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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?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 ?
I think it will not moveDoc Al said:What do you think?
So what happens to the center of mass of the boat+person system?alyafey22 said:I think it will not move
What is required to change the center of mass of a system that is at rest?alyafey22 said:yes it can ,, if we change the positions of the particles of that system with respect to a specified reference point .
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?alyafey22 said:an external force .
Doc Al said:So what must be true about the center of mass of this system?
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?alyafey22 said:it will stay the same before and after the movement of the man .
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?
Why would you think that? Are they the same mass?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 .
Doc Al said:Why would you think that? Are they the same mass?
Of course. So?alyafey22 said:there is a problem here because if the boat moves, the man as well will move .
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.)
Sure. How else can the center of mass remain the same distance to shore?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 ).
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.
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.
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: x_{cm} = (m_{1}x_{1} + m_{2}x_{2} + ... + m_{n}x_{n}) / (m_{1} + m_{2} + ... + m_{n}), where x_{cm} is the coordinate of the center of mass, m_{i} is the mass of each particle, and x_{i} is the position of each particle along a specific axis.
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.
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.