R Figure P11.13

A baseball has a mass of 0.140 kg, and it is pitched towards home plate at a speed of 48.0 m/s. Assume that the ball is pitched horizontally and that the ball is hit horizontally back in the opposite direction. If the bat exerts an average force of 9100 N for 2.80 ms, what is the final speed of the ball in m/s?

James decides to use a ball tied to stiff rod to take out the Road Runner. He first needs to test this idea out on a small scale. A steel ball of mass 0.500 kg is fastened to a cord that is 70.0 cm long and fixed at the far end. The ball is then released when the cord is horizontal (see figure below). At the bottom of its path, the ball strikes a 2.50 kg steel block initially at rest on a frictionless surface. The collision is elastic. a)  Find speed of the ball just before impact. b)  Find the speed of the block just after impact.

An unfortunate astronaut loses his grip during a spacewalk and finds himself floating away from the space station, carrying only a rope and a bag of tools. First he tries to throw a rope to his fellow astronaut, but the rope is too short. In a last ditch effort, the astronaut throws his bag of tools in the direction of his motion, away from the space station. The astronaut has a mass of ma = 124 kg and the bag of tools has a mass of m = 13.0 kg. If the astronaut is moving away from the space station at Vj = 1.20 m/s initially, what is the minimum final speed vpf of the bag of tools with respect to the space station that will keep the astronaut from drifting away forever? Ub.f = m/s

An outlaw cuts loose a wagon with two boxes of gold, of total mass 300 kg, when the wagon is at rest 50 m up a 6.0° slope. The outlaw plans to have the wagon roll down the slope and across the level ground, and then fall into a canyon where his accomplices wait. But in a tree 40 m from the canyon’s cliff wait the Lone Ranger (mass 75.0 kg) and Tonto (mass 60.0 kg). They drop vertically into the wagon as it passes beneath them (Fig.). (a) If they require 5.0 s to grab the gold and jump out, will they make it before the wagon goes over the cliff? The wagon rolls with negligible friction. (b) When the two heroes drop into the wagon, is the kinetic energy of the system of heroes plus wagon conserved? If not, does it increase or decrease, and by how much?

QIIII: 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…

A 11 g bullet is fired into the bob of a ballistic pendulum of mass 1.3 kg. When the bob is at its maximum height, the strings make an angle of 60° with the vertical. The length of the pendulum is 2.3 m. Find the speed of the bullet. m/s еВook

We have a non-rotating space station in the shape of a long thin uniform rod of mass 2.60 x 10^6 kg and length 769 meters. Small probes of mass 8303 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 2888 m/s with respect to the launch points, which are each located 196 m from the center of the rod. After 11 pairs of probes have launched, how fast will the station be spinning?     3.70 rpm     7.71 rpm     4.63 rpm     10.02 rpm

A gun fires a 21-gram bullet on a 1.8 kg wooden block hanging vertically at the end of string (The other end of the string is attached to a ceiling). The bullet embeds in the block, which swings upward a height of H. The speed of the bullet when leaving the gun is 250 m/s. Find H.

The bar has mass M = 1.77 kilograms and length L = 1.25 meters. The puck has mass m = 0.433 kilograms and is initially moving at vi = 6.83 perpendicular to the bar. The puck collides with the bar at a location of b = 0.475 meters from the center of the bar. Note that the size of the puck is negligible compared to the length of the bar. Part (a) Calculate the center of mass speed (in m/s) of the puck-and-bar system just after the collision. Part (b) Calculate the angular speed (rad/s) about the center of mass of the puck-and-bar system just after the collision.