Help- Center of Mass/system of particles problem

In summary, Ricardo and Carmelita, weighing 80 kg and 25 kg respectively, are in a canoe at Lake Merced. They exchange seats, 3.0 m apart and symmetrically located, causing the canoe to move 45 cm relative to a submerged log. Using the fact that the center of mass in a closed system does not change from internal actions, Ricardo calculates Carmelita's mass. This can be done by equating two equations describing the location of the center of mass for the initial and final states.
  • #1
ldh5056
1
0
Hoping someone can help me with this problem:

Ricardo, mass 80 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 25 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and symmetrically located with respect to the canoe's center. Ricardo notices that the canoe moved 45 cm relative to a submerged log during the exchange and calculates Carmelita's mass, which she has not told him. What is it?

Thank you so much!
 
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  • #2
Sorry mis-phrased it. I mean to the say that the center of mass in a closed system does not change from internal actions. What you need to do is write two equations describing the location of the center of the mass for the initial and final states and equate them.
 
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Related to Help- Center of Mass/system of particles problem

1. What is the center of mass/system of particles problem?

The center of mass/system of particles problem is a physics problem that involves determining the overall motion of a system of particles based on their individual positions, velocities, and masses. It is commonly used in fields such as mechanics and astronomy to analyze the motion of large objects composed of many smaller particles.

2. How is the center of mass/system of particles calculated?

The center of mass of a system of particles can be calculated by taking the weighted average of the positions of all the particles, where the weights are given by the masses of the particles. This can be represented mathematically as:

xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)
ycm = (m1y1 + m2y2 + ... + mnyn) / (m1 + m2 + ... + mn)
zcm = (m1z1 + m2z2 + ... + mnzn) / (m1 + m2 + ... + mn)

where xcm, ycm, and zcm represent the coordinates of the center of mass and mx, my, and mz represent the masses and positions of each individual particle.

3. What is the significance of the center of mass/system of particles in physics?

The center of mass is a very important concept in physics because it allows us to simplify the motion of a complex system of particles into a single point. This makes it easier to analyze the overall motion and behavior of the system, as well as predict how it will respond to external forces. It is also crucial in understanding concepts such as torque, rotational motion, and collisions.

4. Can the center of mass/system of particles be located outside of the physical object?

Yes, the center of mass can be located outside of the physical object, especially in irregularly shaped objects. This is because the position of the center of mass is influenced by both the mass and distribution of mass within the object. For example, a thin rod will have its center of mass located at its geometric center, while a hollow sphere will have its center of mass located at its center of volume, which may be outside of the physical object.

5. How does the center of mass/system of particles relate to stability?

The center of mass is closely related to an object's stability. An object will be stable if its center of mass is located within its base of support, which is the area that supports the object's weight. If the center of mass is outside of the base of support, the object will be unstable and may tip over. This is why it is important to consider the center of mass when designing structures or objects to ensure their stability.

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