Solving for Tension & Motion of 2 Masses Connected by String

In summary, two masses of 3.40 kg and 5.50 kg are connected by a light string that passes over a frictionless pulley. The tension in the string can be determined by setting up equations for the motion of each mass and solving for T. The acceleration of each mass can be found by equating the equations and solving for a. The distance each mass will move in the first 1.52 seconds of motion can then be calculated using the acceleration values. It is important to choose an arbitrary direction for positive motion and write the equations accordingly.
  • #1
Chuck 86
27
0

Homework Statement



Two masses of 3.40 kg and 5.50 kg are connected by a light string that passes over a frictionless pulley. Determine the tension in the string.

Calculate the acceleration of m.

Calculate the distance each mass will move in the first 1.52 seconds of motion if they start from rest

EFy=T1-m1g=may
EFy=T2-m2g=may

i have up to those equations but i don't know if I am doing this right
 
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  • #2
Your close. You need to chose an arbitrary direction in which you think the system will move. This direction for both masses will be positive. For example if you say that one mass falling will be the positive direction, the other mass rising will also be the positive direction. Therefore, one of you equations needs to be written the other way around. Instead of T2-m2g=may, what should it be using this information?
 
  • #3
So the rate of gravity for the smaller one has to be positive because it would most likley go up?
 
  • #4
Chuck 86 said:

Homework Statement



Two masses of 3.40 kg and 5.50 kg are connected by a light string that passes over a frictionless pulley. Determine the tension in the string.

Calculate the acceleration of m.

Calculate the distance each mass will move in the first 1.52 seconds of motion if they start from rest
/QUOTE]
You have given two masses. Which is m? Actually both will have the same acceleration.
Find the acceleration of each mass and equate them. Then solve for T. From that find the acceleration.
 
  • #5
So how do u find Y or do u just find ay together then divide by Y?
 
  • #6
When the two masses start moving from rest, heavier mass will move in the downward direction and lighter one will up.
Write down m1g - T = m1a for downward moving mass.
Similarly write down another equation for upward moving mass.
From these two equations find a and equate them, and solve for T.
 
  • #7
so then the second equation would be m2g-T=-m2a?
 
  • #8
Chuck 86 said:
so then the second equation would be m2g-T=-m2a?

Yes.
 

1. What is tension?

Tension is a pulling force that is created when an object is connected to another object by a string, rope, or cable.

2. How do you calculate tension in a system with two masses connected by string?

To calculate tension in a system with two masses connected by string, you can use Newton's second law, which states that the total force on an object is equal to its mass multiplied by its acceleration. In this case, you would calculate the acceleration of each mass separately and then use that value to solve for the tension in the string.

3. What is the relationship between tension and acceleration?

The tension in a string is directly proportional to the acceleration of the masses connected by the string. This means that as the tension increases, the acceleration also increases, and vice versa.

4. Does the angle of the string affect the tension in the system?

Yes, the angle of the string does affect the tension in the system. As the angle of the string increases, the tension in the string also increases. This is because a larger angle results in a greater vertical component of the tension force, which adds to the overall tension in the string.

5. What factors can affect the motion of two masses connected by string?

The motion of two masses connected by string can be affected by the tension in the string, the masses of the objects, the angle of the string, and any external forces acting on the system. Friction and air resistance may also play a role in the motion of the masses.

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