# What is the acceleration of each block?

• siimplyabi
In summary, the conversation discusses the approach to solving a physics problem involving two blocks connected by a rope on a frictionless surface. The solution involves finding the net accelerating force on the pair by subtracting the individual forces of each block and then dividing by the combined mass. The conversation also touches on the role of masses in generating force and acting as the denominator in finding net force. The concept of "canceling out" the masses is clarified as subtracting the masses in the first role and adding them in the second role.
siimplyabi
1. The
problem statement, all variables and given/known data

A pair of blocks are connected by a massless rope and placed on a frictionless surface. The diagram shows the situation at the instant the blocks are released. The left side has a mass of 35 kg and an incline of 25 degrees to the horizontal. The right side has a mass of 20 kg and an incline of 40 degrees to the horizontal.

[/B]

## The Attempt at a Solution

My attempt was solving each blocks acceleration by doing
Σf(+x)= Fgsin(theta)=ma
fg = mg there fore mgsin(theta)=ma
the masses cancel out leaving
gsin(theta)=a
so acc of block 1 =
(9.8m/s^2)(sin(25))=4.142 m/s^2

Should I not be canceling the masses out?

Would a better approach be taking mgsin(25)-mgsin(40)/55 = 0.345s?

The two blocks have to have the same acceleration because of the rope.

Work out the net accelerating force on the pair as the difference between the accel forces on each block - since they are pulling in opposite directions.

Then divide by the combined mass.

andrewkirk said:
The two blocks have to have the same acceleration because of the rope.

Work out the net accelerating force on the pair as the difference between the accel forces on each block - since they are pulling in opposite directions.

Then divide by the combined mass.
So, You're saying

a = m1gsin(theta)-m(ofblock2)gsin(theta)/m(of blk1)+m(blk2) would be the correct approach.

Could you be able to tell me when it would be appropriate to cancel out the masses? in the mgsin(theta) or mgcos(theta)= ma equation only leaving gsin(theta)= a ?

siimplyabi said:
So, You're saying

a = m1gsin(theta)-m(ofblock2)gsin(theta)/m(of blk1)+m(blk2) would be the correct approach.

Could you be able to tell me when it would be appropriate to cancel out the masses? in the mgsin(theta) or mgcos(theta)= ma equation only leaving gsin(theta)= a ?
Also, thank you for your response. I appreciate it.

I'm afraid I don't know what you mean by 'cancel out the masses'. The masses have two different roles in such setups. First, they generate force, via gravity. Second, they are the denominator by which one divides the net force.

In this case, the contributions of the two masses are subtracted in the first role (after adjusting for the different angles) and added in the second role.

andrewkirk said:
I'm afraid I don't know what you mean by 'cancel out the masses'. The masses have two different roles in such setups. First, they generate force, via gravity. Second, they are the denominator by which one divides the net force.

In this case, the contributions of the two masses are subtracted in the first role (after adjusting for the different angles) and added in the second role.

Okay, thank you. I understand what you're telling me. I was just curious as to why I have seen some people refer to canceling out the masses when looking for acceleration of one object. But you've answered my question so thanks!

## 1. What is acceleration?

Acceleration is the rate of change of velocity over time. It is a measure of how quickly an object's velocity is changing.

## 2. How do you calculate acceleration?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## 3. What is the unit of acceleration?

The unit of acceleration is meters per second squared (m/s^2) or feet per second squared (ft/s^2) in the metric and imperial systems, respectively.

## 4. How is acceleration related to force?

Acceleration is directly proportional to force, according to Newton's second law of motion. This means that the greater the force applied to an object, the greater its acceleration will be. The relationship can be expressed as F = ma, where F is force, m is mass, and a is acceleration.

## 5. Can an object have a negative acceleration?

Yes, an object can have a negative acceleration, also known as deceleration. This means that the object's velocity is decreasing over time. It can occur when an object is slowing down or moving in the opposite direction of its initial velocity.

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