1.A long thin uniform rod lies flat on the table as shown.One end of the rod is slowly pulled up by a force that remains perpendicular to the rod at all times. What minimum coefficient of static friction is required so that the rod can be brought to the vertical position without any slipping of the bottom end?
2.A small block slides down a slanted board when released. The upper half of the board is smooth and the lower is rough(each section is of equal length), so that the acceleration of the block on the smooth half is three times greater than it is on the rough half. The block reaches the bottom of the board in time t1. The board is then flipped so that the upper half is rough and the lower part is smooth,and the block is released from the top again. This time,the block reaches the bottom of the board in time t2. In both cases, the board makes the same angle with the horizontal. Find the ratio t1/t2.
3.Imagine that the mass of the Sun instantly doubles. How long would the Earth’s year be?
4.A dumbbell consists of a light rod of length r and two small masses m attached to it. The dumbbell stands vertically in the corner formed by two frictionless planes. After the bottom end is slightly moved to the right, the dumbbell begins to slide. Find the speed u of the bottom end at the moment the top end loses contact withthe vertical plane.
5.A sled is given a quick push up the snowy slope. The sled slides up and then comes back down; the whole trip takes time t. If the coefficient of sliding friction between the sled and the snow is µ, find the time tu it took the sled to reach the top point of its trajectory. The slope makes the angle θ with the horizontal.
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