Question

A ledge on a building is 20 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

t = 5.4 s

Step-by-step explanation:

from the question we are given :

height (s) = 20 m

mass of paint (Mp) = 4 kg

mass of nails (Mn) = 3 kg

acceleration due to gravity (g) = 9.8 m/s^{2}

• The net force accelerating the can of paint should be equal to the difference in weight of the can of paint and the can of nails.

weight of nails = mass of nails x g = 3 x 9.8 = 29.4 N

weight of paint = mass nails x g = 4 x 9.8 = 39.2 N

net force = 39.2 - 29.4 = 9.8 N

• net force = total mass x acceleration

9.8 = (3 +4) x a

a = 1.4 m/s^{2}

• from S = Ut + 0.5at^{2} we can get the time the carpenter has to catch the nails

where U is the initial velocity and is 0 since the can was initially at

rest

20 = (0 x t) + (0.5 x 1.4 x t^{2})

20 = 0.7 x t^{2}

t^{2} = 28.6

t = 5.4 s