Little questions (Force, Moment, Young)

[coconut62]

My questions: (in order of attached images)

1. Why doesn't the vertical component of P affect the mass of the lawnmower? Why isn't the mass = mass of lawnmower + (Psin40)/g?

2. This question, I totally have no idea how it should be calculated. I tried by labelling the weight at the exact middle of the plank, then divide the 120N into two, each for one stool. Then I divide the 80N into two. Then I calculated the moment for each stool by multiplying the distances and the forces. But apparently that's not how it should be done :shy: Does a reaction force act on that object?

3. Using the formula E= stress/strain,

Stress= F/A = 75/ (0.25∏d^2) =1.1 x 10^6 Pa
Strain = (extension,x)/1.8

Adding the Young modulus together = 3.3 x 10^11

so by arranging everything in the formula, I found x = 6 x 10^-6 which is not the answer.

What's wrong?

 

[Doc Al]

1. Why doesn't the vertical component of P affect the mass of the lawnmower? Why isn't the mass = mass of lawnmower + (Psin40)/g?

Why would a force acting on a body affect its mass? Perhaps you are thinking of the normal force with the ground?

2. This question, I totally have no idea how it should be calculated. I tried by labelling the weight at the exact middle of the plank, then divide the 120N into two, each for one stool. Then I divide the 80N into two. Then I calculated the moment for each stool by multiplying the distances and the forces. But apparently that's not how it should be done :shy: Does a reaction force act on that object?

For one thing, while the weight of the board acts in the middle of the board, that point is not in the middle between the two supports. So do not assume each support exerts the same upward force. Consider torques.

3. Using the formula E= stress/strain,

Stress= F/A = 75/ (0.25∏d^2) =1.1 x 10^6 Pa
Strain = (extension,x)/1.8

Adding the Young modulus together = 3.3 x 10^11

so by arranging everything in the formula, I found x = 6 x 10^-6 which is not the answer.

Treat each wire separately. What is the same for each is the extension, not the tension.

 

[coconut62]

Why would a force acting on a body affect its mass? Perhaps you are thinking of the normal force with the ground?

I know it's illogical, but since there is a force acting downwards, wouldn't it be harder for the lawnmower to move? (err...)

For one thing, while the weight of the board acts in the middle of the board, that point is not in the middle between the two supports. So do not assume each support exerts the same upward force. Consider torques.

Yes, I put the 120N at the exact middle of the plank which is 2m away from each end. Now the problem is that I don't see any upward force. There must be an upward force to balance the whole thing so that the total moment becomes zero. Does the upward force come from the reaction force acting on that object by the plank, or does it come from the support itself? If it comes from the reaction force, wouldn't it be canceled off by the weight?

Now what I do is like this:

for A, (120/2)(1.5) + (80/2)(1.25) = 140
same concept for B.

Where is the problem?

Another thing, there's a short length of plank to the left of A, does the weight of that little part counts too?

Now I suddenly have a bigger problem. If Newton's 3rd law says that every action is balanced by a reaction of the same magnitude, then now imagine if I stretch my left arm out, and somebody puts bricks of 10kg on my hand, why would my hand be pressed down? Why wouldn't it just give a 98N reaction?

You get what I mean? :shy:

Treat each wire separately. What is the same for each is the extension, not the tension.

I treated them separately by using 75N for each wire, is that correct?(Or should it be halved?)
Then I get 0.54mm and 0.27mm for each wire respectively. But the answer is 0.36mm. What should I do next?

 

[Doc Al]

I know it's illogical, but since there is a force acting downwards, wouldn't it be harder for the lawnmower to move? (err...)

Since the normal force would be increased, in some problems with friction there may be a greater resistive force. But that's not relevant here. And it has nothing to do with the mass!

Yes, I put the 120N at the exact middle of the plank which is 2m away from each end.

Good.

