Center of mass question (man on a boat)

In summary, the conversation discusses a problem involving a man standing on a boat and the location of the boat's center of mass after the man moves to the right edge of the boat. The equation for finding the center of mass is used, but there is confusion about the interpretation of the term "absolute position" and the origin against which positions are measured. The problem is not clearly worded, which may be causing confusion for the person trying to solve it. There is also a potential error in the online platform being used to solve the problem.
  • #1
ddtozone
8
0

Homework Statement



A man with mass m1 = 60 kg stands at the left end of a uniform boat with mass m2 = 169 kg and a length L = 2.7 m. Positive x is pointing to the right. Assume there is no friction or drag between the boat and water. After the man walks to the right edge of the boat, what is the new location the center of the boat?
(The boat lies on the x-axis, so they're looking for the absolute position of the center.

Homework Equations



X=(m1x1+m2x2)/(m1+m2)
The absolute location of the CM will not change.

The Attempt at a Solution


First the CM equation (169*1.35)/(169+60) gives me x = 1 (relative to the boat) as the position of the center of mass, which I use as a reference point for the x-axis.
When the man moves to the right, I plug in (60*2.7+169*1.35)/(169+60) and I get x = 1.7 relative to the boat. Since the center has moved to the left, I do 1.7 - 1 = 0.7 to find the distance the center has gone. Finally I subtract that change in distance from the original position with 1.35 - 0.7 = 0.65. But SmartPhysics says this is wrong. Does someone have any further insight here? Thank you!
 
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  • #2
ddtozone said:
A man with mass m1 = 60 kg stands at the left end of a uniform boat with mass m2 = 169 kg and a length L = 2.7 m. Positive x is pointing to the right. Assume there is no friction or drag between the boat and water. After the man walks to the right edge of the boat, what is the new location the center of the boat?
(The boat lies on the x-axis, so they're looking for the absolute position of the center.

The question doesn't provide an origin against which positions are to be measured, so how is 'absolute position' to be interpreted? Is this the precise and complete wording of the problem?
 
  • #3
gneill said:
The question doesn't provide an origin against which positions are to be measured, so how is 'absolute position' to be interpreted? Is this the precise and complete wording of the problem?

because this is a question with multiple parts, and the answers to the first parts are based on the reference points of the boat's initial position, with the left of the boat starting at x=0. I guess there's a chance that SmartPhysics has an error, but I'm completely stumped.
 
Last edited:

1. What is the center of mass?

The center of mass is a point in an object or system that represents the average location of all the mass in that object or system. It is the point at which the object can be balanced with equal weights on either side.

2. 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 in an object or system. This is done by multiplying the mass of each particle by its position and then dividing by the total mass of the object or system.

3. Why is the center of mass important?

The center of mass is important because it is the point where the entire weight of an object or system can be considered to act. This is particularly useful for understanding the motion and stability of objects, such as a man on a boat.

4. How does the center of mass change when a person stands on a boat?

When a person stands on a boat, the center of mass of the boat and person together shifts towards the person's location. This is because the person adds more mass to one side of the boat, causing the center of mass to shift towards that side.

5. Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object, especially if the object has a non-uniform mass distribution. For example, in a hollow cylinder, the center of mass is located at the empty space in the middle of the cylinder.

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