Weight distribution over multiple scales

[Alyssa Jesse]

I am in a first year physics course at university, with little background in maths and science.

Homework Statement

When a dog stands at rest with each of its four feet on a separate set of scales, each scale reads a value of 45n. if this dog then carefully lifts one foot of the a scale and up into the air, what is the reading on each of the remaining three scales? (assume the dogs weight is evenly distributed between the three scales)

Homework Equations

I would add the scales up to 180, assume the dogs weight to be 180n, then divide that by three to get 60n. I have been looking through the textbook and I can't find a relevant way of working this problem out, however I am not sure if it is as simple as it seems.

The Attempt at a Solution

45*4 = 180n/3 = 60n

Any help or confirmation would be greatly appreciated :)

 

[voko]

Your solution is correct.

But would you be able to explain WHY it is correct?

 

[Alyssa Jesse]

The dogs weight is evenly distributed over all four scales so 4*45n=180n. When one of the scales is removed the dogs weight is now distributed over three scales, so 180/3 = 60n. However, I don't know how to explain this using physics terminology.

 

[voko]

One missing bit is why the total weight is equal to the sum of readings on all the scales. Have you learned of the free body diagram (FBD)?

 

[Alyssa Jesse]

No not yet, I saw mention of it in another forum I looked over briefly but don't really understand what its purpose is?

 

[voko]

If you have not been introduced to that, then I think we should not touch that matter just yet.

Do you know that for a body to be in equilibrium the sum of all the forces acting on it must be zero? (This is not the only condition, but it is still a necessary condition.)

 

[Alyssa Jesse]

Yes, we have been over that!

 

[voko]

So what forces act on the dog when it's on 4 scales? On 3 scales?

 

[Alyssa Jesse]

Gravity and the upward support force/normal force of the floor?

 

[voko]

The dog is supported by the scales, not by the floor. What force does each scale exert on the dog?

 

[Alyssa Jesse]

In my textbook it uses the example of standing on scales and says - "Two forces act on the scale. One is...gravity...and the other is the upward support force of the floor"

 

[voko]

Yes, these are the forces that act on the SCALE. But in this case we want to know what forces act on the DOG.

Let's take a simpler example. Say you put an apple on a scale. Since the apple is attracted towards the ground by gravity, yet it is stationary, the scale must clearly provide a force opposite in direction and equal in magnitude to the weight of the apple. And the scale does not just provide the force, it also displays to us the magnitude of the force - that's why we need scales to begin with!

 

[Alyssa Jesse]

Thank you! So the two forces acting on the dog are gravity and the support force provided by the scale?

 

[voko]

Not two. There are more than one scales supporting the dog.