# Finding the magnitude of the force

• Muthumanimaran
In summary: Did you figure out the common acceleration?In summary, the problem involves finding the magnitude of the force F applied on the larger mass M, which prevents the smaller masses M1 and M2 from moving with respect to M. The pulley is ideal and the reaction force of the pulley on M is considered. The solution involves finding the common acceleration of the system and drawing free body diagrams for each mass.
Muthumanimaran

## Homework Statement

A force F is applied on the bigger mass 'M', which results in the prevention of smaller masses M1 and M2 moving with respect to larger mass M. The mass 'M' slides smoothly on the frictionless surface. Find the magnitude of the force. The pulley is ideal also consider the reaction force of pulley onto mass 'M'.

## The Attempt at a Solution

The normal force on the pulley is
$$R=2T \sin(\frac{\pi}{4})$$
The force on the system is
$$F=F_{1}+F_{2}+F_{3}$$
F1, F2, F3 are the forces on the masses M, M1 and M2 respectively.

The force F1
$$F_{1}=Ma-R\cos(\frac{\pi}{4})$$
$$F_{2}=M_{1}a$$
$$F_{3}=M_{2}a$$

If the masses M1 and M2 are at rest
$$T=M_{1}g$$
$$M_{2}a=M_{1}g$$

The force on the system is

$$F=(M+M_{1}+M_{2})\frac{M_{1}}{M_{2}}g-2M_{1}g\sin(\frac{\pi}{4})\cos(\frac{\pi}{4})$$
or
$$F=(M+M_{1})\frac{M_{1}}{M_{2}}g$$

I don't know whether my solution is correct. If I made an error, please give me a hint.

#### Attachments

• problem.png
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It looks like you are guessing the magnitudes of forces instead of drawing free body diagrams for each mass. For example, why is this ##R=2T \sin(\frac{\pi}{4})## true?
If the three masses move together as one, then you should start by finding their common acceleration. Then draw FBDs for the masses. Also, do you think that mass M1 is hanging vertically down as it accelerates to the right? What force (or component thereof) would provide the horizontal acceleration?

kuruman said:
It looks like you are guessing the magnitudes of forces instead of drawing free body diagrams for each mass. For example, why is this ##R=2T \sin(\frac{\pi}{4})## true?
If the three masses move together as one, then you should start by finding their common acceleration. Then draw FBDs for the masses. Also, do you think that mass M1 is hanging vertically down as it accelerates to the right? What force (or component thereof) would provide the horizontal acceleration?

#### Attachments

• WhatsApp Image 2017-10-04 at 17.04.48.jpeg
26.3 KB · Views: 506
There is nothing in the original drawing that says the angle is π/4, but OK we will set that aside. What about the other issues I raised in my previous post? Did you draw the FBDs?

## 1. What is the definition of "magnitude of the force"?

The magnitude of the force is the measure of the strength of a force. It is a scalar quantity, meaning it only has a magnitude and not a direction.

## 2. How is the magnitude of the force calculated?

The magnitude of the force can be calculated using the equation F=ma, where F is the force, m is the mass of the object, and a is the acceleration.

## 3. What are the units for measuring the magnitude of the force?

The units for measuring the magnitude of the force depend on the system of measurement being used. In the International System of Units (SI), the unit for force is Newton (N), while in the imperial system, the unit is pound (lb).

## 4. How does the direction of the force affect its magnitude?

The direction of the force does not affect its magnitude, as it is a scalar quantity. However, the direction is important in determining the overall effect of the force on an object.

## 5. Can the magnitude of the force be negative?

Yes, the magnitude of the force can be negative. This indicates that the force is acting in the opposite direction of the chosen positive direction. However, when using the equation F=ma, the magnitude is always positive as acceleration is a vector quantity and cannot be negative.

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