# Finding the acceleration of an object

• EkosGothika
In summary: Yes, it's like I was told. The problem is I'm still in 9th grade and this is the first time I'm learning Newton's laws so I don't really see what you guys see in this.

## Homework Statement

In the picture:
http://postimg.org/image/6gdkm5vpx/
There is a force (F) pushing the car to the right
The car's mass is M
There are two other objects with masses m1 and m2 that are connected by a cord with no mass.
There is no friction
In terms of m1, m2 and M find the acceleration needed to keep m1 and m2 from falling down.

## Homework Equations

This is the second Newton's law.
The only equation I use is

Fnet=m*a

## The Attempt at a Solution

I have tried doing this by placing the 3 m's (m1, m2 and M) in their respective Cartesian planes to get the forces of each one, but the part I don't quite understand is which forces I have to put in the formula...
I understand that I need to add the masses:
Fnet=(M+m1+m2)*a
and I understand that Fnet consists of the F force that is affecting the car, but what other?
Do I need to use the tension of the cord that holds m1 and m2 together? or all I do is:
F=(M+m1+m2)*a
So the acceleration would be
F/(M+m1+m2)=a ?

I suggest that you begin by analyzing the forces on m2.

Welcome to PF!
EkosGothika said:
or all I do is:
F=(M+m1+m2)*a
So the acceleration would be
F/(M+m1+m2)=a ?

yes

as you say, the only equation you need is F = ma, and the trick is simply which bodies to apply it to
Do I need to use the tension of the cord that holds m1 and m2 together?

yes, and use to it apply F = ma (different F of course!) to the top block and the bottom block (separately) …

what do you get?

(btw, there is another way of doing it, by using the fictitious force in the non-inertial rest frame of the car …

if the car is stationary, in which direction would the "effective gravity" have to be for the two blocks not to slide?)

tiny-tim said:
yes, and use to it apply F = ma (different F of course!) to the top block and the bottom block (separately) …

Well the forces in each mass are:
m2: T(tension) and W (weight)
The tension in this case is equal to the weight which is mass*gravity
So T=m*g
and in m1 the forces are weight, Normal force (I don't know how it's called in English but I hope you understand) and the tension which is m2*g, there is no acceleration in Y so I don't need the weight or normal force.

Do I need to use this information to find the car's acceleration that's needed to keep the masses from falling? or is it just the total of the masses and the external force (F)?

EkosGothika said:

## Homework Statement

In the picture:
http://postimg.org/image/6gdkm5vpx/

It's easier to help if the image is posted directly.

#### Attachments

• image.png
2.6 KB · Views: 488
1 person
SammyS said:

It's easier to help if the image is posted directly.

Yes, I'm sorry but when I previewed the post with the image attached it wouldn't show so I just linked it.

EkosGothika said:
Yes, I'm sorry but when I previewed the post with the image attached it wouldn't show so I just linked it.

Oh, I see you're new here. It can be a bit tricky.

Welcome to PF !
What force is required to accelerate m1 with acceleration, a ?

EkosGothika said:
Well the forces in each mass are:
m2: T(tension) and W (weight)
The tension in this case is equal to the weight which is mass*gravity
So T=m*g
and in m1 the forces are weight, Normal force (I don't know how it's called in English but I hope you understand) and the tension which is m2*g, there is no acceleration in Y so I don't need the weight or normal force.
Good. You found the tension. So what's the acceleration of m1?

Doc Al said:
Good. You found the tension. So what's the acceleration of m1?

That would be T/m=a right?

EkosGothika said:
That would be T/m=a right?
That's right. (I think you mean m1, not m.)

But I still don't understand...
is the acceleration that they are asking for
F/(M+m1+m2)=a?

EkosGothika said:
But I still don't understand...
is the acceleration that they are asking for
F/(M+m1+m2)=a?
Are you sure you are posting the problem exactly as given, word for word?

The problem seems a bit over specified. Given the constraints, you should be able to find both the acceleration and the force F in terms of the masses.

Doc Al said:
Are you sure you are posting the problem exactly as given, word for word?

The problem seems a bit over specified. Given the constraints, you should be able to find both the acceleration and the force F in terms of the masses.

Yes, it's like I was told.
The problem is I'm still in 9th grade and this is the first time I'm learning Newton's laws so I don't really see what you guys see in this.
How do I find them, this is still unclear, is my answer correct or not?

EkosGothika said:
Yes, it's like I was told.
The problem is I'm still in 9th grade and this is the first time I'm learning Newton's laws so I don't really see what you guys see in this.
How do I find them, this is still unclear, is my answer correct or not?
It's true in a trivial sense. Given the force, the acceleration must equal what you claim. But they ask for the acceleration in terms of the masses, not the force F (presumably unknown). So I do not think that's the answer they want.

I'm guessing that the instructor meant this as a two part question:
(1) What's the acceleration? (In terms of the masses, not the force F.) You already solved that!
(2) What's the force F needed to produce that acceleration?

So far, it seems you were asked question 1.

This is a tricky question--you are doing great!

1 person
Hi EkosGothika!
EkosGothika said:
Well the forces in each mass are:
m2: T(tension) and W (weight)
The tension in this case is equal to the weight which is mass*gravity
So T=m2*g

Correct.
and in m1 the forces are weight, Normal force (I don't know how it's called in English but I hope you understand) and the tension which is m2*g, there is no acceleration in Y so I don't need the weight or normal force.

Correct.

So your F = ma equation for the X direction is … ?

(if you just keep going, i think you'll find the final answer is simpler than you thought! )

(and yes, we do call it the normal force, or the normal reaction force)

## 1. 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.

## 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 units are used to measure acceleration?

The SI unit for acceleration is meters per second squared (m/s²). Other commonly used units are kilometers per hour squared (km/h²) and miles per hour squared (mi/h²).

## 4. What factors affect an object's acceleration?

Acceleration is affected by the force applied to an object and its mass. The greater the force, the greater the acceleration. Similarly, the greater the mass, the smaller the acceleration.

## 5. How does acceleration relate to motion?

Acceleration is a measure of how quickly an object's velocity changes. If an object is accelerating, it is either speeding up, slowing down, or changing direction. If an object has a constant acceleration, it will have a linear change in velocity over time, resulting in either a constant increase or decrease in speed.

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