Question

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4. A small block of mass $m_{1}=4 k g$ is placed at rest on a larger block of mass $m_{2}=6 \mathrm{kg}$. The coefficient of friction between the two block is $\mu=0.3 .$ And the horizontal surface is smooth. A constant force $\mathrm{F}$ is applied on the block. 

The situation is given in the figure below.

a. Find the value of limiting friction between the two blocks.

b. What is the maximum acceleration by which the upper block can move

c. What is the maximum value of $\mathrm{F}$ at which both the block move together.

d. If $\mathrm{F}=30 \mathrm{N},$ what is the acceleration of each block and what frictional force is acting between the block.

e. What is the normal contact force between the blocks

f. What is the normal contact force between the larger block and the smooth surface

g. If $\mathrm{F}=40 \mathrm{N},$ what is the acceleration of each block and what frictional force is acting between the block.

h. If the force is applied to the upper block, what will be the minimum force required so that there is relative motion between the block. Note: 

$g=10 \mathrm{m} / \mathrm{s}^{2}$

Answer 1

Criven mi= ukg Me = 6kg m, uzo M2 ll- 0.3 g 3 10 m/s² (a) too block not to mace delatively # faung to 0.3 x 4 x 10 Ting f 12 Newton where foemitting function,

apply newton and law of motion ma= f acceleration ca) f mi 4 3 m/s foo moving together accelegation foo both will be Sane from (b) a = 3 m/s F = (mm) a m. mz (4+6)x3 30 Newton accelerator (d) F = 30N Ffm, ma a) m mitm 30-f. uto

put in equation (1) Boro ut6 a 2 3 m/s friction force Loltween blocks fe tempo f = mea f = 4X3 m. f = 12 Newton @) Normal contact force mi IM mig - 4x10 N- yo Newton m, ") 2 = (m, tm.) g = N2 = (4+4)*10 100 Newton)

friction foole lecteren blocks mi fa umg - 0.3xUXlO M₂ f 12 Newton co F = 40 Newton fum, tm.) fox( mm)g f- f Ff mitm 4o-o 4+6 ५० a a = 4 m/s² (6) the minimum fore required = f F=umig m 2 = 0.3x uxlo m = 12 Newton