Question

A 100-kg block being released from rest from a height of 1.0 m. It then takes it 1.40 s to reach the floor. What is the mass m of the other block

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The mass of the other block is
`m_1 = 81.14 \ kg`

Step-by-step explanation:

From the question we are told that

Mass of the first block is
`m_1 = 100 \ kg`

The height is
`s = 1.0 \ m`

The time it takes it is
`t = 1.40 \ s`

Generally from kinematic equation

`s = ut + (1)/(2) at^2`

Here u is the initial velocity which zero given that it was at rest initially

So

`s = 0 * t + (1)/(2) at^2`

=>
`s = (1)/(2) at^2`

=>
`1 = (1)/(2)* a * (1.40 )^2`

=>
`a = 1.0204 \ m/s^2`

Generally from the diagram the resultant force due to the weight of the first object and the tension on the string is mathematically represented as

`mg - T = ma`

=>
`T = m g - ma`

=>
`T = m(g - a)`

=>
`T = 877.96 \ N`

Generally from the diagram the resultant force due to the weight of the second object and the tension on the string is mathematically represented as

`T - m_1g = m_1 a`

=>
`877.96 = m_1 (a + g)`

=>
`877.96 = m_1 (1.0204 + 9.8 )`

=>
`m_1 = 81.14 \ kg`