Atwood Machine Problem and Newton's 2nd Law

[longchina]

【Atwood Machine Problem】

Homework Statement

Regular atwood machine lab where you test the proportionality of net force and acceleration as stated in Newton's 2nd Law.
The regular lab procedure is to release the smaller mass at rest, to let it be lifted by the heavier one.
Question is: "How would the results [experimental values of acceleration] be affected if you give the mass a slight push [to make the Vi＞0]?"

Homework Equations

∑F=ma
a=(Vf—Vi)/t
……?

The Attempt at a Solution

Attempt/guess 1: the acceleration will not be affected by the initial push because acceleration is only due to the unbalanced net force, and the push is only at an instant which would not change the net force (the difference in the weights of the two masses).
【But, how do you justify it by math?】
a=(Vf—Vi)/t → Vi goes up, Vf also goes up, so the a won't change? (how about the t? unchanged?)

Thank you for any input!

 

[Spinnor]

I think you are on the right track. You wrote,

a=(Vf—Vi)/t

For Vf constant, t will be different for different Vi.

F = ma = T - mg

Acceleration as you thought only depends on forces and not velocities.

x = x_i + V_i*t + a*t^2/2

Good luck!