Where is the Center of Gravity of a Lying Person?

In summary, the problem involves a 160cm tall person lying on a light board supported by two scales, with readings of 29.4kg under the feet and 32.8kg under the head. The goal is to find the center of gravity of the person. The solution involves calculating net torque about the center of mass and using the middle of the person as the pivot point. After calculating the torques from both sides, the difference is taken to determine the distance from the center of mass. The distance is then updated to .80m and used to calculate the new torques.
  • #1
VanKwisH
108
0

Homework Statement



A 160cm tall person lies on a light(massless) board which is supported by two scales , on under the feet and the beneath the top of the head. the scale under his feet read 29.4kg
and the scale under his head reads 32.8 kg ... where is the center of gravity of this person??

Homework Equations





The Attempt at a Solution

 
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  • #2
What have you tried so far? It's always a good idea to start with a picture and a force-body diagram.
 
  • #3
the simplest method to solve the problem is to calculate net torque abt the center of mass of person [take it as xi^+ yj^] from both the sides.then calculate the difference in the torques to get the value which gives the distance from the center of mass.

first proceed with the first step and update me of the progress.
 
  • #4
huh ? i don't understand
 
  • #5
what u mean is ... take the torques from each side ... and use the very middle of the person as the pivot point? am i correct ?
if so i got
t1 = 32.8 * 80
= 2624
t2=29.4 * 80
= 2352
does that look right??
 
  • #6
comeon..how can you take the distance as 80 cm??

take it as .80m

the new relations are;

t1=.80*32.8
=26.24

t2=29.4*80=23.52
 
  • #7
yah alright i get that ... next step??
 

1. What is the center of gravity?

The center of gravity is the point at which an object's weight is evenly distributed in all directions. It is the point where an object would balance if suspended.

2. How is the center of gravity determined?

The center of gravity can be determined by finding the balance point of an object using a plumb line or by calculating the weighted average of an object's mass distribution.

3. Why is it important to find the center of gravity?

Finding the center of gravity is important in many areas of science and engineering, as it helps to determine an object's stability, how it will behave when in motion, and its potential for tipping or falling over.

4. How does the shape of an object affect its center of gravity?

The shape of an object plays a significant role in determining its center of gravity. Objects with a larger base will have a lower center of gravity, making them more stable, while objects with an irregular shape may have multiple center of gravity points.

5. Can the center of gravity change?

Yes, the center of gravity can change if the distribution of mass within an object changes. For example, if weight is added to one side of an object, the center of gravity will shift towards that side. In addition, the center of gravity can also change if an object is tilted or rotated.

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