Question

The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes it 0.90 s to reach the floor. What is the mass m of the other block? The pulley has no appreciable mass or friction.

Answer 1

Answer:

The mass of the another block is 60 kg.

Explanation:

Given that,

Mass of block M= 100 kg

Height = 1.0 m

Time = 0.90 s

Let the mass of the other block is m.

We need to calculate the acceleration of each block

Using equation of motion

$s=ut+\dfrac{1}{2}at^2$

Put the value into the formula

$1.0=0+\dfrac{1}{2}\times a\times(0.90)^2$

$a=\dfrac{2\times1.0}{(0.90)^2}$

$a=2.46\ m/s^2$

We need to calculate the mass of the other block

Using newton's second law

The net force of the block M

$Ma=Mg-T$

$T=Mg-Ma$....(I)

The net force of the block m

$ma=T-mg$

Put the value of T from equation (I)

$ma=Mg-Ma-mg$

$m(a+g)=M(g-a)$

$m=\dfrac{M(g-a)}{(a+g)}$

Put the value into the formula

$m=\dfrac{100(9.8-2.46)}{2.46+9.8}$

$m=59.8\ \approx60\ kg$

Hence, The mass of the another block is 60 kg.