Calculating Acceleration of a Pulley Off 6-Story Building

[vericolorful]

Homework Statement

There is a pulley suspended off a 6 story building. One side of the pulley is attached to a mass of 250lb and the other 130lb. What's the acceleration?

Homework Equations

a=[(m2-m1)/(m2+m1)]g
g = 32 ft/s2

The Attempt at a Solution

Well, I think I'm suppose to use the equation listed above because it's linked with a atwood's machine lab we just did. I got the answer of -10.1ft/s2. I don't know if this is correct because my teacher said something about taking into the account of how high the building is. Each story is 10 ft. Thanks in advance.

 

[Dick]

You could also work it out just using a free body diagram. The equation for atwood's machine isn't so important you want to memorize it. The answer is correct, though I'm not sure why you included the minus sign. One weight is accelerating up and the other down. What could the minus add to that? I think your teacher was teasing you by suggesting the height of the building is a factor. How could it be? Don't believe that every number given in a problem statement is necessary to the solution of the problem.

 

[m2003]

I would first clarify the given information and assumptions. Is the pulley assumed to be frictionless? Is the mass of the pulley itself taken into account? Are the masses attached to the pulley assumed to be point masses or do they have a certain size and shape? These details can affect the accuracy of the calculated acceleration.

Assuming that the pulley is frictionless and the masses are point masses, the given equation can be used to calculate the acceleration. However, the negative sign in the answer (-10.1 ft/s2) indicates that the pulley is accelerating downwards, meaning that the heavier mass is moving downwards faster than the lighter mass is moving upwards. This makes sense, as the heavier mass of 250lb will have a greater gravitational force pulling it downwards compared to the lighter mass of 130lb.

To take into account the height of the building, we can use the equation for gravitational potential energy: PE = mgh, where m is the mass, g is the gravitational acceleration (32 ft/s2), and h is the height. By setting the potential energy of the system (pulley and masses) at the top of the building to be equal to the kinetic energy of the system at the bottom of the building, we can calculate the final velocity of the masses and use this to determine the acceleration.

Overall, it is important to clearly state all assumptions and considerations when calculating the acceleration of a pulley off a 6-story building. Additionally, it may be helpful to draw a free body diagram and consider all forces acting on the pulley and masses.