A bullet of mass m and speed v is fired at, hits, and passes completely through a pendulum bob of mass M = 2m on the end of a stiff rod of negligible mass and length L. The bullet emerges with a speed of v/2 and the pendulum bob just makes it over the top of the trajectory without falling backward in its circular path. Determine an expression (in terms of g and L only) for the minimum initial speed the bullet must have in order for the pendulum bob to just barely swing through a complete vertical circle.

A ball of mass 0.45 kg is fired with velocity 120 m/s into the barrel of a spring gun of mass 2.0 kg initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. No energy is lost to friction. What fraction of the ball's initial kinetic energy is stored in the spring?

A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.7 kg and 2.5 kg, and the length of the wire is 1.36 m. Find the velocity (magnitude and direction) of the ball just after the collision.

You fire a bullet at a ballistic pendulum. The large block of wood has a mass M2 = 3 kg, and the bullet has a mass of m1 = 35 g. The bullet completely penetrates the wood and emerges with a speed of vf = 80 m/s. The wood, as part of a pendulum, swings up to a maximum height of h = 11 cm. (a) Determine the speed of the block of wood after the bullet has passed through it. m/s(b) What is the speed of the bullet just before it hits the block? m/s(c) If the pendulum length is 0.8 m, what angle does the pendulum string make with the vertical when it reaches the top of its swing? degrees

A uniform chain of mass m and length l is lying on a slippery table. When one-quarter of its length hangs over the edge, the chain begins to slip off. How fast is it moving when the last bit of it slips off the table? Ignore friction.

Apollo and Artemis are playing on the teeter‑totter in their school's playground. They both have approximately the same mass. They are sitting on either side of the teeter‑totter at about the same distance from the teeter‑totter's pivot point. The teeter‑totter is going up and down and they are having a great time! Mercury, the new kid in school, wanders by. Since they are very friendly kids, Apollo and Artemis ask Mercury to join them. Mercury joins Apollo on his side of the teeter‑totter and sits next to him. What should Artemis do in order to keep the fun going? 1)Move farther from the teeter‑totter's pivot point in order to balance out the new smaller torque provided by Mercury and Apollo. 2)Move closer to the teeter‑totter's pivot point in order to balance out the new larger torque provided by Mercury and Apollo. 3)Move farther from the teeter‑totter's pivot point in order to balance out the new larger torque provided by Mercury and Apollo. 4)Move closer to the…

In the figure, block 2 (mass 1.10 kg) is at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 216 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 1.80 kg), traveling at speed v1 = 5.90 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring compressed?

A small ball of mass mb = 0.050 kg is projected into a pendulum of mass Mp = 0.200 kg in a ballistic pendulum experiment. How fast does the ball need to go in order to get the pendulum to swing up to a height of h = 0.25 m above its original position?     2.21 m/s     0.111 m/s     11.1 m/s     0.553 m/s

. What is the initial kinetic energy in joules of the bullet in problem 1? What is the final kinetic energy of the combined bullet/pendulum?

Two identical blocks of mass M = 2.60 kg each are initially at rest on a smooth, horizontal table. A bullet of very small mass m = 20 g (m << M) is fired at a high speed v. = 120 m/s towards the first block. It quickly exits the first block at a reduced speed of 0.40 v, then strikes the second block, quickly getting embedded inside of it. All the motion happens on the x-axis. (a) find the speeds of the two blocks after their encounters with the bullet. (b) Now the first block catches up with the second one and collides with it. They got stuck together afterward and move forward. Find their common speed V after the collision. (c) The two blocks now hit a light spring of spring constant k = 35 N/m mounted on the wall. How far is the spring compressed before the blocks reach a momentary stop?