Atwood System - max. height of the lighter object

[laurs]

Homework Statement

The two masses are each initially 2.60 m above the ground, and the massless frictionless pulley is 10.00 m above the ground. The masses are m1 = 1.71 kg and m2 = 4.59 kg. What maximum height does the lighter object reach after the system is released?
(Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground.
This is its "launch" speed. Assume it doesn't hit the pulley.)

Relevant Equations

a = (m2-m1)(g)/(m2+m1)
vf^2 = vi^2 + 2ad
Fnet = ma
Fg = mg

Magnitude of acceleration of system:
a = (4.59kg - 1.71kg)(9.81N/kg)/(4.59kg + 1.71kg)
= 4.48 m/s^2

Velocity of lighter mass when heavier one hits the ground:
vf^2 = vi^2 + 2ad
= 0 + 2(4.48m/s^2)(2.60m)
vf = 4.83 m/s [up]

I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?

 

[SammyS]

Homework Statement: The two masses are each initially 2.60 m above the ground, and the massless frictionless pulley is 10.00 m above the ground. The masses are m1 = 1.71 kg and m2 = 4.59 kg. What maximum height does the lighter object reach after the system is released?
(Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground.
This is its "launch" speed. Assume it doesn't hit the pulley.)
Homework Equations: a = (m2-m1)(g)/(m2+m1)
vf^2 = vi^2 + 2ad
Fnet = ma
Fg = mg

Magnitude of acceleration of system:
a = (4.59kg - 1.71kg)(9.81N/kg)/(4.59kg + 1.71kg)
= 4.48 m/s^2

Velocity of lighter mass when heavier one hits the ground:
vf^2 = vi^2 + 2ad
= 0 + 2(4.48m/s^2)(2.60m)
vf = 4.83 m/s [up]

I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?

I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?

Hello, @laurs .



It's helpful to include all information in the body of your post, even if it's also included in thread's title.

Many of us are familiar with Atwood's machine. (Atwood system as you refer to it.) However, the point at which you are puzzled, indicates that you may not be familiar with it.

Is this the case?

 

[laurs]

Hi @SammyS
I am familiar with the machine, however am not accustomed to seeing questions asking for the height of the lighter weight. Most of the questions ask about the acceleration or the forces acting on the weights, which is a simple calculation, but I don't really know how to approach this one. I have been able to calculate time as well, assuming initial speed is 0, using the vf = vi + at, getting a value of t = 1.077s, but still am unsure how to approach the projectile portion of the question.

 

[SammyS]

Hi @SammyS
I am familiar with the machine, however am not accustomed to seeing questions asking for the height of the lighter weight. Most of the questions ask about the acceleration or the forces acting on the weights, which is a simple calculation, but I don't really know how to approach this one. I have been able to calculate time as well, assuming initial speed is 0, using the vf = vi + at, getting a value of t = 1.077s, but still am unsure how to approach the projectile portion of the question.

As for the point you're stuck on:

...

I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?

The direction of "launch" is vertically upward at a distance of 5.20 m above the ground. The pulley is not involved. It's 10.00 m above the ground.

If an object is launched vertically with some initial speed, how high above the launch point will it get before it begins descending?