Calculating the Center of Mass for a Dog on a Flatboat

In summary, the dog and boat system has a constant center of mass and the dog's movement towards the shore causes the boat to move away from the shore by the same distance. Using the formula x_cm = m_1 x_1 + m_2 x_2 / m_1 + m_2, with the given masses and distances, it can be determined that the dog is now 10.0 m from the shore.
  • #1
Punchlinegirl
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A dog, with a mass of 12.0 kg, is standing on a flatboat so that he is 25.5 m from the shore. He walks 6.0 m on the boat toward the shore and then stops. The boat has a mass of 46.0 kg. Assuming there is no friction between the boat and the water, how far is the dog from the shore now?
i used [tex] x_cm = m_1 x_1 + m_2 x_2 / m_1 + m_2 [/tex]
x= (12)(25.5) + (46)(6) / 12+46
and got 10.0 m
Which wasn't right.. can someone please help me?
 
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  • #2
The key is that the center of mass of the "boat + dog" system cannot change. So, if the dog ends up X meters closer to shore, how much further from the shore must the boat end up (in terms of X)? Now make use of the fact that you know how far the dog moved with respect to the boat to solve for X. (To help visualize what's going on, pretend the dog was standing on a line painted on the boat. The dog moves toward the shore; the boat--and line--moves away from the shore. But you know how far apart the dog moved from the line.)
 
  • #3
Ok I get it now. Thank you!
 

FAQ: Calculating the Center of Mass for a Dog on a Flatboat

What is the "center of mass problem"?

The center of mass problem refers to the calculation of the point at which the mass of an object can be considered to be concentrated, as if all the mass were located at that single point. It is an important concept in physics, engineering, and other fields.

How is the center of mass calculated?

The center of mass is calculated by taking into account the mass and position of each individual particle or object that makes up the system. The center of mass is then determined using the formula:
xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn) where m is the mass of each object and x is its position in the x-axis (the same applies for the y and z-axis).

Why is the center of mass important?

The center of mass is important because it helps us understand the overall behavior of a system. It can be used to determine the stability, balance, and motion of an object or system. It is also useful for solving problems involving collisions, rotations, and other physical phenomena.

Can the center of mass be located outside of the object?

Yes, the center of mass can be located outside of the object, especially in irregularly shaped objects. This can happen when the mass is not evenly distributed throughout the object. In cases like this, the center of mass may be located at a point where there is no actual mass present.

How does the center of mass affect the motion of an object?

The center of mass plays a crucial role in the motion of an object. If there is no external force acting on an object, its center of mass will continue to move at a constant velocity. Additionally, the center of mass determines the rotational motion of an object. If the center of mass is not aligned with the axis of rotation, the object will experience torque, causing it to rotate.

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