Problem 7 - Leaning pole with friction (KK 3.1) Two identical masses M are pivoted at each end of a massless pole of length L. The pole is held leaning against a fric- tionless wall at angle 0, as shown. The coefficient of fric- tion with the floor is u. The pole is released and starts to slide. Find the initial acceleration of each mass.

P T M1 M2 Table (3) The figure above illustrates a block (object 1) having mass Mi positioned on top of a slab (object 2) having mass M2. The slab is positioned on a stationary friction-less horizontal table (object 3). The contacting horizontal surfaces between the block and slab are rough. An ideal rope extends horizontally from the block to an ideal pulley having a fixed pivot (i.e. it can rotate about a fixed axis). The rope wraps half-way around the pulley and continues horizontally to the slab. An external agent applies a leftward horizontal pulling force (P) onto the block, which causes the block to speed up to the left, the rope to have tension (T), and the slab to speed up to the right. Both the slab and block have the same magnitude of acceleration (A), relative to the table. Do not apply the model of friction covered in chapter 5. The symbol (g) is the gravitational acceleration. a) Write a list of symbols representing the magnitudes of the normal and friction forces acting…

A spring-loaded ball launcher (I)Context A spring-loaded ball launcher is embedded in the floor. When the ball launcher is triggered, the ball is propelled into the air and then falls to the ground. We are looking for the horizontal distance travelled by the ball. Information The pitcher is tilted at a known angle theta.The spring, whose spring constant is known, is initially compressed.At its natural length, the end of the spring coincides with the ground.The mass of the ball is known, but its diameter is neglected. Find the horizontal distance the ball travels (in metres) from the mouth of the pitcher to where it hits the ground with these following values: Pitch launcher lean angle(theta): 22.2 degrees Spring constant: 64.1 N/m Initial spring compression: 19.8 cm Ball mass A : 130 g

1. Examine the diagram below and then sketch the extended free-body diagram for the plank. Assume that the plank has a uniform mass so that its center of mass is located at its center. Sn