A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T (Figure 1). The walls of the cone make an angle B with the horizontal. The coefficient of static friction between the block and the cone is µg. If the block is to remain at a constant height h above the apex of the cone, what are (a) the maximum value of T and (b) the minimum value of T? (That is, find expressions for Tmax and Tmin in terms of B and h.)
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- A small box of mass m1m1 is sitting on a board of mass m2m2 and length LL (Figure 1). The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is μsμs μsμs Throughout the problem, use gg for the magnitude of the free-fall acceleration. In the hints, use ff for the magnitude of the friction force between the board and the box. Find Fmin, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board) Express your answer in terms of some or all of the variables μsμs m1m1 m2m2 g L Do not include ff in your answer.A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 . State the forces that act on the basket. Draw a force diagram showing them, defining the symbols that you use to represent the forces and marking the sizes of the angles to show the directions of the forces. Take the unit vector i to point up the slope and the unit vector j to point upwards and perpendicular to the slope. Add these unit vectors to your force diagram.A skydiver weighing 65 kg jumps out of a helicopter hovering at a height of 3 kilometers. Assume a cross-sectional area of 0.5 square meters. After thirty seconds of free fall, the skydiver deploys the parachute and the cross-sectional area becomes 40 square meters. Reproduce the model for the skydiver in Excel or VenSim. In VenSim you may have to make At quite small in order not to throw an error. Because you reach terminal velocity relatively quickly your answer should not be particularly sensitive to the value of At you choose. What is the skydiver's terminal velocity without the parachute? meters/second What is the skydiver's terminal velocity with the parachute? meters/second
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