# Mechanics problem -- a mass on a table that can freely move on wheels

• Clara Chung
In summary, the conversation discusses a problem involving a point-like body with mass m1 placed on a table that can move on wheels with a static friction coefficient of u=0.3. The question asks for the maximum horizontal acceleration the table can have before the body starts moving with respect to it. In the second part, the body is attached to a massless and frictionless rope, which turns around a frictionless pulley and holds another body with mass m2. The forces acting on the system are calculated in the reference frame of the table, and the maximum acceleration is determined in the direction opposite to m2, neglecting the change in the angle of the string. The equations used are um1g = mtable atable and
Clara Chung

## Homework Statement

A point like body with mass m1 is placed on top of a table, that can freely move on wheels with respect to the ground. There is a static friction coefficient of u=0.3 between the body and the table. If the body is subject to the gravitational acceleration g, what is the maximal horizontal acceleration that the table can have, before the body start moving with respect to it?

Consider now the case of where the body is attached to a horizontal massless and frictionless rope. This rope turns around a frictionless pulley placed at the side of the table, and below it hangs another body with mass m2. Calculate the forces acting on the system in the reference frame of the table. Calculate the maximum acceleration (in the direction opposite to m2) that the table can stand before the masses start to move, neglecting the change in the angle of the string supporting m2.

## Homework Equations

The answer of the first part is um1. The answer of the second part is a=(m2-um1)/(m1+m2).

## The Attempt at a Solution

I have no idea how to do both parts of the questions. I want to solve the first part first. I attempted to solve the question by equating um1g = mtable atable, because the friction force is equal to the force m1 acting on the table. Without the mass of the table, how can I know its acceleration?

The mass of the table does not matter. When the table accelerates, you are applying whatever force is needed.
If you still think the mass of the table matters, take it to be zero.

Clara Chung
You do not need to know the mass of the table. However, you do need that the acceleration of the mass is the same as that of the table and you need to compare that with the maximal possible force that can be provided by the friction.

Clara Chung
Shouldn't it be um1g=m1a
so a=ug?

Clara Chung said:
Shouldn't it be um1g=m1a
so a=ug?

Where did you get the answer ##a_{max} = um_1##?

PS The dimensions are wrong, for one thing.

PPS Same for part b). The dimensions are wrong there too.

Last edited:

## 1. How do the wheels affect the movement of the mass on the table?

The wheels reduce the friction between the table and the mass, allowing it to move more easily. They also provide a smooth surface for the mass to roll on, instead of sliding or dragging.

## 2. What factors affect the acceleration of the mass on the table?

The acceleration of the mass is affected by the mass of the object, the force applied to it, and the amount of friction between the wheels and the table. The angle of the surface and any external forces, such as air resistance, can also affect the acceleration.

## 3. How does the surface of the table impact the movement of the mass?

The surface of the table can affect the movement of the mass by providing more or less friction. A smooth surface with low friction will allow the mass to move more easily, while a rough surface with high friction will make it more difficult for the mass to move.

## 4. Can the mass on the table reach a constant velocity?

Yes, if there is no external force acting on the mass, it can reach a constant velocity. However, if there is friction present, the mass will eventually come to a stop due to the force of friction opposing its motion.

## 5. How can the velocity and acceleration of the mass be calculated?

The velocity of the mass can be calculated by dividing the distance traveled by the time it took to travel that distance. The acceleration can be calculated by dividing the change in velocity by the change in time. Both velocity and acceleration can also be calculated using equations from Newton's laws of motion.

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