A flat hockey puck of mass M is rotating in a circle of radius R on a frictionless air hockey table. It is held in motion by a massless cord which is connected to a dangling mass m through a small hole. Show that the speed of the puck is given by v = /mgR/M. M. TR

Spheres A (mass 0.040 kg), B (mass 0.060 kg) and C (mass 0.080 kg) are approaching the origin as they slide on a frictionless air table. The initial velocities of A and B are v₁ = 1.60 m/s in the negative x direction and VB = 0.90 m/s at an angle 08 = 60°, as shown. All three spheres arrive at the origin at the same time and stick together. After the collision, the masses move at a speed of 0.50 m/s in the -x direction. UC y OB B UB VA A X C a. What is the x-component of the initial velocity of C? b. What is the y-component of the initial velocity of C? c. Calculate the change in mechanical energy of the collision. d. What type of collision is this? Explain.

Silid or to god o An object of mass m₁ = 4.00 kg is tied to an object of mass m2 = 4.00 kg with String 1 of length = 0.500 m. The combination is swung in a vertical circular path on a second string, String 2, of length = = 0.500 m. During the motion, the two strings are always collinear as shown in the figure. At the top of its motion, m2 is traveling at v = 4.80 m/s. Take the radial axis positive downward. (a) ( each mass. (b) What is the tension in String 1 at this instant? What is the tension in String 2 at (c) Draw the free body diagram of this instant? Which string will break first if the combination is rotated faster and faster? d) 1 m1 String 1 M DOVO dito 00101 String 2

Consider as a system the Sun with Mars in a circular orbit around it. Find the magnitude of the change in the velocity of the Sun relative to the center of mass of the system during the time Mars completes half an orbit. Assume the mass of the Sun is 5.68 x 1029 kg, the mass of Mars is 6.42 x 1023 kg, its period is 5.94 x 107 s, and the radius of its orbit is 2.28 x 10¹¹ m. Ignore the influence of other celestial objects. 19.4 x m/s