Question

Two blocks of mass 2 kg and 5 kg are connected by and ideal string passing over a Pulley.the block of mass 2 kg is free to slide on surface inclined at an angle of 30 degree with horizontal where is 5 kg block hang freely . find acceleration of system and tension in the string here u0.30

Answer 1

Put the value in above equations and get the result.

Answer 2

Given that,

One block of mass = 2 kg

Another block of mass = 5 kg

Angle = 30 °

Friction coefficient = 0.3

Let a be the acceleration of the system and T is the tension in the string

We need to calculate the friction force

Using formula of friction

$f=\mu g\cos\theta$

$f=0.3\times 2g\cos\theta$

We need to calculate the acceleration

Using balance equation

For first block,

$5g-T=5a$......(I)

For second block,

$T-2a\sin\theta-f=2a$.......(II)

From equation (I) and (II)

$5g-2g\sin\theta-f=7a$

$5g-2g\sin30=0.6g\cos30=7a$

Put the value into the formula

$g(5-2\times0.5-0.6\times0.866)=7a$

$a=\dfrac{9.8(5-2\times0.5-0.6\times0.866)}{7}$

$a=4.8\ m/s^2$

We need to calculate the tension

Using equation of (I)

$T=5g-5a$

Put the value into the formula

$T=5\times9.8-5\times4.8$

$T= 25\ N$

Hence, The acceleration of system and tension in the string is 4.8 m/s² and 25 N.