Two solld, unlform dlsks are placed on a fiictionless lable. Disk 1 has a radius of R and is initially at rest. Disk 2 has a radius of 3/2 R and is initially moving with at speed of vo. Disk 2 makes a glancing collision with Disk 1, and the disks stick together. The disks are made of the same material. R2=3/2 R a. What is the center of mass speed for the combined Disk 1, Disk 2 system after the collision? Express your answer in terms of Vo. R,= R
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- Three solid, uniform boxes are aligned as in the figure below. Find the x- and y-coordinates (in m) of the center of mass of the three boxes, measured from the bottom left corner of box A. (Consider the three-box system.) X HINT cm Y cm = Origin Need Help? E E m Read It 0.300 m A 0.750 kg Watch It 0.350 m B 1.00 kg 0.150 m с 0.650 kg 0.418 mLook for the center of mass of a uniform solid right circular cone using M as mass, R as radius and H as Height.In the figure, two identical containers of sugar are connected by a cord that passes over a frictionless pulley. The cord and pulley have negligible mass, each container and its sugar together have a mass of 740 g, the centers of the containers are separated by 55 mm, and the containers are held fixed at the same height. What is the horizontal distance between the center of container 1 and the center of mass of the two-container system (a) initially and (b) after 20 g of sugar is transferred from container 1 to container 2? After the transfer and after the containers are released, (c) what is the acceleration of the center of mass, taking up to be the positive direction? (a) Number 27.5 (b) Number 28.24 (c) Number i 0.5297 Units Units Units mm mm m/s^2 2
- Four identical train cars are on a track. Three of the cars are initially attached to eachother and rolling toward the fourth car that is moving in the opposite direction. What is thefinal speed of the cars right after they collide and stick together? Assume that the three cars areinitially moving at 12.3 m/s and the single car is initially moving at 1.6 m/s.Three solid, uniform boxes are aligned as in the figure below. Find the x- and y-coordinates (in m) of the center of mass of the three boxes, measured from the bottom left corner of box A. (Consider the three-box system.) HINT Xcm Y cm = Origin 0.300 m m m A 0.700 kg 0.350 m B 1.00 kg 0.150 m 0.450 kg L. 0.418 mHockey puck B rests on a frictionless ice surface, and is struck by a second A disc, which was originally moving east to 40.0 m / s. After the collision, disk A moves at 30.0 degrees while disk Disk B acquires speed and moves in the direction 45.0 degrees below the horizontal. Assume that the two discs have the same mass. Calculate the speed of each disc after the collision.
- A thin wire has mass m and length L. It is bent into a semicircular shape. The wire is placed in the x-y plane such that it is symmetrical across the x-axis, and the two end points of the wire are placed at x = 0. 1. Write an expression for the center of mass XCM of the wire about the x-axis. 2. Write an expression for the center of mass YCM of the wire about the y-axis. 3. The mass of the wire is 47 g and the length of the wire is 2.4 m. Determine the x-coordinate for the center of mass in meters.In the figure, two identical containers of sugar are connected by a cord that passes over a frictionless pulley. The cord and pulley have negligible mass, each container and its sugar together have a mass of 620 g, the centers of the containers are separated by 55 mm, and the containers are held fixed at the same height. What is the horizontal distance between the center of container 1 and the center of mass of the two-container system (a) initially and (b) after 38 g of sugar is transferred from container 1 to container 2? After the transfer and after the containers are released, (c) what is the acceleration of the center of mass, taking up to be the positive direction? (a) Number i (b) Number i BY (c) Number i 2 Units Units Units < <A 3 kg plank is 0.6 m in length and has its center of mass at the geometrical center. Masses of 1 kg an 3 kg are attached at opposite ends of the plank. Find the center of mass of the whole system. 1 kg 3 kg Where is the COM? 3 kg
- A gymnast with a mass of 55 kg flipped in the air and achieved a maximum angular velocity of 445 degrees/sec just before landing from the flip. a) What is the magnitude of the angular impulse in kg*m2/s exerted by the floor on the gymnast when they stuck the landing and came to a complete stop, if they had a radius of gyration of 0.75 meters throughout the landing and their initial angular velocity just as they hit the floor was equal to the maximum angular velocity of 445 degrees/sec?A 6.45 kg bowling ball moving at 10.0 m/s collides with a 1.60 kg bowling pin, scattering it with a speed of 8.00 m/s and at an angle of 29.5° with respect to the initial direction of the bowling ball. Calculate the final velocity (magnitude in m/s and direction in degrees counterclockwise from the original direction) of the bowling ball. Ignoring rotation, what was the original kinetic energy in joules of the bowling ball before the collision? Ignoring rotation, what is the final kinetic energy in joules of the system of the bowling ball and pin after the collision?A 0.00600 kg bullet traveling horizontally with speed 1.00 103 m/s strikes a 16.0 kg door, embedding itself 11.9 cm from the side opposite the hinges as shown in the figure below. The 1.00 m wide door is free to swing on its frictionless hinges. Imagine that the door is hanging vertically downward, hinged at the top, so that the figure is a side view of the door and bullet during the collision. What is the maximum height (in cm) that the bottom of the door will reach after the collision?