Ch 10 HW: Problem 10.1 - Spring Force A 3.40-kg block is held against a vertical wall by a spring force in the setup shown below. The spring has a spring constant k = 725 N/m. Someone pushes on the end of the spring in a direction perpendicular to the wall, and the block does not slip downward. a) If the spring is compressed by 2.40 cm, what is the magnitude and direction of the force of static friction by the wall on the block? You may wish to review worksheets 4.10, 4.11 and 4.12. b) If the spring constant is 3230 N/m, what is the minimum compression of the spring (in cm) that will still ensure the mass does not to begin to slide down the wall? Assume the coefficient of static friction between the block and wall is 0.555.
Ch 10 HW: Problem 10.2 - Reference Circle, Energy and Harmonic Motion A vertically oriented spring (k = 2960 N/m) is used as a projectile launcher for a 1.75-kg mass. The spring is initially compressed by 4.40 cm and at rest, then released. a) To what maximum height above the release point does the mass rise? Be sure to consider the initial vertical spring displacement as part of the overall vertical motion. b) If the spring compression is doubled initially and the mass launched again, the mass rises to a different height. What is the ratio of the (new height) / (old height from part a)?
Ch 10 HW: Problem 10.3 - Reference Circle, Energy and Harmonic Motion A 7.50-gram bullet is fired into an initially stationary 2.25-kg block. The block is attached to a horizontal spring (k = 822 N/m) and is free to slide across a frictionless, horizontal surface. The other end of the spring is connected to a rigid wall. Upon impact, the bullet becomes embedded in the block, and the bullet-block system causes the spring to compress by a maximum amount of 14.3 cm. a) What was the initial speed of the bullet. b) After momentarily coming to rest, the bullet-block system begins to oscillate back and forth on the spring with what angular frequency? c) How many oscillations does the system complete in 60.0 seconds?
Ch 10 HW: Problem 10.4 - The Pendulum A pendulum is made from a 75.0-cm long string with a 50.0-gram mass attached to one end. The pendulum is released from rest at an angle of 8.45 with respect to the vertical and allowed to move frictionlessly. a) What is the speed of the pendulum bob when it passes through its lowest point? b) What is the kinetic energy of the pendulum bob when it passes through its lowest point? c) What is the initial potential energy of the pendulum bob before it is released, assuming it is zero at its lowest point? d) What is the angular frequency of the motion? e) How much time elapses after the ball is released until it reaches the lowest point of its motion for the first time?
Ch 10 HW: Problem 10.5 - Reference Circle, Energy and Harmonic Motion A 25-gram block is resting on a horizontal, frictionless surface and is attached to a horizontal spring of k = 210 N/m. The spring is stretched so that the block is 27 cm away from the spring s equilibrium position and released from rest. a) What is the velocity of the block when it passes through the equilibrium point? b) At what distance from equilibrium is the spring s potential energy equal to the block s kinetic energy? c) Suppose the block has a speed of 21 m/s when it passes through the equilibrium point for the first time, how much work is done by the force of kinetic friction during that first part of the block s motion?