Solving Two 6.20 kg Blocks Connected by Pulley

In summary, a system consisting of two 6.20 kg blocks connected by a massless string over a pulley of radius 2.40 cm and rotational inertia 7.40x10^-4 kgm^2 is released from rest. The pulley turns through 1.30 rad in 91.0 ms and the acceleration of the blocks is constant. The magnitude of the pulley's angular acceleration is unknown, as it is not known if there is friction between the table and the sliding block. Using the equation Torque = FR sin theta, the net torque on the pulley can be found to be T1R - T2R = Torque. This is due to the torque applied by the tension in
  • #1
craig22
5
0

Homework Statement



For the picture, go to http://s16.photobucket.com/albums/b21/arbilvoldy/pulley.jpg" [Broken].
T1 is for the hanging string with mass m1, and T2 is for the string over the table with mass m2.

Two 6.20 kg blocks are connected by a massless string over a pulley of radius 2.40 cm and rotational inertia 7.40x10^-4 kgm^2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 1.30 rad in 91.0 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T1, and (d) string tension T1?


Homework Equations



The one with which I'm concerned: Torque = FR sin theta

The Attempt at a Solution



From drawing free-body diagrams, you get
m1g-T1=m1a1 and T2-f2=m2a2

The part I don't get is with getting the net torque on the pulley. The torque is 0 for both the normal force and the weight, that I do know. However, in the student solutions manual, they have the net torque as T1R - T2R = Torque. Why is it that way? Wouldn't the torque from T2 be 0 because the sin of the angle b/w the center of the pulley and the radius is sin0=0?
 
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  • #2
Hi craig22,

craig22 said:

Homework Statement



For the picture, go to http://s16.photobucket.com/albums/b21/arbilvoldy/pulley.jpg" [Broken].
T1 is for the hanging string with mass m1, and T2 is for the string over the table with mass m2.

Two 6.20 kg blocks are connected by a massless string over a pulley of radius 2.40 cm and rotational inertia 7.40x10^-4 kgm^2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 1.30 rad in 91.0 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T1, and (d) string tension T1?


Homework Equations



The one with which I'm concerned: Torque = FR sin theta

The Attempt at a Solution



From drawing free-body diagrams, you get
m1g-T1=m1a1 and T2-f2=m2a2

The part I don't get is with getting the net torque on the pulley. The torque is 0 for both the normal force and the weight, that I do know. However, in the student solutions manual, they have the net torque as T1R - T2R = Torque. Why is it that way? Wouldn't the torque from T2 be 0 because the sin of the angle b/w the center of the pulley and the radius is sin0=0?

Your drawing is not quite accurate and I think it is leading you in the wrong direction. The top part of the rope will leave the pulley at the highest point, like this:

http://img159.imageshack.us/img159/70/pulley.jpg [Broken]

(If that does not make sense, try it: wrap a string around something round and see how it behaves if one end come off horizontal and the other side of the string is vertical.) Do you see why the torque is not zero?
 
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  • #3
The pulley has an angular acceleration and rotational inertia. There must be a torque increasing the rate of rotation of the pulley.

Add this to alphysicist's improved diagram and comments.
 
  • #4
I agree that when the system is released from rest, there's a torque on both T1 and T2. However, at rest, is that still true? If so, how? Sorry, this stuff is very new to me!
 
  • #5
craig22 said:
I agree that when the system is released from rest, there's a torque on both T1 and T2.

Just to be careful, we would say there is a torque from T1 and T2 on the pulley.

However, at rest, is that still true? If so, how? Sorry, this stuff is very new to me!

The problem is asking about what happens after the system is released so it is not at rest, and the two tensions are applying a torque to the pulley.

(Before it is released, there is something keeping it from moving: there might be something holding the pulley in place, which would mean an extra torque involved, or something might be holding up the hanging block, so that the tension would be zero, etc. The details aren't given, but the point is you just need to figure out what happens after it is released.)
 

1. How does a pulley system work?

A pulley system is a simple machine consisting of a grooved wheel and a rope, cable, or belt that is used to change the direction or magnitude of a force. When a force is applied to one end of the rope, the pulley redirects the force to the other end, making it easier to lift or move a heavy load.

2. What is the purpose of connecting two blocks with a pulley?

Connecting two blocks with a pulley allows for the transfer of force and motion between the blocks. This can be useful in various applications, such as lifting heavy objects or creating a mechanical advantage in a system.

3. How do you calculate the tension in the rope connecting the two blocks?

The tension in the rope can be calculated using Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the difference between the weight of the blocks and the tension in the rope, so the equation would be: Tension = (m1 - m2)g, where m1 and m2 are the masses of the blocks and g is the acceleration due to gravity (9.8 m/s^2).

4. How do you determine the acceleration of the blocks?

The acceleration of the blocks can be determined using Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the difference between the weight of the blocks and the tension in the rope, so the equation would be: Acceleration = (m1 - m2)g / (m1 + m2), where m1 and m2 are the masses of the blocks and g is the acceleration due to gravity (9.8 m/s^2).

5. What factors can affect the motion of the blocks in this system?

The motion of the blocks can be affected by various factors, such as the masses of the blocks, the tension in the rope, and the surface friction between the blocks and any surfaces they may be resting on. Other factors, such as air resistance and the shape of the pulley, may also play a role in the motion of the blocks.

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