M is larger than m. About which of the coordinate axes does the system have (i) the smallest and (ii) the largest moment of inertia? (a) the x axis (b) the y axis (c) the z axis. (d) The moment of inertia has the same small value for two axes. (e) The moment of inertia is the same for all three axes. Figure OQ10.8arrow_forwardA cam of mass M is in the shape of a circular disk of diameter 2R with an off-center circular hole of diameter R is mounted on a uniform cylindrical shaft whose diameter matches that of the hole (Fig. P1 3.78). a. What is the rotational inertia of the cam and shaft around the axis of the shaft? b. What is the rotational kinetic energy of the cam and shaft if the system rotates with angular speed around this axis?arrow_forward
- In Figure P10.40, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2 = 0.850 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table. (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. (b) Find the angular speed of the pulley at the same moment. Figure P10.40arrow_forwardA wheel of inner radius r1 = 15.0 cm and outer radius r2 = 35.0 cm shown in Figure P12.43 is free to rotate about the axle through the origin O. What is the magnitude of the net torque on the wheel due to the three forces shown? FIGURE P12.43arrow_forwardA projectile of mass m moves to the right with a speed vi (Fig. P10.81a). The projectile strikes and sticks to the end of a stationary rod of mass M, length d, pivoted about a frictionless axle perpendicular to the page through O (Fig. P10.81b). We wish to find the fractional change of kinetic energy in the system due to the collision. (a) What is the appropriate analysis model to describe the projectile and the rod? (b) What is the angular momentum of the system before the collision about an axis through O? (c) What is the moment of inertia of the system about an axis through O after the projectile sticks to the rod? (d) If the angular speed of the system after the collision is , what is the angular momentum of the system after the collision? (e) Find the angular speed after the collision in terms of the given quantities. (f) What is the kinetic energy of the system before the collision? (g) What is the kinetic energy of the system after the collision? (h) Determine the fractional change of kinetic energy due to the collision. Figure P10.81arrow_forward
- A bowling ball (which we can regard as a uniform sphere) has a mass of 7.26 kg and a radius of 0.216 m. A baseball has a mass of 0.145 kg. If you connect these two balls with a lightweight rod, what must be the distance between the center of the bowling ball and the center of the baseball so that the system of the two balls and the rod will balance at the point where the rod touches the surface of the bowling ball?arrow_forwardIn the figure, a small 0.473 kg block slides down a frictionless surface through height h = 1.06 m and then sticks to a uniform vertical rod of mass M = 0.946 kg and length d = 2.74 m. The rod pivots about point O through angle before momentarily stopping. Find 0. A Number Units harrow_forwardReview. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ = 30.0° as shown in Figure P10.16. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. Determine (b) the acceleration of the two blocks and (c) the tensions in the string on both sides of the pulley. Figure P10.16arrow_forward
- An entertainer has perched a 281 g spinning plate on top of a pole. The plate has a radius of 12 cm and is spinning at 68 rpm. A 277 g cup with a moment of inertia of 0.005 kg•m2 is then placed in the center of the plate. The cup beings to spin with the plate. Once the two objects are spinning together, what rate of spin, in revolutions per minute do they have? Answer to one decimal placearrow_forwarda small 0.383 kg block slides down a frictionless surface through height h = 0.752 m and then sticks to a uniform vertical rod of mass M = 0.766 kg and length d = 2.34 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ.arrow_forwardConsider the following figure. A strand has one end tied to a wall, extends across a small fixed pulley, and the other end is tied to a hanging object. M The total length of the strand is L = 7.00 m, the mass of the strand is m = 9.00 g, the mass of the hanging object is M = 5.50 kg, and the pulley is a fixed a distance d = 4.00 m from the wall. You pluck the strand between the wall and the pulley and it starts to vibrate. What is the fundamental frequency (in Hz) of its vibration?arrow_forward
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