A wad of sticky clay with mass mand velocity v, is fired at a solid cylinder of mass Mand radius R (Fig. Pl1.29). The cyl- inder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a dis- tance d< Rfrom the center. (a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. (b) Is the mechanical energy of the clay- cylinder system constant in this process? Explain your answer. (c) Is the momentum of the clay-cylinder system constant in this process? Explain your answer. M R d Figure P11.29

A wad of sticky clay with mass mand velocity v, is fired at a solid cylinder of mass Mand radius R (Fig. Pl1.29). The cyl- inder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a dis- tance d< Rfrom the center. (a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. (b) Is the mechanical energy of the clay- cylinder system constant in this process? Explain your answer. (c) Is the momentum of the clay-cylinder system constant in this process? Explain your answer. M R d Figure P11.29

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

In the figure below, the disk, of mass 440 g and radius 3.5 cm, is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 270 g and radius 2.3 cm, is initially not rotating. It drops freely down onto the lower dis, and frictional forces bring the two disk to a common rotational speed. Find (a) that common speed and (b) the fraction of the initial kinetic energy lost to friction.
A playground merry-go-round with an axis at the center (radius R = 1.5 m and rotational inertia | = 1.33 x 103 kgm²) is initially rotating at angular velocity wo = 1.1 rad/s (counter-clockwise). A girl of mass m = 39 kg is running at speed vo = 3.3 m/s in a direction tangent to the disk of the merry-go-round, intending to jump on to the point labeled with the green "x" (she is indicated by the purple circle in the figure). What is the angular momentum of the girl relative to the rotation axis of the merry-go-round? Your answer should be in kgm²/s, but enter only the numerical part in the box. R Wo
A solid, horizontal cylinder of mass 10.0 kg and radius 1.00 mrotates with an angular speed of 7.00 rad/s about a fixedvertical axis through its center. A 0.250-kg piece of putty isdropped vertically onto the cylinder at a point 0.900 m fromthe center of rotation and sticks to the cylinder. Determinethe final angular speed of the system.
A disk of mass M is spinning freely at 4.77 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. (a)What is the angular speed of the new system (in rad/s)? (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s).
A solid disk rotates in the horizontal plane at an angular velocity of 4.20 × 10-2 rad/s with respect to an axisperpendicular to the disk at its center. The moment of inertia of the disk is 0.14 kg.m2. From above, sand is droppedstraight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis.The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?
A wad of sticky clay with mass m and velocity vi is fired at a solid cylinder of mass M and radius R. The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d < R from the center. (a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. (b) Is mechanical energy of the clay–cylinder system conserved in this process?
Someone frequently throws a tennis ball for their dog to chase.Throughout the throwing motion, the angular velocity of their arm is 6.7radians/s, and the radius of rotation of the ball is 63.0 cm.One day they decide to test out a ball-throwing tool which effectivelyextends the radius of rotation by an extra 36 cm. Assuming all othervariables are equal, how much faster (in m/s) can they throw the ballwhen they use the launcher compared to when they don't?Express your answer to 2 decimals, and don't include units+. Please type answer not write by hend
A string is wrapped severaltimes around the rim of a small hoopwith radius 8.00 cm and mass 0.180 kg.The free end of the string is held inplace and the hoop is released from rest. After the hoop hasdescended75.0 cm, calculate (a) theangular speed of the rotating hoop and(b) the speed of its center.
A disk of radius R and mass M has initial angular velocity ωi. It is flat on a horizontal surface and friction is present. The center of mass speed is zero (always) in this problem. Find the time it takes for the disk to stop spinning.
A massless, frictionless merry-go-round of radius R has one child of mass M sitting on the outer edge and is spinning with angular velocity ωi. If the child walks towards the center until she is 0.50R from the center, by what factor does the angular velocity increase? (i.e. solve for F where ωf=Fωi)
A person of mass m = 75 kg stands in the center of a large rotating disk with radius R = 5.0 m and total mass M. The rotates without friction and without any external torque, initially at an angular velocity of w. The moment of inertia of a disk is MR. Assume that the person can be approximated as point-like, i.e. the angular momentum is r x p. The person then walks radially outward. (a) What is the angular momentum of the system (person + disk) as a function of the person's radius, r, from the center? Write it in terms of m, M, R, and w. (b) If the disk is initially rotating at wo and it slows to wp =0.8 rad/s when the person is at the very edge, what is the mass of the disk? 1.1 rad/s when the person is in the exact center, (c) What is the rotational kinetic energy of the system before and after the person walks to the edge?
A uniform disk of mass 2.00m and radius 6.00r can rotate freely about its fixed center like a merry-go-round. A smaller uniform disk of mass mand radius r lies on top of the larger disk, concentric with it. Initially the two disks rotate together with an angular velocity of 26.6 rad/s. Then a slight disturbance causes the smaller disk to slide outward across the larger disk, until the outer edge of the smaller disk catches on the outer edge of the larger disk. Afterward, the two disks again rotate together (without further sliding). (a) What then is their angular velocity about the center of the larger disk? (b) What is the ratio K/Ko of the new kinetic energy of the two-disk system to the system's initial kinetic energy?