Question

Block 2 has four times the mass of Block 1. Assume a frictionless pulley and that both the rope and pulley are massless. Use g=9.8 m/s2.
Calculate the magnitude of acceleration of the blocks.

Answer 1

The magnitude of acceleration of the block is  5.88 m/s²

Block and tackle system of pulleys

Pulley are often used in construction sites to raise or lower heavy load. Pulley system is one of the most widely used type of machine. and Block and tackle system of pulleys is the practical system of pulleys in which one or more pulleys are mounted on the same axle, with one continuous rope passing all round the pulleys.

Given that Block 2 has four times the mass of Block 1. Assume a frictionless pulley and that both the rope and pulley are massless and     g = 9.8 m/s2.

That means M2 = 4M1

The acceleration will be toward the M1

To calculate the magnitude of acceleration of the blocks, we will consider the following

T - $m_{1}$g = $m_{1}$a ...... (1)

T - $m_{2}$g = -$m_{2}$a ..... (2)

Where

• T = tension in the rope which is the same

• g = acceleration due to gravity

• $m_{1}$ = mass of the block 1

• $m_{2}$ = mass of the bloc 2

• a = acceleration

Minus equation 2 from equation 1

( $m_{1}$ + $m_{2}$ )a = ( $m_{2}$ - $m_{1}$)g

But $m_{2}$  =  4$m_{1}$

Substitute in the equation above.

($m_{1}$ + 4$m_{1}$)a = (4$m_{1}$ - $m_{1}$)g

5$m_{1}$a = 3$m_{1}$g

$m_{1}$ will cancel out

5a = 3 x 9.8

a = 29.4/5

a = 5.88 m/s²

Therefore, the magnitude of acceleration of the block is  5.88 m/s²

Learn more about Block and Pulley here: https://brainly.com/question/13889684

#SPJ1