Man on a plank- Center of Mass pb.

In summary, the problem involves a man standing on one end of a plank with a large rock on the other end. The total mass of the man, plank, and rock is given, along with the position of their center of mass. The objective is to determine how far the plank moves when the man walks to the other end and sits on the rock. Using the equation for center of mass, the solution involves setting the initial and final positions of the center of mass equal to each other and solving for the distance the plank moves, which is found to be 2.9 m.
  • #1
Footballer010
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Homework Statement



A man is standing at one end of a plank of length L = 10 m. The man has mass Mman = 100 kg and the plank has mass Mplank = 40 kg and the plank is atop a frictionless sheet of ice. At the other end of the plank sits a large rock of mass Mrock = 200 kg. The center of mass of the man+plank+rock is 6.5 m from the end of the plank where the man is standing.

The man walks to the other end of the plank and sits down on the rock. How far did the plank move along the ice?

Homework Equations




Xcm= m1x1+m2x2[tex]\div[/tex]m1+ m2


The Attempt at a Solution



SO I added one more mass and plugged in the numbers, solving for Xplank

Xcm= m1x1+m2 x2+m3x3[tex]\div[/tex]m1+ m2+m3

6.5=((100)(10)+(40)(Xplank)+(200)(0))[tex]\div[/tex](340 kg)

And... I wasn't even close. Help
 

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  • #2
If it helps... the answer is 2.9 m, but I have no idea why.
 
  • #3
When man moves forward, to keep the CM constant, the whole plank with man must back. So Man*L = Total mass*x.
Find x.
 

Related to Man on a plank- Center of Mass pb.

1. What is the concept of "Man on a plank- Center of Mass pb."?

The concept refers to a physics problem where a man stands on a narrow plank, and the goal is to determine the position of the plank's center of mass, which is the point where the weight of the plank and the man are evenly balanced.

2. Why is it important to understand the center of mass?

Understanding the center of mass is crucial in many fields, including engineering, architecture, and sports, as it helps determine the stability and balance of objects. It also plays a significant role in understanding the movement of objects and predicting their behavior.

3. How is the center of mass calculated for a "Man on a plank" scenario?

The center of mass is calculated by finding the weighted average of the man's position and the plank's position. The man's weight is multiplied by his position, and the plank's weight is multiplied by its position. These two values are then divided by the total weight of the system (man + plank) to get the center of mass position.

4. What factors can affect the center of mass in this scenario?

The center of mass can be affected by several factors, including the position and weight of the man, the length and weight of the plank, and the distribution of the man's weight on the plank. Any changes in these factors can alter the center of mass position.

5. How does the center of mass affect the stability of the system?

The center of mass is directly related to the stability of the system. If the center of mass is located within the base of support (the area where the plank touches the ground), the system is considered stable. However, if the center of mass falls outside the base of support, the system becomes unstable, and the man on the plank may fall.

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