Physics Question Over 2 Dimensional Friction Problems

[Xazerd]

1. Angela has a bucket of mass 2 kg tied to a string. She places a drinking glass of mass 0.5 kg in the bucket. She spins the bucket in a vertical circle of radius 1.5 m. You want to find out how fast she must swing the bucket to keep the glass from falling out.

a. Draw the free-body diagram for the glass when it is at the top of the circle.

b. What is the equation for the net force on the glass at the top of the circle in terms of w, FN, m, v, and r?

c. The glass will fall out of the bucket if the normal force between the glass and bucket equals zero. How fast must she spin the bucket to prevent this from happening?

d. The string will break if the tension on it is more than 100 N. Over what range of speeds can she keep the glass in the bucket and prevent the string from breaking?

2.
Force: F = ma
Net force: Fnet = F1 + F2 + F3 + ...
Weight: w = mg = FN
Centripetal force:
Force of friction, kinetic: Fk = μkFN
Force of friction, static: Fs = μsFN

3.
a. Cant show
b. F(Net)=F(Normal force)-w+(centripetal force)
c. I am lost...
d. Still lost...

Thank You for your help

 

[Simon Bridge]

(a) you can describe it, and your reasoning - it is also possible to upload pictures.
(b) ignore that equation ... to move into a circle, which direction must the net force have to point?
Where does the centripetal force come from - what is pushing or pulling on the glass?

 

[Xazerd]

(a) you can describe it, and your reasoning - it is also possible to upload pictures.
(b) ignore that equation ... to move into a circle, which direction must the net force have to point?
Where does the centripetal force come from - what is pushing or pulling on the glass?

a) My picture has the glass with an upwards arrow representing the normal force and a downwards arrow representing the weight.

b) In order to move in a circle the net force would have be pointed inwards. I used centripetal force because the object was moving in a circle.

 

[haruspex]

a) My picture has the glass with an upwards arrow representing the normal force

This is at the top of the circle? How is the bucket supplying an upward force on the glass? Are you supposing the glass is glued to the bucket??
Why does the title mention friction?

 

[Simon Bridge]

a) My picture has the glass with an upwards arrow representing the normal force and a downwards arrow representing the weight.

haruspex has covered this one.

b) In order to move in a circle the net force would have be pointed inwards. I used centripetal force because the object was moving in a circle.

... you are saying: the sum of the weight and the normal force must be non-zero and pointing towards the center.
The force that keeps an object in circular motio points towards the center and is called the centripetal force.
The glass is moving in a circle.

Therefore, the sum of the weight and the normal force must be called...

 

[Xazerd]

haruspex has covered this one.

... you are saying: the sum of the weight and the normal force must be non-zero and pointing towards the center.
The force that keeps an object in circular motio points towards the center and is called the centripetal force.
The glass is moving in a circle.

Therefore, the sum of the weight and the normal force must be called...

Thank You, but I already solved that one now ( I got Net Force= Normal Force- Weight + (Mass*Velocity^2)/radius.) It took me awhile but I figured it out on my own. The main ones I need help on are part c and d. Much appreciated!

 

[Xazerd]

This is at the top of the circle? How is the bucket supplying an upward force on the glass? Are you supposing the glass is glued to the bucket??
Why does the title mention friction?

My mistake, I just used the title of my worksheet. Did not check the particular problem. I have changed the upward force on the glass.

 

[pgardn]

For c)

What is the only force acting on the glass if the normal force = 0 ?

 

[Xazerd]

If the normal force is 0, won't centripetal force be the only force acting on the glass?

 

[haruspex]

If the normal force is 0, won't centripetal force be the only force acting on the glass?

A centripetal force is the force required to produce an arc in the trajectory. In general, it is the sum of the forces perpendicular to the velocity at that instant. It isn't a source of force. So what actual forces act on it? I.e. which forces will add up to provide the required centripetal force?

 

[Simon Bridge]

Net Force= Normal Force- Weight + (Mass*Velocity^2)/radius.

That says that the net force is the sum of the weight, the normal force, and the centripetal force ... this is incorrect.

If the normal force is 0, won't centripetal force be the only force acting on the glass?

You appear to think that the centripetal force is an extra force that appears when something moves in a circle.
This is not correct. The "centripetal force" is another name for the unbalanced force that points along the radius. The force itself comes from something definite - i.e. the centripetal force on the bucket comes from the tension in the string.

Redo post #5 - those are not rhetorical questions.

 

[Xazerd]

A centripetal force is the force required to produce an arc in the trajectory. In general, it is the sum of the forces perpendicular to the velocity at that instant. It isn't a source of force. So what actual forces act on it? I.e. which forces will add up to provide the required centripetal force?

The force that comes from the tension of the string and the weight of the bucket.

