Question

The masses of blocks A and B are 20kg and 10kg, respectively. The blocks are initially at rest on the floor and are connecte by a massless string passing over a massless and frictionless pulley. An upward force is applied to the pulley. Find the acceleration of block A and of block B if the magnitude of the force is

Answer 1

Answer

mass of the block A = 20 Kg

mass of block B = 10 Kg

acceleration of Block A = ?

acceleration of Block B = ?

Assuming the magnitude of force = 124 N

Applying newton's second law

F = 2 T

T = F/2

now, Tension in the string =

T = 124/2 = 62 N

Weight of the block A

W = m₁ g

W = 20 x 9.8 = 196 N

Weight of the block B

W = m₂ g

W = 10 x 9.8

W = 98 N

Weight of blocks is greater than force applied by the pulley so, the blocks will not move.

Hence, acceleration of the block A and B = 0 m/s²

If the Force magnitude is increased to 294 N

T = F/2 = 294/2 = 147 N

Since this Force is less than Weight A  acceleration of the block A = 0 m/s².

For Block B

Tension is more than Weight hence block will move

Net Force = 147 - 98 = 49 N

acceleration =$\dfrac{F}{m}$

              $a = \dfrac{49}{10}$

                    a = 4.9 m/s²