# Determine the location of her center of mass

• ual8658
In summary, a physics student lies on a plank of weight 100.0 N and length 2.5 m supported by two scales 2.50 m apart to determine the location of her center of mass. The left scale reads 420.0 N and the right scale reads 210.0 N. The student's weight is not 630 N as the weight of the plank should not be neglected. When calculating the distance of her center of mass from the left scale, the calculation should not involve dividing by 630. By accounting for the torque from the plank and the student's center of mass, the correct values for the distance can be obtained.
ual8658

## Homework Statement

To determine the location of her center of mass, a physics student lies on a plank of weight 100.0 N and length 2.5 m supported by two scales 2.50 m apart. The left scale reads 420.0 N, and the right scale reads 210.0 N. (Note: Don’t neglect the weight of the plank when you do this problem.) a. Find the student’s weight. [4] b. Find the distance of her center of mass from the left scale (x=0). [4]

## Homework Equations

T = rF
Wgirl = 420 + 210

## The Attempt at a Solution

I get her weight as 630 N. But when I go to solve for the distance using center of mass, when I place the point of rotation at the left support I get her center of mass as .635 m from the left side, but using the right support, I get her center of mass as 1.47 m away from the right side or 1.03 m from the left side. What am I doing wrong to get two different center of masses.

ual8658 said:

## Homework Statement

To determine the location of her center of mass, a physics student lies on a plank of weight 100.0 N and length 2.5 m supported by two scales 2.50 m apart. The left scale reads 420.0 N, and the right scale reads 210.0 N. (Note: Don’t neglect the weight of the plank when you do this problem.) a. Find the student’s weight. [4] b. Find the distance of her center of mass from the left scale (x=0). [4]

## Homework Equations

T = rF
Wgirl = 420 + 210

## The Attempt at a Solution

I get her weight as 630 N. But when I go to solve for the distance using center of mass, when I place the point of rotation at the left support I get her center of mass as .635 m from the left side, but using the right support, I get her center of mass as 1.47 m away from the right side or 1.03 m from the left side. What am I doing wrong to get two different center of masses.
The girl's weight is not 630 N. Recall the problem says: "don't neglect the weight of the plank when you do this problem".

ual8658 said:

## Homework Statement

To determine the location of her center of mass, a physics student lies on a plank of weight 100.0 N and length 2.5 m supported by two scales 2.50 m apart. The left scale reads 420.0 N, and the right scale reads 210.0 N. (Note: Don’t neglect the weight of the plank when you do this problem.) a. Find the student’s weight. [4] b. Find the distance of her center of mass from the left scale (x=0). [4]

## Homework Equations

T = rF
Wgirl = 420 + 210

## The Attempt at a Solution

I get her weight as 630 N.
How does the weight of the plank figure into that calculation?

But when I go to solve for the distance using center of mass, when I place the point of rotation at the left support I get her center of mass as .635 m from the left side, but using the right support, I get her center of mass as 1.47 m away from the right side or 1.03 m from the left side. What am I doing wrong to get two different center of masses.
How did you calculate either number?

Edit: Too late.

mattbeatlefreak said:
The girl's weight is not 630 N. Recall the problem says: "don't neglect the weight of the plank when you do this problem".
jbriggs444 said:
How does the weight of the plank figure into that calculation?How did you calculate either number?

Edit: Too late.

So I placed the point of rotation on either scale. The plank is 100 N with its cm 1.25 m from either side. I then used the other scale's reading and multipled that by 2.5 m, and subtracted the plank's torque contribution before dividing the whole thing by 630.

ual8658 said:
So I placed the point of rotation on either scale. The plank is 100 N with its cm 1.25 m from either side. I then used the other scale's reading and multipled that by 2.5 m, and subtracted the plank's torque contribution before dividing the whole thing by 630.

Why divide by 630? You have done the calculation for the torque from the plank. Again, the girl does not weigh 630 N.

mattbeatlefreak said:
Why divide by 630? You have done the calculation for the torque from the plank. Again, the girl does not weigh 630 N.
But isn't there a torque from the plank's cm, and then an added torque of the girl's cm?

EDIT: I now understand why you say the girl does not weigh 630 N. I now get the correct values. Thanks!

Last edited:

## What is the center of mass?

The center of mass is the point at which the mass of an object can be considered to be concentrated.

## Why is it important to determine the location of an object's center of mass?

Determining the location of an object's center of mass is important because it helps us understand how an object will behave when acted upon by external forces.

## How can the location of an object's center of mass be determined?

The location of an object's center of mass can be determined by finding the balance point of the object. This can be done by hanging the object from different points and marking the vertical line that passes through the center of mass.

## What factors affect the location of an object's center of mass?

The mass and distribution of mass within an object are the main factors that affect the location of its center of mass. The shape and size of the object can also play a role.

## Why is it important to consider the location of an object's center of mass in engineering and physics?

In engineering and physics, it is important to consider the center of mass because it affects the stability and movement of objects. It also plays a role in designing structures and predicting how they will respond to external forces.

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