Find Center of Gravity of Person Using Torque

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In summary, the problem involves using a gravity board to locate the center of gravity of a person. The setup consists of a horizontal board, a fulcrum, and a scale. By calculating torques around the fulcrum, the scale force can be determined in terms of the weight of the board. This information is then used to calculate the center of gravity of the student, which is found to be 0.73m away from the fulcrum point.
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CACain
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DISCLAIMER: For the sake of academic integrity, I would like to place a warning on this question and say that it is NOT a test question, nor is it a homework question that will receive grading. This is simply a random question out of the textbook to practice torque.

Problem:

A gravity board for locating the center of gravity of a person consists of a horizontal board supported by a fulcrum at one end and by a scale at the other end. A physics student lies horizontally on the board with the top of his head above the fulcrum point. The scale is 2m from the fulcrum. The stuent has a mass of 70kg and when he is on the gravity board, the scale advances 250N. Where is the center of gravity of the student?


Okay, I have the answer to this question because I have a study guide along with the textbook, but I can't follow the steps... Does anyone know of a more logical step progression on how to work this problem?
 
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  • #2
First consider the setup without the student. By calculating torques around the fulcrum you will get the scale force in terms of the weight of the board. Use this to eliminate the weight of the board in the second setup - that is by calculating the torques around the fulcrum again (I get 0.73 m).
 
  • #3


I would approach this problem by first understanding the concept of torque and how it relates to finding the center of gravity. Torque is the measure of the force that can cause an object to rotate around an axis. In this case, the axis is the fulcrum point and the force is the weight of the person.

To find the center of gravity, we need to consider the balance of torque on both sides of the fulcrum point. The formula for torque is T = F x d, where T is the torque, F is the force, and d is the distance from the fulcrum point. In this case, we have two torques acting on the board - one from the weight of the person and one from the scale.

The torque due to the weight of the person can be calculated by multiplying the person's weight (in Newtons) by the distance from the fulcrum point to the center of gravity. This distance is unknown, so we can represent it as x. Therefore, the torque from the person's weight is 70kg x 9.8m/s^2 x x = 686x Nm.

The torque from the scale can also be calculated by multiplying the reading on the scale (in Newtons) by the distance from the fulcrum point to the scale, which is 2m. This gives us a torque of 250N x 2m = 500Nm.

Since the board is in equilibrium, the sum of these two torques must be equal to zero. This gives us the equation 686x Nm + 500Nm = 0. Solving for x, we get x = -500/686 = -0.73m.

This negative value means that the center of gravity is located 0.73m to the left of the fulcrum point. This makes sense since the person's head is above the fulcrum point, meaning their center of gravity must be below it to maintain balance.

In summary, the center of gravity of the person is located 0.73m to the left of the fulcrum point. This calculation can also be verified by using other methods, such as finding the point of intersection of the person's weight and the scale's reading on a free-body diagram.
 

1. What is the center of gravity of a person?

The center of gravity of a person is the point at which their mass is evenly distributed in all directions. It is the point around which the person's weight is evenly balanced.

2. Why is it important to find the center of gravity of a person?

Finding the center of gravity of a person is important for understanding their stability and balance. It can also be useful in various activities such as sports, dance, and physical therapy.

3. How is the center of gravity of a person determined using torque?

The center of gravity of a person can be determined by applying torque, or a force that causes rotation, to different parts of the body. By measuring the amount of torque required to balance the person, the center of gravity can be calculated.

4. What factors can affect the center of gravity of a person?

The center of gravity of a person can be affected by their body composition, distribution of muscle mass, and posture. It can also change with movement, such as when a person shifts their weight or extends their limbs.

5. Can the center of gravity of a person be outside of their body?

Yes, the center of gravity of a person can be outside of their body if they are holding an object or in a specific position that shifts their weight. It is important to consider the location of the center of gravity in relation to the person's body to maintain balance and prevent injury.

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