A 30.0-kg block is resting on a flat horizontal table. On top of this block is r

Question

A 30.0-kg block is resting on a flat horizontal table. On top of this block is resting a 15.0-kg block, to which a horizontal spring is attached, as the figure illustrates. The spring constant of the spring is 337 N/m. The coefficient of kinetic friction between the lower block and the table is 0.659, and the coefficient of static friction between the two blocks is 0.973. A horizontal force is applied to the lower block as shown. This force is increasing in such a way as to keep the blocks moving at a constant speed. At the point where the upper block begins to slip on the lower block, determine (a) the amount by which the spring is compressed and (b) the magnitude of the force .

Explanation / Answer

let us take lower block as 1 and upper blockas 2, then m1 = 30.0 kg m2 = 15.0 kg k = 337 N / m µk = 0.659 µs = 0.973 as shown in the figure when the force is applied tothe lower block the kinetic frictional force Fk1 on the bottom block is givenby Fk1 = µk (m1 +m2) g as a result static frictional force is applied on thetop block given by Fs2 = µs m2g when we apply newtons second law to the bottom weget F - Fk1 - k x = 0 and for the top block we get Fs2 - k x = 0 (a) so the amount by which the spring is compressed willbe x = Fs2 / k = µsm2 g / k = ............. m (b) the magnitude of the force F willbe F = k x + Fk1 = k x + µk(m1 + m2) g = ................N

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