Question

4. Experiment 1 (see this first diagram, which is not to scale) A straight, thin rod of non-uniform density is held initially at rest, as shown, by a frictionless pin located at the base of the wall and also by a horizontal, massless thread that connects the rod to the wall The rod's total length is 7.94 m, and the tension in the thread is 150 N Defining the pin as r 0 m, the rod's linear mass density can be described as this wall rod r)A- Br5, where A 3.21 kg/m, and B 0.534 kg m-35 The thread is then cut (at its right end), which allows the rod to pivot downward, rotating freely around the pin, until it strikes the floor Result: The impact speed of the rod's midpoint is 6.87 m/s pin fioor Experiment 2 (see this second diagram-also not to scale) The rod is removed, and a solid, uniform sphere is placed at rest, as shown, on a ramp attached to the top of the wall. heikit As it happens, the diameter of the sphere is equal to half the thread's length; and the ramp height is twice the thread's length; and the wall height is six times the thread's length 义 When released from rest, the sphere rolls, without slipping, down the ramp and off the horizontal edge of the wall wall Predict this result: Through how many revolutions will the sphere turn while it is a projectile? Ignore all air drag and rolling friction, and assume that g 9.80 m/s2. Jloor

Answer 1

First we need to find relation between radius thread length ramp height and height of wall then solve as follows

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