A 4.8kg block is resting at the top of a 30 degrees slope of height 1 m. It is attached to a cylindrical pulley of mass 1.7kg and radius 8 cm by a massless string that unwinds as the block slides downhill with friction. If the acceleration of the block is 2m/s^2, what is ? Find the velocity at the bottom of the slope using forces and torques. Repeat the solution using energy concepts.

A ball of mass 2.3 kg, at one end of a string of length L=4.5 m, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball (in m/s) at the bottom of the circle is: m a. 10.50 Ob. 8.13 Oc. 9.39 Od. 14.85 Oe. 6.64

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The figure shows a ball with mass m = 0.69 kg attached to the end of a thin rod with length L = 0.99 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. (a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed? What then is its speed at (b) the lowest point and (c) the point on the right at which the ball is level with the initial point? (d) If the ball's mass were doubled, what would the answer to (a) be?

Problem 151. One end of a rod of mass 1 kg and of length 1 m can freely rotate about a lixed horizontal axis. Initially the rod makes an angle of 30° to the horizontal. A thread of length 1.3 m is attached t0 the (wo ends of the rod. A small pulley can run without friction along the thread, and a weight of mass 0.2 kg is suspended on the axis of the pulley. Determine the work needed to lit the rod to a horizontal position. (Use the value g= 10 m/s? for the acceleration due to gravity.) 30° 1 m

(a) Calculate the force (in N) the woman in the figure below exerts to do a push-up at constant speed, taking all data to be known to three digits. (You may need to use torque methods from a later chapter.) N 0.88 m m = 56 kg CG W 1.46 m W Freaction (b) How much work (in J) does she do if her center of mass rises 0.180 m? (c) What is her useful power output (in W) if she does 24 push-ups in 1 min? (Should work done lowering her body be included? See the discussion of useful work in Work, Energy, and Power in Humans.)

A hoop of radius RH and mass mH and a solid cylinder of radius Rc and mass mc are released simultaneously at the top of a plane ramp of length L inclined at angle θ above horizontal. Which reaches the bottom first, and what is the speed of each there?

A hollow cylinder (hoop), a solid cylinder (disk), and a solid sphere, each of mass M and radius R, roll down a hill of height h. Rank the objects based on their total kinetic energy at the bottom of the hill. Rank the one with the most energy 1, etc. If two are equal, give them the same ranking. hoop___________ disk_______________sphere_______________Justify your ranking

a small 0.171 kg block slides down a frictionless surface through height h = 0.893 m and then sticks to a uniform vertical rod of mass M = 0.342 kg and length d = 2.12 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ.