Concept explainers
CP Two uniform solid spheres, each with mass M = 0.800 kg and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant k = 160 N/m has one end attached to the wall and the other end attached to a frictionless ring that passes over the rod at the center of mass of the spheres, which is midway between the centers of the two spheres. The spheres are each pulled the same distance from the wall, stretching the spring, and released. There is sufficient friction between the tabletop and the spheres for the spheres to roll without slipping as they move back and forth on the end of the spring. Show that the motion of the center of mass of the spheres is simple harmonic and calculate the period.
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
University Physics (14th Edition)
Additional Science Textbook Solutions
College Physics: A Strategic Approach (4th Edition)
The Cosmic Perspective Fundamentals (2nd Edition)
Essential University Physics: Volume 2 (3rd Edition)
Modern Physics
Introduction to Electrodynamics
Applied Physics (11th Edition)
- A giant swing at an amusement park consists of a 365-kg uniform arm 10.0 m long, with two seats of negligible mass connected at the lower end of the arm (Fig. P8.53). (a) How far from the upper end is the center of mass of the arm? (b) The gravitational potential energy of the arm is the same as if all its mass were concentrated at the center of mass. If the arm is raised through a 45.0 angle, find the gravitational potential energy, where the zero level is taken to be 10.0 m below the axis, (c) The arm drops from rest from the position described in part (b). Find the gravitational potential energy of the system when it reaches the vertical orientation. (d) Find the speed of the seats at the bottom of the swing.arrow_forwardA massless spring of constant k = 78.4 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance d, as in Figure P7.74. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5 m. The entire track and the loop-the-loop are frictionless, except for the section of track between points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is k = 0.30 and that the length of AB is 2.5 m, determine the minimum compression d of the spring that enables the block to just make it through the loop-the-loop at point C. Hint: The force exerted by the track on the block will be zero if the block barely makes it through the loop-the-loop. Figure P7.74arrow_forwardA arrow of mass 0.01 kg moving horizontal suddenly strikes a block of wood of mass 8.6 kg that is suspended by a light string, like a pendulum. The arrow passes through the wood, then the wood swings upward and momentarily stops when the string is horizontal. The length of the string is 2.0 cm. How long did it take the arrow to go through the wood if the friction force between the bullies and the wood is 100 N?arrow_forward
- The ball B shown in the figure has a mass of 1.5 kg and is suspended from the ceiling by a 1 m long elastic cord. If the cord is stretched downward 0.25 m and the ball is released from rest, determine how far the cord stretches after the ball rebounds from the ceiling. The stiffness of the cord is k = 800 N/m and the coefficient of restitution between the ball and ceiling is e = 0.8. The ball makes a central impact with the ceiling.arrow_forwardYou are working with a team that is designing a new roller coaster-type amusement park ride for a major theme park. You are present for the testing of the ride, in which an empty 190 kg car is sent along the entire ride. Near the end of the ride, the car is at near rest at the top of a 102 m tall track. It then enters a final section, rolling down an undulating hill to ground level. The total length of track for this final section from the top to the ground is 250 m. For the first 230 m, a constant friction force of 400 N acts from computer-controlled brakes. For the last 20 m, which is horizontal at ground level, the computer increases the friction force to a value required for the speed to be reduced to zero just as the car arrives at the point on the track at which the passengers exit. (a) Determine the required constant friction force (in N) for the last 20 m for the empty test car. N (b) Find the highest speed (in m/s) reached by the car during the final section of track length…arrow_forwardYou are working with a team that is designing a new roller coaster-type amusement park ride for a major theme park. You are present for the testing of the ride, in which an empty 190 kg car is sent along the entire ride. Near the end of the ride, the car is at near rest at the top of a 102 m tall track. It then enters a final section, rolling down an undulating hill to ground level. The total length of track for this final section from the top to the ground is 250 m. For the first 230 m, a constant friction force of 400 N acts from computer-controlled brakes. For the last 20 m, which is horizontal at ground level, the computer increases the friction force to a value required for the speed to be reduced to zero just as the car arrives at the point on the track at which the passengers exit. (a) Determine the required constant friction force (in N) for the last 20 m for the empty test car. 4905.89 N (b) Find the highest speed (in m/s) reached by the car during the final section of track…arrow_forward
