Homework SolutionCalculating Winch Power Requirement

[karmatic]

Homework Statement

I need to write an equation to find the necessary power requirements of a winch used to raise and lower a lift of an undetermined mass and a counterweight that is half the mass of the lift. The maximum speed of the lift is 3m/s, and the lift travels a total of 30m.

Homework Equations

So far I have p=w*s where p is power, w is the work done and s is speed in m/s. Substituting the known value for speed I get p=w*3

Then I have w=f*d where f is force and d is distance in m. Substituting the value for d i get w=f*30

Next I have f=m*a where m is mass and a is acceleration in m/s squared. So I get a bit stuck on this part, should a be acceleration due to gravity? in which case I would have f=(m+1/2m)*9.81...?

Then I want to put all this into one formula, so I THINK this is right..
p={[(m+1/2m)*a]*d}*s

The Attempt at a Solution

which if i substitute in the correct values, the equation should look like this, with only the value of m being unknown...
P={[(m+m/2)*9.81]*30m}*3m/s

Is that the neatest way to set out the formula, and have I gotten the right formulas? I'm fairly sure I've done it right, just wanted to double check. Thanks in advance for having a read =)

 

[rl.bhat]

So far I have p=w*s where p is power, w is the work done and s is speed in m/s

The above equation is wrong.
It should be P = f*v, where f is the force applied and v is the velocity.

 

[karmatic]

Okay thanks, so it should instead be - P=[(m+m/2)*9.81]*3 ?
I thought there would be a difference between the velocity and the maximum speed given for the lift.

 

[karmatic]

One more question, if the value for M was known the answer to P would be in watts correct?

 

[rl.bhat]

One more question, if the value for M was known the answer to P would be in watts correct?

Yes.

 

[rl.bhat]

Okay thanks, so it should instead be - P=[(m+m/2)*9.81]*3 ?
I thought there would be a difference between the velocity and the maximum speed given for the lift.

The acceleration of the lift can be found as follows.

2mg - T = 2m*a...(1)
T - mg = m*a...(2)

Solvr these to equations to find a.