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

Answer:

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

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:

$d= \frac{1}{2}*a*t^2$

$t=\sqrt{\frac{2*d}{a}}=\sqrt{\frac{2* 23m}{1.4 m/s^2}}$

$t=5.73 s$