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

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

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

$g=7a$

$a=\frac{g}{7}$

So time taken to cover 18 m is

$h=ut+\frac{at^2}{2}$

$18=0+\frac{g\cdot t^2}{7\times 2}$

$t^2=\frac{18\times 2\times 7}{g}$

$t=5.07 s$