A hollow sphere of mass 2.6 kg and radius 2 cm starts to roll (without slipping) down an incline of height 0.5 m. At the bottom of the incline, the sphere makes a head-on and perfectly inelastic collision with a box of mass 5.4 kg and the two objects slide together accross the ground. The coefficient of kinetic friction between the objects and the ground is 0.4. Determine the following quantities (take g = 9.81 m/s^2); (a) Kinetic energy of the sphere at the bottom of the incline (before collision) (in joules) (b) The speed of the system of two objects right after the collision (m/s) Hint: during the collision, model the two objects as point-like particles (c) The distance that the system of two objects travels from the bottom of the incline until they stop (m) (Give your answers as numbers (without any units or percentage) with 3 significant figures Use dot () for decimal point)

two blocks, of mass m1 = 400 g and m2 = 600 g, areconnected by a massless cord that is wrapped around a uniform diskof mass M= 500 g and radius R=12.0 cm.The disk can rotate withoutfriction about a fixed horizontal axis through its center; the cordcannot slip on the disk.The system is released from rest. Find (a) themagnitude of the acceleration of the blocks, (b) the tension T1 in thecord at the left, and (c) the tension T2 in the cord at the right.

In the figure, the driver of a car on a horizontal road makes an emergency stop by applying the brakes so that all four wheels lock and skid along the road. The coefficient of kinetic friction between tires and road is 0.49. The separation between the front and rear axles is L = 4.2 m, and the center of mass of the car is located at distance d = 1.9 m behind the front axle and distance h = 1.2 m above the road. The car weighs 12 kN. Find the magnitude of (a) the braking acceleration of the car, (b) the normal force on each rear wheel, (c) the normal force on each front wheel, (d) the braking force on each rear wheel, and (e) the braking force on each front wheel. (Hint: Although the car is not in translational equilibrium, it is in rotational equilibrium.) L.

A skateboard of mass m rests on the top of a hemispheric dome of radius R. After giving the skateboard a small kick, imparting an initial speed of vo, it begins rolling down the dome. Let the angle 0 indicate the location of the skateboard as it rolls down the surface of the dome. R 1. Eventually, the skateboard will lose contact with the dome. Given m, R, vo, and g, find the angle 0. at which the skateboard loses contact. Express your answer symbolically (i.e. without numbers). Check your work. Suppose you choose m = 1.5 kg, vo = g = 9.81 m/s. In this case, your answer should evaluate to 0. = 34.2°. 4.5 m/s, R = 4.3 m, and 2. Given m, R, and g, determine the range of speeds for which it is impossible to remain in contact with the wall at all.