Now the problem is that I don't see any upward force. There must be an upward force to balance the whole thing so that the total moment becomes zero. Does the upward force come from the reaction force acting on that object by the plank, or does it come from the support itself? If it comes from the reaction force, wouldn't it be canceled off by the weight?

The upward forces come from the supports. The total upward force had better be equal and opposite to the weight of the plank plus weight, otherwise the thing will collapse. (You'll need this fact to solve the problem.)

Now what I do is like this:

for A, (120/2)(1.5) + (80/2)(1.25) = 140
same concept for B.

Where is the problem?

Why did you divide by 2?

You want clockwise torque to equal counter-clockwise torques. Set up that equation. (Just do it once, using A or B as the pivot.)

You also want total upward force equal to total downward force. Set up that equation.

Another thing, there's a short length of plank to the left of A, does the weight of that little part counts too?

The 120 N weight of the plank includes every bit of the plank. And it acts at the middle of the plank. So you already have that short length covered.

Now I suddenly have a bigger problem. If Newton's 3rd law says that every action is balanced by a reaction of the same magnitude, then now imagine if I stretch my left arm out, and somebody puts bricks of 10kg on my hand, why would my hand be pressed down? Why wouldn't it just give a 98N reaction?

The action/reaction forces act on different bodies. If the bricks push down your hand with some force, then your hand must be pushing up with an equal and opposite force. If you are strong enough to hold up the bricks without letting your hand drop, then the upward force you exert must also be equal to the weight of the bricks.

I treated them separately by using 75N for each wire, is that correct?(Or should it be halved?)

Neither. All you know is that the total force acting on both wires is 75 N. So T1 + T2 = 75 N.

You know that the extension of each wire is the same and that the total tension must add to 75 N. Set up and solve those equations.

 

[coconut62]

The upward forces come from the supports.

Why doesn't the plank give a reaction on the object?

Why did you divide by 2?

I thought because there are two supports so the weight is evenly distributed between them?

You want clockwise torque to equal counter-clockwise torques. Set up that equation. (Just do it once, using A or B as the pivot.)

Taking A as pivot:
80(1.25) + 120(1.5) = RB(2.5)

Still wrong

You also want total upward force equal to total downward force. Set up that equation.

RA+RB= 200.

 

[Doc Al]

Why doesn't the plank give a reaction on the object?

I'm not sure what you mean (what object?). But the plank does exert forces on the supports. So what?

I thought because there are two supports so the weight is evenly distributed between them?

No, it depends on how the weight is distributed. (You have two feet. Does that mean that your weight is always equally divided between them? No, of course not. You can lean your weight to one side.)

If the plank were placed evenly over the supports, then you'd be right.

Taking A as pivot:
80(1.25) + 120(1.5) = RB(2.5)

Still wrong

Looks OK to me.

RA+RB= 200.

Good!

 

[coconut62]

I'm not sure what you mean (what object?). But the plank does exert forces on the supports.So what?

The 80N object.

Looks OK to me.

Not ok. I got 112 and 88 but the answer is 120 and 80. Why is it exactly the same as the two weights provided?
I have a weird feeling that the author merely looked at the question and then immediately knew: "Ah, this should be 80 and that should be 120." Is that possible?

 

[Doc Al]

The 80N object.

Yes. The plank exerts an upward 80 N force on that object and the object exerts a downward 80 N force on the plank. In your analysis, all you care about are the forces on the plank.

Not ok. I got 112 and 88 but the answer is 120 and 80.

I agree with your answers and think the book is wrong. (What book are you using?)

Why is it exactly the same as the two weights provided?
I have a weird feeling that the author merely looked at the question and then immediately knew: "Ah, this should be 80 and that should be 120." Is that possible?

Could be. There are many ways to get the wrong answer.

 

[coconut62]

Yes. The plank exerts an upward 80 N force on that object and the object exerts a downward 80 N force on the plank. In your analysis, all you care about are the forces on the plank.

But if they exert the same force on each other, why is there still a turning effect? This is what I'm confused about, similar to the brick and hand thing before.

I agree with your answers and think the book is wrong. (What book are you using?)

https://www.amazon.com/dp/0340945648/?tag=pfamazon01-20 this.

Could be. There are many ways to get the wrong answer.

For instance? (I just want to know how they think)

 

[Doc Al]

But if they exert the same force on each other, why is there still a turning effect? This is what I'm confused about, similar to the brick and hand thing before.

What determines the net torque on an body are the forces acting on that body. It's certainly true that the 80 N object and the plank exert forces on each other, but if you want to analyze the torques on the plank you don't need to worry about forces on the object.

If for some reason you wanted to analyze the forces on the object, then you'd see that two forces act: The downward force of gravity (80 N) and the upward supporting force from the plank (which you know must also be 80 N). Nothing more to say about that.

When you hold that brick in your outstretched hand, the brick exerts a force on you that creates a downward torque on your arm. Since you're holding it up, muscles and such at your shoulder must be exerted the necessary upward counter torque.

https://www.amazon.com/dp/0340945648/?tag=pfamazon01-20 this.

Not familiar with that one.

For instance? (I just want to know how they think)

No specific examples in mind. I was just making the point that there are many ways to be wrong. And only a few ways to be right.

 

[coconut62]

What determines the net torque on an body are the forces acting on that body. It's certainly true that the 80 N object and the plank exert forces on each other, but if you want to analyze the torques on the plank you don't need to worry about forces on the object.

If for some reason you wanted to analyze the forces on the object, then you'd see that two forces act: The downward force of gravity (80 N) and the upward supporting force from the plank (which you know must also be 80 N). Nothing more to say about that.

So technically, it's not the object itself that exerts 80N on the plank, it's rather the pull of gravity on the object that causes a force of 80N to act on the plank. So there is a R force and an equal but opposite W force that act on that particular object itself, making it at rest. And what actually act on the plank is just a downward 80N pull. Is my understanding correct?

 

[Doc Al]

So technically, it's not the object itself that exerts 80N on the plank, it's rather the pull of gravity on the object that causes a force of 80N to act on the plank.

The weight of the object (gravity) acts on the object, not directly on the plank. Of course, since the plank is there preventing the object from falling, the plank and the object end up exerting equal and opposite 80 N forces on each other. So I would say that it is the object itself that exerts an 80 N contact force on the plank. (Note that the force that the object exerts is not a gravitational force, although it happens to equal the weight of the object in this case. If the plank were accelerating downward, the object would be exerting a smaller force on the plank, even though its weight would be the same.)

So there is a R force and an equal but opposite W force that act on that particular object itself, making it at rest.

Yes. Two forces act on the object. Since they happen to be equal and opposite, the object is in equilibrium.

And what actually act on the plank is just a downward 80N pull.

Better to think of the object as exerting an 80 N downward push on the plank.

 

[coconut62]

The weight of the object (gravity) acts on the object, not directly on the plank. Of course, since the plank is there preventing the object from falling, the plank and the object end up exerting equal and opposite 80 N forces on each other. So I would say that it is the object itself that exerts an 80 N contact force on the plank. (Note that the force that the object exerts is not a gravitational force, although it happens to equal the weight of the object in this case. If the plank were accelerating downward, the object would be exerting a smaller force on the plank, even though its weight would be the same.)


Yes. Two forces act on the object. Since they happen to be equal and opposite, the object is in equilibrium.


Better to think of the object as exerting an 80 N downward push on the plank.

So, the whole thing is actually one single force resulting in three forces?

gravitational force --> gravity pull on object + weight exerted on plank + reaction on the object

If there is no gravity, all the three forces wouldn't exist, and even the mass of the object itself won't have any effect on the plank. Correct?

 

[Doc Al]

Sounds reasonable to me.