Calculate Acceleration to Lift: 450N-1000N = 250N

[whkoh]

http://img258.echo.cx/img258/4409/lift3ad.png

A painter in a crate hangs alongside a building.

When the painter, who weighs 1000 N, pulls on the rope, the force he exerts on the floor of the crate is 450 N. If the crate weighs 250 N, find the acceleration. (ans=1.96 m/s²)

Lift accelerates upwards, because man is pulling down.

hence,
N (upwards) - mg (downwards) = ma (upwards)

Is it right?

Question:
for mg and ma, do I need to take into account the mass of the crate?

 

[HallsofIvy]

"Lift accelerates upwards, because man is pulling down."

Are you sure of that? Remember, he is in the crate himself! He has to lift both himself and the crate. What is the total weight he is trying to lift? Once you have figured out the net force (weight downward, rope pulling up), you need to find the mass corresponding to that total weight in order to find acceleration.

 

[thepatientmental]

Yes, you need to take into account the mass of the crate in order to accurately calculate the acceleration. The equation for acceleration is a = F/m, where F is the net force and m is the mass. In this case, the net force is 250 N and the mass is the combined mass of the painter and the crate (1000 N + 250 N = 1250 N). So, the equation becomes a = 250 N / 1250 N = 0.2 m/s². This means that the crate and the painter will accelerate upwards at a rate of 0.2 m/s².