# A center of mass problem

• alyafey22
In summary, the boat and person are in a system with negligible friction between them. If the person moves a certain distance, the center of mass of the system will change in position, but the boat is not required to move. However, if the boat does move, it will move the same distance as the person in order to maintain the same center of mass. This is because the boat and person have the same mass and any movement of one will affect the center of mass.

#### alyafey22

Gold Member
MHB
If someone is on a boat that rests in a placid river with negligible friction between the boat and the river ,, suppose that person moves a certain distance ,Does that boat move as well , if so why ?

alyafey22 said:
If someone is on a boat that rests in a placid river with negligible friction between the boat and the river ,, suppose that person moves a certain distance ,Does that boat move as well , if so why ?
What do you think?

Doc Al said:
What do you think?
I think it will not move

alyafey22 said:
I think it will not move
So what happens to the center of mass of the boat+person system?

well ,, if the person moves for a certain distance , surely the center of mass will change in position ,but does that mean the boat has to move ?!

Can the center of mass of the system change? What is required for such a change?

yes it can ,, if we change the positions of the particles of that system with respect to a specified reference point .

alyafey22 said:
yes it can ,, if we change the positions of the particles of that system with respect to a specified reference point .
What is required to change the center of mass of a system that is at rest?

an external force .

alyafey22 said:
an external force .
Right! Note that the problem states "negligible friction between the boat and the river". So what must be true about the center of mass of this system?

Doc Al said:
So what must be true about the center of mass of this system?

it will stay the same before and after the movement of the man .

alyafey22 said:
it will stay the same before and after the movement of the man .
Exactly. So, if the man moves a distance X closer to shore (say), how can you figure out how much the boat must move in order that the center of mass of the system stay put?

Doc Al said:
Exactly. So, if the man moves a distance X closer to shore (say), how can you figure out how much the boat must move in order that the center of mass of the system stay put?

so the boat will move the same x-displacement as the man in order to maintain the same center of mass of the system .

alyafey22 said:
so the boat will move the same x-displacement as the man in order to maintain the same center of mass of the system .
Why would you think that? Are they the same mass?

Doc Al said:
Why would you think that? Are they the same mass?

there is a problem here because if the boat moves, the man as well will move .

alyafey22 said:
there is a problem here because if the boat moves, the man as well will move .
Of course. So?

If the boat moves a certain distance to the left, how far must the man move? (Note that if you measure the man's movement with respect to the boat, then you have to add the movement of the boat to find his movement with respect to the shore.)

Doc Al said:
Of course. So?

If the boat moves a certain distance to the left, how far must the man move? (Note that if you measure the man's movement with respect to the boat, then you have to add the movement of the boat to find his movement with respect to the shore.)

you mean if the man moves towards the right , so he is getting closer to the shore, the boat will move in the opposite direction (to the left ).

alyafey22 said:
you mean if the man moves towards the right , so he is getting closer to the shore, the boat will move in the opposite direction (to the left ).
Sure. How else can the center of mass remain the same distance to shore?

## 1. What is a center of mass problem?

A center of mass problem refers to a physics problem in which you must determine the location of the center of mass of an object or system. The center of mass is the point at which the mass of the object or system is evenly distributed.

## 2. Why is the center of mass important?

The center of mass is important because it is used to describe the overall motion and stability of an object or system. It is also used in calculations related to forces and torques.

## 3. How is the center of mass calculated?

The center of mass is calculated by finding the weighted average of the positions of all the individual particles that make up the object or system. This can be done using the formula: xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn), where xcm is the coordinate of the center of mass, mi is the mass of each particle, and xi is the position of each particle along a specific axis.

## 4. What factors can affect the center of mass?

The center of mass can be affected by changes in the distribution of mass within an object or system, as well as external forces acting on the object or system. For example, if a person lifts one leg while standing, their center of mass will shift towards the leg that is still on the ground.

## 5. How is the center of mass used in real-world applications?

The concept of center of mass is used in various real-world applications, such as designing stable structures and vehicles, calculating the trajectory of projectiles, and understanding the motion of celestial bodies. It is also used in sports, such as diving and gymnastics, to determine the most efficient movements for maintaining balance and stability.

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