# Quick forces conceptual question

• bcjochim07
In summary, the conversation discusses finding an expression for the acceleration of m1 in a double pulley problem. The sum of forces for m1 and m2 are given, with a question raised about the tension in the rope. It is clarified that as long as the rope and pulley are massless and frictionless, the tension is the same throughout the rope.
bcjochim07

## Homework Statement

Find an expression for the acceleration of m1.

## The Attempt at a Solution

I did this earlier, and looking back on it I have a question:

Sum of forces for m1:
Fx= F2 on 1= m1a1

Sum of forces for m2:
Fy = F1 on 2 + T1 - m2g = m2a2

I got the expression after substituting them into each other and saying a2 = -.5a1, I'm just wondering why you can say T1= F1 on 2 , because since there is acceleration, can you consider the tension throughout the rope to be the same?

It's a double pulley problem with m1 sitting on a table, attached to a rope that goes around a pulley at the edge of the table. Then the string passes through another pulley attached to the top of a suspended m2. Then the rope goes up and is attached to a ceiling.

bcjochim07 said:
Sum of forces for m1:
Fx= F2 on 1= m1a1
The only horizontal force on m1 is the rope tension T.

Sum of forces for m2:
Fy = F1 on 2 + T1 - m2g = m2a2
Careful. The tension force pulls up twice on m2 (via the pulley).

I got the expression after substituting them into each other and saying a2 = -.5a1, I'm just wondering why you can say T1= F1 on 2 , because since there is acceleration, can you consider the tension throughout the rope to be the same?
As long as the rope is massless and the pulley is massless and frictionless, then the tension is the same throughout the rope.

## 1. What is a quick force?

A quick force is a force that acts on an object for a short period of time. It can cause a sudden and rapid change in an object's velocity or shape.

## 2. How is a quick force different from a constant force?

A quick force has a shorter duration and typically has a larger magnitude compared to a constant force. A constant force acts on an object continuously, while a quick force only acts for a brief moment.

## 3. What are some examples of quick forces?

Examples of quick forces include a hammer hitting a nail, a ball being kicked, or a car crashing into a wall. These forces occur suddenly and have a short duration of action.

## 4. How does Newton's second law apply to quick forces?

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Quick forces can cause a large acceleration on an object due to their short duration and large magnitude.

## 5. How do quick forces affect an object's momentum?

Quick forces can cause a sudden change in an object's momentum. If the force is in the same direction as the object's initial velocity, it will increase the momentum. If the force is in the opposite direction, it will decrease the momentum. Quick forces can also change the direction of an object's momentum, causing it to change direction or turn.

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