Question

Find the acceleration of the two blocks of 4 kg and 5 kg mass if a force of 40 N is
applied on 4 kg block. Friction coefficients between the respective surfaces are
shown is figure​

Answer 1

Answer:

first box acceleration is 10 2nd box acceleration is 8

Answer 2

Answer:

Only the block of mass 4kg moves with an acceleration of 5m/s².

Explanation:

Let's consider that the blocks are not sliding but moving with the same acceleration.

The frictional force acting on block 5kg is given as,

$f_1=\mu_1(m_1+m_2)g$       (1)

Where,

f₁=frictional force on 5kg block

μ₁=coefficent of friction between the 5kg block and the ground=0.3

m₁=5kg

m₂=4kg

g=acceleration due to gravity=10m/s²

By substituting the required values in equation (1) we get;

$f_1=0.3\times (5+4)\times 10$

$f_1=27N$           (2)

And the net acceleration on the blocks is given as,

$a=\frac{F-f_1}{m_1+m_2}$     (3)

F=40N       (given)

By substituting the required values in equation (3) we get;

$a=\frac{40-27}{9}=\frac{13}{9}m/s^2$     (4)

And the net force on a mass of 4kg is given as,

$F-f_2=4a$       (5)

By substituting the value of F and a in equation (5) we get;

$40-f_2=4\times \frac{13}{9}$

$f_2=40-\frac{52}{9}=34.22N$           (6)

The maximum value of f₂ will be,

$f_2'=\mu_2m_2g$

$f_2'=0.5\times \times 4\times 10=20N$     (7)

From equations (6) and (7) we can see that the force of friction acting on the block of mass 4kg is more than the maximum value of friction.

∴ Only 4 kg block moves with acceleration,

$a=\frac{40-20}{4} =5m/s^2$

Hence, only the block of mass 4kg moves with an acceleration of 5m/s².