Consider two objects with m1, m2 connected by a light string

• Ab17
In summary, the two objects with M1 greater M2 connected by a light string that passes over a pulley have translational speeds and angular speeds at the time of their encounter.

Ab17

1. The problem statement, all variables and given/known

Consider two objects with M1 greater M2 connected by a light string that passes over a pulley having a moment of inertia I about its axis of rotation. The string does not slip on the pulley or stretch. The pulley turns with friction. The two objects are released from rest separated by a vertical distance 2h

(a) use the principal of conservation energy to find the translational speeds of the objects as they pass each other

(B) find angular speed of the pulley at this time

Homework Equations

m1gh = m2gh + 1/2mv^2 + 1/2m1v^2 + 1/2I(V^2/R^2)[/B]

V= sqrt(2(m1gh-m2gh)/m2 + m1 + I/R^2)

Is this the right answer because it considers when the m1 block moves 2h down not when it passes the other block. How is this solved then??

The Attempt at a Solution

Ab17 said:
Is this the right answer because it considers when the m1 block moves 2h down not when it passes the other block.
No it doesn't. Hint: How far has each block moved when they pass each other?

2h? Thats the only height in the problrm

Ab17 said:
2h? Thats the only height in the problrm
Draw yourself a diagram. Hint: If one block goes up a distance x, the other goes down a distance x.

So if one block goes a distance 2h down then the other block goes a distance 2h up since they are connected by the same string

Ab17 said:
So if one block goes a distance 2h down then the other block goes a distance 2h up since they are connected by the same string
That would be true, of course, but how far have they moved when they pass? If they start out at 2h apart, how far must each move to reach the other?

H?

Ab17 said:
H?
Right. They meet after M1 moves down a distance h and M2 moves up a distance h. (If you're unsure of this, play it out with a piece of string.)

Ab17 said:
The pulley turns with friction.
Should this say without?

Yes mistake there

I assumed it was just a typo.

1. What is the purpose of connecting two objects with a light string in an experiment?

The purpose of connecting two objects with a light string in an experiment is to study the effects of tension on the objects and to observe their motion under the influence of this tension.

2. How does the mass of the objects affect the motion of the system?

The mass of the objects affects the motion of the system by determining the magnitude of the tension in the string. The heavier object will experience a greater force from the tension, causing it to accelerate less than the lighter object.

3. What happens to the motion of the objects if the string is replaced with a heavier rope?

If the string is replaced with a heavier rope, the motion of the objects will be affected by the increased weight of the rope. This will result in a slightly lower acceleration for both objects due to the additional weight being pulled by the tension in the rope.

4. How does the length of the string affect the motion of the objects?

The length of the string affects the motion of the objects by changing the distance between them and altering the tension in the string. A longer string will have a greater distance between the objects, resulting in a lower tension and slower acceleration for both objects.

5. What is the significance of using a light string instead of a heavy one in this experiment?

The use of a light string allows for the effects of tension to be observed more easily as it minimizes the impact of the string's weight on the motion of the objects. This allows for a more accurate study of the relationship between tension, mass, and acceleration in the system.