# What are the accelerations of the blocks?

• Vitani11
In summary: In this problem, it makes no difference.For the 1st mass, the forces are ##m_1g## down and ##T_1## up, pick "up=positive" and write ##T_1-m_1g = m_1a## call it eq(1).For the 2nd mass, the forces are ##m_2g## down and ##T_2## up, pick "up=positive" and write ##T_2-m_2g = m_2a## call it eq(2).For the pulley, the forces are ##F_p## down and ##T_p## up, pick "up=positive" and write ##
Vitani11

## Homework Statement

Two blocks of mass m1 = 0.500kg and m2 = 0.510kg are connected by a string that passes over a pulley with frictionless bearings. The pulley is a uniform 0.050kg disk with a radius of 0.04m. Assume that the string is massless and inextensible and that it does not slip on the pulley.

a. What are the accelerations of the blocks?

b. What is the tension in the string between block 1 and the pulley? Block 2 and the pulley? By how much do these tensions differ?

c. If the pulley were massless, what would your answers for a) and b) be?

## Homework Equations

T1 = tension in string attached to mass 1
T2 = tension in string attached to mass 2
m1 = 0.500kg mass of mass 1
m2 = 0.510kg mass of mass 2
m3 = 0.050kg mass of pulley
r = 0.04m radius of pulley
I = 1/2MR^2 moment of inertia for pulley
alpha = angular acceleration of pulley

## The Attempt at a Solution

I set up three equations using force diagrams. For mass 1 I have T1 = m1a. For mass two I have T2 = m2a. For the pulley I used Torque = (1/2)MR^2 * alpha = rF where there are two cases of F being T1 or being T2.

I'm not sure what to do about finding the acceleration. I would like help with the a) but if you can help with b) that would be greatly appreciated.

My solution for a) is a=2T1/m3 for mass one which is obviously wrong. I got the same for mass two.

#### Attachments

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Your diagram shows both blocks on a horizontal surface, with the pulley between them.
So how would anything be in motion at all?

Could it be that one or both blocks should be acted on by gravity?
ie. neither are sitting on a surface?

Your approach to free body diagrams needs to be revised: for instance, make sure you pice a direction to count as positive. Newton's law is ##\sum \vec F = m\vec a## Not ##\sum F = T-ma = 0##. (ma is the result of an unbalanced force, not a force itself).

Vitani11
Simon Bridge said:
Your diagram shows both blocks on a horizontal surface, with the pulley between them.
So how would anything be in motion at all?

Could it be that one or both blocks should be acted on by gravity?
ie. neither are sitting on a surface?

Your approach to free body diagrams needs to be revised: for instance, make sure you pice a direction to count as positive. Newton's law is ##\sum \vec F = m\vec a## Not ##\sum F = T-ma = 0##. (ma is the result of an unbalanced force, not a force itself).
They're literally both as the diagram says unless you can interpret the problem statement differently. I also didn't understand how they could be moving but I figured this is what had to be going on since they're accelerating

Vitani11 said:
They're literally both as the diagram says unless you can interpret the problem statement differently. I also didn't understand how they could be moving but I figured this is what had to be going on since they're accelerating
In fact now that I think of it you're likely correct in saying gravity would come into play because that's all general physics one was about. My professor is not so explicit - sorry for the ambiguity.

Okay so it is a typical Atwood machine just with a mass and so torque for the pulley... still sort of stuck

Vitani11 said:
Okay so it is a typical Atwood machine just with a mass and so torque for the pulley... still sort of stuck
That's what I thought ... generally when things are supposed to be sitting on a surface, the problem statement will say that in pretty much those words. When they hang by a string that passes over a pulley, it's usually an Atwood machine.

You go through the free body diagrams as usual - remember to pick a direction for positive, be careful to consistently link the equations.
ie. if m1 is on the left and m2 on the right of the pulley, then the pulley will rotate which way?

I'll start you off:
For the 1st mass, the forces are ##m_1g## down and ##T_1## up, pick "up=positive" and write ##T_1-m_1g = m_1a## call it eq(1).
(Since the string does not stretch, both masses have the same magnitude acceleration.)
You will need a similar equation for the other mass and the pulley.
You can save some work by thoughtful selection of which way to call "positive".

## What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

## What are the units of acceleration?

The units of acceleration are typically meters per second squared (m/s^2) in the International System of Units (SI).

## How is acceleration calculated?

Acceleration can be calculated by dividing the change in an object's velocity by the time it takes for that change to occur, using the formula a = (vf - vi)/t, where a is acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval.

## What factors affect the acceleration of an object?

The acceleration of an object can be affected by factors such as the object's mass, the force applied to it, and any external forces acting upon it (such as friction or air resistance).

## How does acceleration differ from velocity?

Velocity is the rate of change of an object's position, while acceleration is the rate of change of an object's velocity. In other words, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how quickly its speed and/or direction are changing.

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