# How is the acceleration proportional to the removed force?

• B
• Mr.Husky
In summary: In the first equation, they are including the mass and the velocity of the object. The momentum is equal to the product of the mass and the velocity. Thanks Scott for helping me! In the first equation, they are including the mass and the velocity of the object. The momentum is equal to the product of the mass and the velocity.
Mr.Husky
Gold Member

Image above is the question. Below image depicts solution.

if F1 is removed then the acceleration of that mass must be sum of accelerations of remaining forces. Right??
But answer says that acceleration of that mass is equal to acceleration of F1. I don't understand it. Can someone explain it??

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Ganesh Mammu said:
But answer says that acceleration of that mass is equal to acceleration of F1. I don't understand it. Can someone explain it??
If initial acceleration is 0 and you remove a force F, then the acceleration is -F/m (opposite to the removed force).

Mr.Husky
The sum of the remaining forces must be -F1, otherwise the mass would have been accelerating before F1 was removed.
If you include the direction in the acceleration, it is A=-F/m.

Mr.Husky
.Scott said:
The sum of the remaining forces must be -F1, otherwise the mass would have been accelerating before F1 was removed.
I don't like their answer. In should be a=-F1/m.
Oh I got it. It is just a typo. Right??

A.T. said:
If initial acceleration is 0 and you remove a force F, then the acceleration is -F/m (opposite to the removed force).

Ganesh Mammu said:
Oh I got it. It is just a typo. Right??
No. They are not including the direction vector. Note the F1 with and without the direction arrow on top.

Mr.Husky
.Scott said:
No. They are not including the direction vector. Note the F1 with and without the direction arrow on top.
I forget about the vector notation. Sorry for it.
By the way I also have another example can you explain it??
What I don't understand in the following example is how did they got to know that the total force exerted must be equal to the weight of y part resting on table+ force due to the momentum imparted

By the way the text I am using is prepared by my school and is it worth going through these types of questions (there are about 300 of them per chapter) ??
Can you compare the difficulty of questions of this book to kleppner kolenkow classical mechanics book?

Ganesh Mammu said:
What I don't understand in the following example is how did they got to know that the total force exerted must be equal to the weight of y part resting on table+ force due to the momentum imparted
If I throw a link against the wall, it will exert a momentary force on the wall.
If I throw a link onto a table, it will exert a momentary force and then come to rest on the table.
A link resting on the table exerts a downward force on the table.

Regarding the Physics books: It's been decades since I took a Physics course.

Mr.Husky
.Scott said:
If I throw a link against the wall, it will exert a momentary force on the wall.
If I throw a link onto a table, it will exert a momentary force and then come to rest on the table.
A link resting on the table exerts a downward force on the table.

Regarding the Physics books: It's been decades since I took a Physics course.
Now I am slowly understanding the answer.
Can you rate difficulty of the questions generally??

It would be on par for introductory Physics - either High School or College PH101.

Can anybody compare the difficulty of the question to that of kleppner and kolenkow. Because I am not sure whether to go on with this book or should I change to kk which explains theory brilliantly.

.Scott said:
If I throw a link against the wall, it will exert a momentary force on the wall.
If I throw a link onto a table, it will exert a momentary force and then come to rest on the table.
A link resting on the table exerts a downward force on the table.

Regarding the Physics books: It's been decades since I took a Physics course.
Scott can you explain how they got the momentum in the first equation. And also why did they considered momentum rather than downward force??

Ganesh Mammu said:
Scott can you explain how they got the momentum in the first equation. And also why did they considered momentum rather than downward force??
Thanks Scott for helping me!

## 1. How is acceleration related to the removed force?

According to Newton's Second Law of Motion, acceleration is directly proportional to the net force acting on an object. This means that if the force acting on an object is increased, its acceleration will also increase. Similarly, if the force is removed or decreased, the acceleration will also decrease.

## 2. What is the mathematical relationship between acceleration and removed force?

The mathematical relationship between acceleration and removed force is given by the equation F = ma, where F represents the net force, m represents the mass of the object, and a represents the acceleration. This equation shows that as the force is removed, the acceleration will decrease proportionally.

## 3. How does the acceleration change when the force is removed?

When the force acting on an object is removed, the acceleration will decrease. This is because there is no longer a net force acting on the object to cause it to accelerate. The object will continue to move at a constant velocity or come to a stop, depending on the initial velocity and the magnitude of the removed force.

## 4. Is there a limit to how much the acceleration can change when the force is removed?

Yes, there is a limit to how much the acceleration can change when the force is removed. This is because the mass of the object also plays a role in determining the acceleration. The greater the mass of the object, the smaller the change in acceleration will be when a force is removed.

## 5. Can the acceleration be greater than the removed force?

No, the acceleration cannot be greater than the removed force. This is because acceleration is directly proportional to the force, meaning that the acceleration will always be smaller or equal to the force acting on the object. If the acceleration were to be greater than the force, it would violate Newton's Second Law of Motion.

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