As shown below, a block of mass 3.00 kg is placed on top of a larger block of ma

Question

As shown below, a block of mass 3.00 kg is placed on top of a larger block of mass 10.0 kg, and the two-block system rests on a horizontal surface. There is friction between the two blocks, as well as between the larger block and the surface, with static and kinetic friction coefficients of /is = 0.300 and = 0.200, respectively. As shown below, a horizontal force F is applied to the larger block. Use g = 10 m/s2, and try doing this problem without a calculator. If the blocks are initially at rest, what Is the minimum value of the horizontal force F necessary to start the system moving? N Once the blocks ore moving, what is the minimum value of the horizontal force F necessary to keep the system moving at constant velocity? N Once the blocks are moving, what is the maximum value the horizontal force F can be such that the small block does not slide on the large block? N

Explanation / Answer

Given,
m = 3 Kg
M = 10. Kg
us = 0.300
uk = 0.200

(1)
Minimum Value of Horizontal Force F necessary to keep the system moving at constant velocity
F = us*(m +M)*g
F = 0.3*(3+10)*10 N
F = 0.3*13 *10N
F = 39 N

(2)

Minimum Value of Horizontal Force F necessary to start system moving,
F = uk*(m +M) *g
F = 0.2*(3+10)*10 N
F = 0.2*13*10 N
F = 26 N

(3)

F = m*a
Maximum acceleration of System = us*g

(m+M)*a = F - uk*(m +M)g
F = us(m+M)*g + uk*(m +M)g
F = 0.3*(3+10)*10 + 0.2*(3+10)*10
F = 65 N

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