A block of mass m is moving with speed v along a horizontal surface when it collides with a uniform rod of mass 2m and length L attached at one end to a pivot. The surface and pivot have negligible friction. The rod is vertical when the block collides with the end of the rod. The block sticks to the rod, and the block-rod system rotates so that the end of the rod reaches a height h, as shown above. The total rotational inertia of the rod about the pivot is 2mL/3. Express answers in parts (a), (b), and (c) in terms of m, L, v, and physical constants as appropriate. c. Derive an expression for the mechanical energy dissipated during the collision.

A block of mass m is moving with speed v along a horizontal surface when it collides with a uniform rod of mass 2m and length L attached at one end to a pivot. The surface and pivot have negligible friction. The rod is vertical when the block collides with the end of the rod. The block sticks to the rod, and the block-rod system rotates so that the end of the rod reaches a height h, as shown above. The total rotational inertia of the rod about the pivot is 2mL/3. Express answers in parts (a), (b), and (c) in terms of m, L, v, and physical constants as appropriate. c. Derive an expression for the mechanical energy dissipated during the collision.

Similar questions

You are riding your bicycle down the street at a speed of 16 m/s. Your bicycle's frame has a mass of 6.0 kg, and each of its two wheels has mass 2.2 kg and radius 0.34 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules), taking into account both the translational and rotational motion?
Consider a person who is sitting on a frictionless rotating stool. The person initially has his arms outstretched and is rotating with an angular speed of 5.0 rad/s. He then pulls his arms close to his body, thus reducing his moment of inertia to 80% of the initial one. What is his final angular speed?
A flat uniform circular disk (radius = 6.22 m, mass=320 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 51.0-kg person, standing 2.32 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 3.00 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.
Block 1 with mass m1=502 kg rests on a horizontal ledge with negligible friction. This block is then attached to a string that passes over a pulley, and the other end of the string is attached to the hanging block 2 of mass m2=251 kg, as shown. The pulley is a uniform disk of radius 9.40 cm and mass 1.770 kg. Calculate the speed of block 2 after it is released from rest and falls a distance of 2.15 m. What is the angular speed of the pulley at the instant when block 2 has fallen a distance of 2.15 m?
A student sits on a rotating stoll holding two 8.0kg objects. When his arms are extended horizontally, the objects are 1.3m from the axis rotation and he rotated with an angular speed of 1.8rad/s. The moment of intertidal of the student plus stoll is 4.5kg•m^2 and is assumed to be constant. if the student pulls in the two objects horizontally to 0.50m from the rotation axis. What is the new angular speed in rad/s of the student? (3 sig fig)
A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.30 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 = 465 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 = 2mrvw. t N-m (b) Find the value of this torque at t= 465 s, just before the sliding block finishes its motion. N.m 2.52 (c) Find the power which the drive motor must…
A 26 g block hangs from a 350 g rotating solid disk, as shown below. If the radius of the disk is12 cm, what is the speed of the block after it has dropped 55 cm starting from rest? If a disk with radius5.0 cm is used instead, how does your answer change?
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?