As seen in the first part of the diagram above, a 0.50kg thin rod of 2.0m in length is suspended vertically 0.25m from its top end by a nail to a surface. A 0.20kg ball of clay is propelled at the rod at 3.75 m/s, and it sticks to the rod, causing it to swing. If the clay can be consider a point mass at the end of the rod, what is the period of the system's oscillation?

A ball of radius R=25cm and mass M=0.43kg is compressed against a spring of spring constant k=316N/m by an amount x=49.7cm measured from the equilibrium of the spring as shown in the figure below. The system is released from rest and when the spring reaches its equilibrium position the ball loses contact with the spring. Assume the ball rolls without slipping along the 0=29° incline after it is released. Find the translational speed of the ball after it travels d= 70.4cm from the point of losing contact with the spring. Isphere =2/5 MR. Take g=9.8 m/s2 and express your answer using two decimal places. d MR www

18° The figure shows a thin rod, of length L = 2.20 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m =.10 kg is attached to the other end. The rod is pulled aside to angle 0 = 18 ° and released with initial velocity 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if the mass is increased? 8.10 I.

only type answer with all steps please

On a frictionless table, a 0.56 kg glob of clay strikes a uniform 1.26 kg bar perpendicularly at a point 0.35 m from the center of the bar and sticks to it. If the bar is 1.06 m long and the clay is moving at 9.30 m/s before striking the bar, what is the final speed of the center of mass?