Question

A ledge on a building is 18 m above the ground. A taut rope attached to a 4.0-kg can of paint sitting on the ledge passes up over a pulley and straight down to a 3.0-kg can of nails on the ground.If the can of paint is accidently knocked off the ledge, what time interval does a carpenter have to catch the can before it smashes on the floor?

Answer 1

Answer:t=5.07 s

Step-by-step explanation:

Given

height of Building h=18 m

mass of Paint can
`m_1=4 kg`

mass of second can
`m_2=3 kg`

let T be the Tension in the rope

For 4 kg can

`4g-T=4a`

`T=4(g-a)`----1

For 3 kg can

`T-3g=3a`

`T=3(g+a)`----2

From 1 and 2

`4(g-a)=3(g+a)`

`g=7a`

`a=(g)/(7)`

So time taken to cover 18 m is

`h=ut+(at^2)/(2)`

`18=0+(g\cdot t^2)/(7* 2)`

`t^2=(18* 2* 7)/(g)`

`t=5.07 s`