Question

A ledge on a building is 23 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 accidentally knocked off the ledge, what time interval does a carpenter have to catch the can of paint before it smashes on the ground?

Answer 1

The time can catch before it smashes on the ground is
`t=5.73 s`

Step-by-step explanation:

Using the force equation

`F=m*a`

`F_(net)=m*a`

So replacing and solving to find the acceleration

`a = (m_1*g-m_2*g) / m_1+m_2`

Finding the factor

`a = g *( m_1-m_2)/m_1+m_2`

`a=9.8m/s^2 *( 4.0 kg- 3.0 kg) / (4.0 + 3.0) kg`

`a=1.4 m/s^2`

Now replacing in Newtons law to find the time before can catch so:

`d= (1)/(2)*a*t^2`

`t=\sqrt{(2*d)/(a)}=\sqrt{(2* 23m)/(1.4 m/s^2)}`

`t=5.73 s`