- You are advising a fellow student who wants to learn to perform multiple flips on the trampoline. You have him bounce vertically as high as he can, keeping his body perfectly straight and vertical. You determine that he can raise his center of mass by a distance of h = 6.00 m above its level when he initiates the jump. He can do a single flip by bouncing gently, throwing his arms forward over his head, and tucking his body. You use your smartphone to make a video of him doing a single flip. Based on analysis of this video, you determine that his moment of inertia is Istraight = 26.7 kg . m2 when his body is straight and Ituck = 5.62 kg . m2 in the tuck position. You suggest that he keep his body in the straight position for Δt, = 0.400 s after leaving the trampoline surface and then immediately go into a tuckposition. As he lands, he should straighten his body out Δt, = 0.400 s before he lands. From analysis of the video recording, you determine that throwing his arms forward causes…arrow_forward1. An inventor patents a "golf machine". It consists of a "golf club" which is really a pendulum of length L = 2 (m), with a massles string and a mass M = 30 (kg) on the end. By pulling back on the pendulum until the string makes an angle 0= 10° from the vertical, and then releasing it from rest, the golf club strikes the "golf ball" exactly horizontally. The golf ball is a mass m = 0.1 (kg) that rests on a platform which is h = 20 (cm) above the horizontal ground. Assume that all collisions are elastic and all masses are point masses. Finally you should ignore air resistance but gravity acts down as usual. L %3D M) m h How far does m travel horizontally (before it hits the ground)? |How long does it take from the time M is released from rest to the time it strikes m? [Hint: think pendulum]arrow_forwardConsider a flat-bed truck whose mass, including its contents, is supported equally by its four tires. Assume the truck has four-wheel drive, so the drive train translates the power of the motor equally to all four wheels. The mass of just the truck is m2, and the coefficient of static friction between the tires and the road is μs. A metal crate of mass m1 sits on the flat, horizontal, wooden bed of the truck, and μk is the coefficient of kinetic friction between the bed and the metal crate. Part (b) Assume the crate slips in the bed of the truck as the truck is accelerating. Write an expression for the maximum possible acceleration of the truck so that its tires don't slip. The picture is a hint that they providedarrow_forward
- A metal cannonball of mass m rests next to a tree at the very edge of a cliff 36.0 m above the surface of the ocean. In an effort to knock the cannonball off the cliff, some children tie one end of a rope around a stone of mass 80.0 kg and the other end to a tree limb just above the cannonball. They tighten the rope so that the stone just clears the ground and hangs next to the cannonball. The children manage to swing the stone back until it is held at rest 1.80 m above the ground. The children release the stone, which then swings down and makes a head-on, elastic collision with the cannonball, projecting it horizontally off the cliff. The cannonball lands in the ocean a horizontal distance R away from its initial position. (a) Find the horizontal component R of the cannonball’s displacement as it depends on m. (b) What is the maximum possible value for R, and (c) to what value of m does it correspond? (d) For the stone– cannonball–Earth system, is mechanical energy conserved…arrow_forwardQIIII: A thin uniform rod of mass Mr and length L is suspended from the ceiling and mounted on a horizontal frictionless axle at the top. The rod is initially at rest in its equilibrium position when a ball of play dough, of mass mb, strikes the rod at its lower end and remains stuck to the rod. The sticky ball is thrown with an initial speed v0 at a 60 degree angle from the horizontal direction, and strikes the rod when it reaches the top of its trajectory, as shown in Fig.4. The acceleration due to gravity has magnitude g and air resistance is negligible. a. Determine the velocity of the ball of play dough right before it sticks to the rod. Use the x- y coordinate system defined in Fig.4. b. Determine the angular velocity of the rod+ball system right after the collision. Take counterclockwise as positive. c. - Establish the differential equation satisfied by the rod+ball system after the collision and determine the angular frequency of the system. You may assume that the small…arrow_forwardA thin rod of length L = 3.00 m with variable mass density (x) = 3.00x² kg/m lies on the x-axis with one end at the origin. Where on the %3D %3D X-axis is the center of mass of this rod? {note this is a variable mass density} O 2.50 m O 1.50 m O 2.25 m O 2.70 m O 1.88 m 吕0 000 DII F1 F2 F3 F4 F5 F 6 F7 F8 F9 # $4 & 4 7 Q E A D K 00 LLarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning