3 masses connected by a pulley

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In summary, the problem involves three blocks released from rest with no friction between the table and one of the blocks. The masses of the blocks are given and the goal is to calculate the speed of one of the blocks at a specific time. The equations needed to solve the problem are V=Vo+at and a1=a2=a3, but the specific value for acceleration is still unknown.
  • #1
sheri1987
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Homework Statement



The three blocks shown are relased at t=0 from the position shown in the figure. Assume that there is no friction between the table and M2, and that the two pulleys are massless and frictionless. The masses are: M1 = 3.0 kg, M2 = 7.0 kg, M3 = 5.0 kg.

Calculate the speed of M2 at a time 1.35 s after the system is released from rest.

http://nplq1.phyast.pitt.edu/res/msu/physicslib/msuphysicslib/09_Force_and_Motion/graphics/prob81_pulley2

Homework Equations


I figure I need an equation with time like V= Vo +at and then I also need to use an equation to solve for a. I know all of the a's are equal (a1=a2=a3), yet I do not know which equation to use.


3. The Attempt at a Solution
for the first equation I plugged in V=Vo +at, t was the 1.35s, Vo = 0, v is unknown, and a I am unsure how to get still? Could you please help me out?
 
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  • #2
Not able to see the picture.
 
  • #3
Thank you.

I would approach this problem by first identifying the known quantities and the unknown quantity. In this case, the known quantities are the masses of the three objects (M1, M2, M3), the time (1.35 s), and the initial velocity (Vo = 0). The unknown quantity is the final velocity of M2.

Next, I would use the equations of motion to solve for the final velocity. Since the objects are connected by a pulley, the acceleration of each object is equal (a1 = a2 = a3). Therefore, we can use the equation Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and t is the time.

To solve for the acceleration, we can use Newton's second law, F = ma, where F is the net force acting on the object, m is the mass, and a is the acceleration. In this case, the net force is the weight of the object, which is equal to mg, where g is the acceleration due to gravity (9.8 m/s^2).

So, for M2, we have F = ma = mg. Therefore, a = g = 9.8 m/s^2.

Plugging this value of acceleration into the first equation, we get Vf = 0 + (9.8)(1.35) = 13.23 m/s.

Therefore, the final velocity of M2 after 1.35 seconds is 13.23 m/s.

It is important to note that this solution assumes ideal conditions, such as no friction and massless and frictionless pulleys. In real-world scenarios, these factors may affect the final velocity and should be taken into consideration.
 

1. How does the presence of a pulley affect the motion of 3 masses connected by a rope?

The presence of a pulley allows for the distribution of forces between the masses, resulting in a more balanced and smoother motion. The pulley also changes the direction of the force, making it easier to lift or move the masses.

2. What are the factors that determine the acceleration of the masses in a pulley system?

The acceleration of the masses depends on the mass of the objects, the tension in the rope, and the friction between the pulley and the rope. It also depends on the direction and magnitude of the applied force.

3. Is the tension in the rope the same throughout the entire pulley system?

No, the tension in the rope varies depending on the position of each mass and the direction of the applied force. The tension is highest on the side of the rope that is pulling the heaviest mass.

4. Can the direction of motion be reversed in a 3-mass pulley system?

Yes, by changing the direction of the applied force, the direction of motion can be reversed. This is due to the pulley's ability to change the direction of the force acting on the masses.

5. How does the distance between the masses affect the motion in a 3-mass pulley system?

The distance between the masses does not directly affect the motion of the system. However, it can affect the tension in the rope, which in turn can affect the acceleration and direction of motion of the masses.

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