Centre of mass - board on ice

In summary, a person of mass M standing on a board of mass m and length l, resting on a frictionless ice surface with uniform mass distribution, walks to the center of the board and stops. The center of mass of the person-board system does not move with respect to the ice, as there are no external forces acting on the system. However, the center of mass does shift with respect to the board.
  • #1
Werg22
1,431
1

Homework Statement



A person of mass M is standing at one end of a board of mass m and length l. The board rests upon frictionless ice surface, and its mass is uniformly distributed along its length. The person now walks to the center of the board and stops. In terms of the given quantities, M, m and l, how far from his starting position relative to the ice surface has he moved? Note that there are no external forces acting on the system, only internal forces.

Homework Equations





The Attempt at a Solution



I am not sure how to determine how the system will move. I have determined where the center of mass of the person-board system is, and I suspect it will enter the solution, but I can't figure anything out at the moment.
 
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  • #2
Will the location of the center of mass with respect to the ice of the "person + board" be affected by the motion of the person?

Will the location of the center of mass with respect to the board of the "person + board" be affected by the motion of the person?
 
  • #3
I am not sure where the difference lies...
 
  • #4
Werg22 said:
I am not sure where the difference lies...
In order for the center of mass to move with respect to the ice, there would have to be some external force on the system. (Since it wasn't moving before the person started walking.) But the ice is frictionless.

But with respect to the board, the center of mass does shift: Calculate the position of the center of mass before and after the person moves to the center.
 
  • #5
So the new position of the board will be so that the position of the center of mass of the person-board system hasn't changed in respect to the ice? I must say I've been acquainted with the concept of center of mass less than 2 hours ago and haven't caught on its intuitive meaning yet.
 
  • #6
Werg22 said:
So the new position of the board will be so that the position of the center of mass of the person-board system hasn't changed in respect to the ice?
That's right.
I must say I've been acquainted with the concept of center of mass less than 2 hours ago and haven't caught on its intuitive meaning yet.
Give it time. (This question's a bit tricky.)
 

1. What is the Centre of Mass?

The Centre of Mass is the point at which the entire mass of a body is considered to be concentrated. It is the point where the body would balance if it were suspended at that point.

2. How is the Centre of Mass calculated?

The Centre of Mass can be calculated by finding the weighted average of the positions of all the particles that make up the body. It can also be determined by balancing the body on a pivot point and finding the point where it is in equilibrium.

3. Why is the Centre of Mass important in regards to a board on ice?

The Centre of Mass is important for a board on ice because it determines the point at which the board will balance. If the Centre of Mass is not over the point of contact between the board and the ice, the board will tip over. This is crucial for maintaining balance and stability while ice skating or playing ice hockey.

4. How does the Centre of Mass affect the movement of a board on ice?

The Centre of Mass affects the movement of a board on ice by determining the direction and speed of its movement. If the Centre of Mass is not aligned with the direction of movement, the board will rotate. The location of the Centre of Mass also affects the amount of friction between the board and the ice, which can impact the speed and control of the board.

5. Can the Centre of Mass be changed on a board on ice?

Yes, the Centre of Mass can be changed on a board on ice by altering the distribution of weight on the board. For example, shifting your body weight forward or backward can change the location of the Centre of Mass. Additionally, adding or removing objects from the board can also change the Centre of Mass.

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