Chapter 19, Problem 72P

A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.55 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 360 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by t = 2mrvw. t N.m (b) Find the value of this torque at t = 360 s, just before the sliding block finishes its motion. N.m (c) Find the power which the drive motor must…

(a) A planet is in an elliptical orbit around a distant star. At its closest approach, the planet is 0.670 AU from the star and has a speed of 54.0 km/s. When the planet is at its farthest distance from the star of 36.0 AU, what is its speed (in km/s)? (1 AU is the average distance from the Earth to the Sun and is equal to 1.496 × 1011 m. You may assume that other planets and smaller objects in the star system exert negligible forces on the planet.) km/s (b) What If? A comet is in a highly elliptical orbit around the same star. The comet's greatest distance from the star is 25,700 times larger than its closest distance to the star. The comet's speed at its greatest distance is 2.40 x 10-2 km/s. What is the speed (in km/s) of the comet at its closest approach? km/s

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 = 0.505 kg and length = 2.70 m hangs from a friction-free pivot at its upper end as shown in the figure. Pivot Velcro M Incoming Velcro-covered ball m The front surface of the rod is covered with Velcro. You are to throw a Velcro-covered ball of mass m = 1.25 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 (that is, rotate 180° opposite of its starting 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…