Static EQ/Center of Mass problem

In summary, the conversation discussed the problem of finding the mass and center of mass of a non-uniform board with a person standing on it. After finding the mass of the board, the conversation focused on using Newton's first law of rotational equilibrium to solve for the unknown distance of the center of mass from the left end of the board. The correct solution involved fixing the signs and accounting for the torque from the right end reaction.
  • #1
Ben is Dumb
3
0

Homework Statement



A 65.0-kg person stands on a horizontal board. The board is 10.0-m long and is NOT perfectly uniform. The person stands 1/4 of the way from the left end of the board. The board is supported at each end by a scale. The scale on the left reads 753 N and the scale on the right reads 619 N.

What is the mass of the board?
How far from the left end is the board's center of mass?

Staticsproblem.jpg


My digital drawing skills are just as solid as my math skills.

Homework Equations



None/unsure

The Attempt at a Solution



I was able to get the mass of the board (75kg) but unable to calculate the center of mass. It seems like integration would do the trick, but my class has been a bit skimpy on the calculus and I'm unsure how to set it up. Otherwise balancing the torques makes sense, but I can't get rid of the person's influence on the scales. I apologize if this isn't much of an attempt at a solution, but I've tried to look at this thing a bunch of different ways and can't seem to get very far.

Thanks for the help!

Ben
 
Last edited:
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  • #2
You've found the mass of the board, so now find its weight. You should be familiar with Newton's first law of rotational equilibrium: The sum of the torques of all forces about any point must equal zero. So try summing torques of all forces about the left end, to solve for the unknown distance of the center of the boards mass from the left end.
 
  • #3
Alright, here's what I did.

(CCW is positive)
Torque= -75kg(9.8m/s^2) X(COM) + 2.5m(65kg)(9.8m/s^2) = 0

I actually got a reasonable answer (2.17m), just not the right one (6.26m). I must still be setting something up the wrong way. Thanks for the help Jay.
 
  • #4
The boards weight and the person's weight both produce clockwise torques about the left end, so why did you choose plus for the person's weight? Also, what about the torque from the right end reaction?
 
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  • #5
I talked to my prof, fixed the signs and put the 619N(L) on the other side and got the correct answer. Thanks again.
 

What is a Static EQ/Center of Mass problem?

A Static EQ/Center of Mass problem is a physics problem that involves determining the position of an object's center of mass and the forces acting on it in a state of equilibrium.

Why is it important to understand Static EQ/Center of Mass problems?

Understanding Static EQ/Center of Mass problems is important in physics and engineering as it allows us to analyze and predict the stability and balance of structures and objects.

What are the steps to solve a Static EQ/Center of Mass problem?

The steps to solve a Static EQ/Center of Mass problem are:
1. Draw a free body diagram of the object
2. Identify all the forces acting on the object
3. Calculate the net force in each direction (horizontal and vertical)
4. Set up equations for the sum of forces in each direction
5. Solve the equations to find the unknown variables (e.g. center of mass, mass, etc.)

What are some common mistakes when solving Static EQ/Center of Mass problems?

Some common mistakes when solving Static EQ/Center of Mass problems include forgetting to include all the forces acting on the object, not considering the direction of the forces correctly, and not setting up the equations properly.

How can understanding Static EQ/Center of Mass problems be applied in real life?

Understanding Static EQ/Center of Mass problems can be applied in real life situations such as building structures, designing vehicles, and even maintaining proper posture and balance in our daily activities.

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