Two blocks connected by string passing over a pulley on an incline

In summary, the conversation is about solving for the tensions in a string and the moment of inertia of a pulley, given the masses and acceleration of two blocks connected by the string. The tension in the string is found by setting the weight of each block equal to the net force acting on it, and the moment of inertia of the pulley is found using the equation T2 - T1 = I*α/r^2.
  • #1

Homework Statement

Two blocks, as shown below, are connected by a string of negligible mass passing over a pulley of radius 0.225 m and moment of inertia I. The block on the frictionless incline is moving up with a constant acceleration of 1.97 m/s2 on an angle of 35.1 degrees.

m1 = 15.4 kg
m2 = 19.5 kg

A set up of the blocks and incline can be seen below, but the values above are used in all calculations

(a) Determine the tensions in the two parts of the string.
(b) Find the moment of inertia of the pulley.

Homework Equations

The Attempt at a Solution

K, so I solved for T2 but I am unable to solve T1.

For T2, I set m2g-T2 = m2a
(19.5)(9.8) - T2 = (19.5)(1.97)
T2 = 152.6 N

For T1, I found the x component of acceleration to be 1.97cos35.1 = 1.612 m/s^2
From there I though T1 would be mgsin35.1 but that was wrong. I know I need the acceleration to find T1 (at least I think so) because the question specifically stated the acceleration so it must be used to equate T1 with ma or something like that. Please help!

As for B, I know the moment of inertia of a pulley to be 1/2Mr^2.
Rotational Kinetic energy = 1/2Iw^2 ( I don;t know if this is needed to solve the question)

Please, some guidance for both of the questions would be greatly appreciated!
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  • #2
The values given in the diagram and the problem are different. Why?

T1 - m1g*sinθ = m1a.

And (T2 - T1)*r = I*α where α is the angular acceleration which is equal to a/r.
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  • #3
The diagram I found off the internet has different values because it is not from my actual question. I posted it as a pictorial representation of what my question looks like.

Thank you for T1, it worked :)!

Now to try the second part :)
  • #4
Ok, so I tried the second part

T2 - T1 = Ialpha
152.6N - 117.1 N = I (a/r)
35.5 N = I (1.97/0.225)
4.05 kg*m^2 = I

The answer came out to be wrong :( I don't see why this answer is wrong, it makes sense to me. Any ideas?
  • #5

T2 - T1 = I*α/r. = I*a/r^2
  • #6
T2 - T1 = I*α/r. = I*a/r^2

T2 = 152.6N
T1 = 117.1 N

a = 1.97 m/s^2
r = 0.225m

T2 - T1 = I*a/r^2
152.6 - 117.1 = I (1.97/0.225^2)
35.5 = I (38.9)
0.912 kg*m^2 = I

Thank you :)

1. What is the purpose of using a pulley in this experiment?

The pulley is used to change the direction of the force being applied to the system. In this particular experiment, it allows for the force of gravity to act on the blocks while also allowing them to move in the same direction.

2. How does the angle of the incline affect the motion of the blocks?

The angle of the incline affects the acceleration of the blocks. As the angle increases, the acceleration decreases, and as the angle decreases, the acceleration increases. This is due to the component of the force of gravity acting parallel to the incline, which changes with the angle.

3. What is the relationship between the masses of the blocks and their acceleration?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, the acceleration of the blocks will increase as the mass of the blocks decreases and vice versa.

4. How does the tension in the string change as the blocks move?

The tension in the string remains constant throughout the experiment. This is because the string is inextensible and the force acting on one end of the string is transferred to the other end without any loss of energy.

5. Can the experiment be performed with more than two blocks?

Yes, the experiment can be performed with more than two blocks. However, the acceleration and motion of the blocks will be more complex as the number of blocks increases. The pulley and string setup would also need to be adjusted to accommodate the additional blocks.

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