110FORCES AND EQUATIONS OF MOTIONHowever, the integral is simply the total mass of the sphere, and we findthat for r > R, the force between m and the sphere is identical to theforce between two particles m and M separated a distance r.ProblemsFor problems marked *, refer to page 520 for a hint, clue, oranswer.3.1 Leaning pole with frictionTwo identical masses M are pivoted at each end of a massless poleof length L. The pole is held leaning against frictionless surfaces atangle 6, as shown, and then released. Find the initial accelerationof each mass.3.2 Sliding blocks with friction*Mass MA = 4 kg rests on top of mass Mg = 5 kg that rests on a fric-tionless table. The coefficient of friction between the two blocks is4 kg5 kgsuch that the blocks just start to slip when the horizontal force Fapplied to the lower block is 27 N. Suppose that now a horizontalforce is applied to the upper block. What is its maximum value forthe blocks to slide without slipping relative to each other?3.3 Stacked blocks and pulleyMass Ma lies on top of mass M, as shown. Assume M > Ma.The two blocks are pulled from rest by a massless rope passingover a pulley. The pulley is accelerated at rate A. Block M, slideson the table without friction, but there is a constant friction force fbetween M, and M, due to their relative motion. Find the tensionin the rope.M.3.4 Synchronous orbitFind the radius of the orbit of a synchronous satellite that circlesthe Earth. (A synchronous satellite goes around the Earth once ev-ery 24 h, so that its position appears stationary with respect to aground station.) The simplest way to find the answer and give yourresults is by expressing all distances in terms of the Earth's radiusRe.453.5 Mass and axleA mass m is connected to a vertical revolving axle by two strings oflength I, each making an angle of 45 with the axle, as shown. Boththe axle and mass are revolving with angular velocity w. Gravityis directed downward.(a) Draw a clear force diagram for m.(b) Find the tension in the upper string, Tup, and lower string,45"Tow.

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Leaning pole with friction Two identical masses M are pivoted at each end of a massless pole of length L. The pole is held leaning against frictionless surfaces at angle 6, as shown, and then released. Find the initial acceleration of each mass.