Center of Mass - Man on Boat Homework help

In summary, a man with mass m1 = 55 kg stands at the left end of a uniform boat with mass m2 = 175 kg and a length L = 2.7 m. If the man now walks to the right edge of the boat, his new location is 2.054 m from his original location. After walking to the right edge of the boat, the man has moved 2.054 m from his original location. If the man now walks to the very center of the boat, his new location is at 1.027 m from his original location.
  • #1
Lydia5
4
0

Homework Statement


A man with mass m1 = 55 kg stands at the left end of a uniform boat with mass m2 = 175 kg and a length L = 2.7 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water.
1) What is the location of the center of mass of the system? 1.027m
2) If the man now walks to the right edge of the boat, what is the location of the center of mass of the system? 1.027m
3) After walking to the right edge of the boat, how far has the man moved from his original location? (What is his new location?) 2.054m
4)After the man walks to the right edge of the boat, what is the new location the center of the boat?
5) Now the man walks to the very center of the boat. At what location does the man end up?

Homework Equations


(m1x1 + m2x2..+mnxn)/(m1+m2...+mn)

The Attempt at a Solution


I have calculated the answers for 1, 2, and 3. However, I have not been able to answer questions 4 and 5. Any help would be nice!
 
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  • #2
Hey, I think you will want to double check your answers. Without doing any calculations you can see something is off; considering the man moves position between part 1 and 2 yet the location of center of mass stays the same according to what you have written? Is the boat moving for part 3? Please include all information given in the question or possibly a picture of it.
 
  • #3
manonboat.png

This is the image and according to the online homework checker these 3 answers of mine are right. And since there is 0 net force acting on the body it stays same on both edges. Also, for part 3 the boat is moving to the left and I am asked to find where the man moves relative to this specific coordinate system.
 
  • #4
How fast does the problem state that the boat is moving, which direction is it moving in, is the boat only moving in the latter parts of the problem? In your original post you only state the length/mass of boat and position of the man/his mass relative to the boat, it seems some information is omitted.

Sometimes when we paraphrase things we forget to include information critical to the problem. If you could give the problem exactly as it is written figuring out the problem will be much smoother.
 
  • #5
Chillguy said:
How fast does the problem state that the boat is moving, which direction is it moving in, is the boat only moving in the latter parts of the problem? In your original post you only state the length/mass of boat and position of the man/his mass relative to the boat, it seems some information is omitted.

Sometimes when we paraphrase things we forget to include information critical to the problem. If you could give the problem exactly as it is written figuring out the problem will be much smoother.

None of this is included in the problem. I copied and pasted the full problem as it was.
 
  • #6
Lydia5 said:
Also, for part 3 the boat is moving to the left and I am asked to find where the man moves relative to this specific coordinate system.

What is the information given about the movement, only that it is moving left?
 
  • #7
Yes, that's it. And I've done number 4 now so the only one left to do is number 5!
 
  • #8
A post on how it was done would be great =)!
 

1. What is the center of mass and why is it important?

The center of mass is the point at which the mass of an object or system is evenly distributed in all directions. It is important because it helps us understand how an object or system will behave under different forces, and it also helps us determine the stability and balance of an object.

2. How is the center of mass calculated for a man on a boat?

The center of mass for a man on a boat can be calculated by finding the individual center of mass for the man and the boat separately, and then using the principle of superposition to find the overall center of mass of the system. This is done by multiplying the mass of each object by its respective distance from a chosen reference point, and then dividing the sum of these products by the total mass of the system.

3. What factors can affect the center of mass for a man on a boat?

The center of mass for a man on a boat can be affected by the position and weight of the man, the shape and weight distribution of the boat, and any external forces acting on the system such as wind or waves. Additionally, the movement of the man or the boat can also change the center of mass.

4. How does the center of mass affect the stability of a man on a boat?

The stability of a man on a boat is directly affected by the location of the center of mass. If the center of mass is above the boat's center of buoyancy, the system will be unstable and more prone to tipping over. If the center of mass is below the boat's center of buoyancy, the system will be stable and less likely to capsize.

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

Yes, the center of mass can be outside of the physical object. This is often the case for asymmetrical objects or objects with irregular shapes. The center of mass is a theoretical point and does not have to be located within the physical boundaries of the object.

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