 

[Xazerd]

That says that the net force is the sum of the weight, the normal force, and the centripetal force ... this is incorrect.


You appear to think that the centripetal force is an extra force that appears when something moves in a circle.
This is not correct. The "centripetal force" is another name for the unbalanced force that points along the radius. The force itself comes from something definite - i.e. the centripetal force on the bucket comes from the tension in the string.

Redo post #5 - those are not rhetorical questions.

If this is incorrect, then what is it?

 

[pgardn]

What force acts AS the center seeking force if the normal force=0 ?

Only one "real" force acting on the glass for c)...

 

[Xazerd]

For c) I got 3.83m/s, and for d) I got v ≤9.47m/s. Did I do these correctly?

 

[Xazerd]

What force acts AS the center seeking force if the normal force=0 ?

Only one "real" force acting on the glass for c)...

Centripetal Force? If I am wrong, could you please break it down for me...

 

[pgardn]

Centripetal Force? If I am wrong, could you please break it down for me...

What is supplying the centripetal force?

Hint: it's acting straight down

Centripetal force just means center seeking force. So what force is acting towards the center of the circular path when the glass is at the top position? You already mentioned it in your 2nd post...The third post of this topic.

 

[Xazerd]

What is supplying the centripetal force?

Hint: it's acting straight down

Centripetal force just means center seeking force. So what force is acting towards the center of the circle when the glass is at the top position? You already mentioned it in your 2nd post.

The weight of the bucket.

 

[pgardn]

The weight of the bucket.

Yessssss

-N. Dynamite

So the weight and the centripetal force are an equality. Solve for v.

 

[pgardn]

And I see you are lacking an equation for cent. force. In your 1st post.

What is the equation?

 

[Xazerd]

And I see you are lacking an equation for cent. force. In your 1st post.

What is the equation?

(mv^2)/r

 

[Xazerd]

Yessssss

-N. Dynamite

So the weight and the centripetal force are an equality. Solve for v.

I solved for v and I got 3.88.

 

[Simon Bridge]

The force that comes from the tension of the string and the weight of the bucket.

I stand corrected :)

I solved for v and I got 3.88.

... units.
show working.

I'm getting a slightly different value - are you using g=10N/kg or g=9.8N/kg?

 

[pgardn]

I solved for v and I got 3.88.

Cool.

That looks about right sq rt of about 15


Mr. Simon Bridge was asking you important questions about cent. Force.

It's a real problem for some students to understand that is supplied by other force(s).

 

[pgardn]

So now you got part of the answer for d)

Now find the upper limit for v knowing that T can't be more than 100 N.

 

[Xazerd]

I stand corrected :)

... units.
show working.

I'm getting a slightly different value - are you using g=10N/kg or g=9.8N/kg?

Im using 9.8.

 

[Xazerd]

for d I got 9.47m/s.

 

[pgardn]

for d I got 9.47m/s.

Ima not going to check the math.

Equation used

T + mg = (mv^2)/r ?

And you solved for v?

Your answer is bigger than the 3.88 m/s, so that should make sense. Does my equation jive with your free body diagram?

 

[haruspex]

The force that comes from the tension of the string and the weight of the bucket.

The glass is blissfully unaware of the tension in the string and of gravity acting on the bucket. Which forces act directly on the glass, and by doing so provide the centripetal force ( so don't answer "centripetal force").

 

[pgardn]

The glass is blissfully unaware of the tension in the string and of gravity acting on the bucket. Which forces act directly on the glass, and by doing so provide the centripetal force ( so don't answer "centripetal force").

Ohhhhh.

Indeed more correct.

I skipped a step.

My equation should work if you combined the masses but Mr. H is conceptually much more accurate.

 

[Xazerd]

The glass is blissfully unaware of the tension in the string and of gravity acting on the bucket. Which forces act directly on the glass, and by doing so provide the centripetal force ( so don't answer "centripetal force").

Normal Force?

 

[haruspex]

Thank You, but I already solved that one now ( I got Net Force= Normal Force- Weight + (Mass*Velocity^2)/radius.)

That equation is not correct, in a couple of ways. Perhaps you've typed it out wrongly?

 

[haruspex]

T + mg = (mv^2)/r

Think again. At what point in the loop is the tension greatest?

 

[pgardn]

Think again. At what point in the loop is the tension greatest?

Aha again!

I was using the FBD for part a)

The problem said Maximum tension. This would happen at the bottom of the loop.

So T - mg = (mv^2)/r

It always helps to answer the questions that are actually asked.
Sorry to the OP. Thanks to Mr. H!

 

[Xazerd]

Aha again!

I was using the FBD for part a)

The problem said Maximum tension. This would happen at the bottom of the loop.

So T - mg = (mv^2)/r

It always helps to answer the questions that are actually asked.
Sorry to the OP. Thanks to Mr. H!

So is this the equation I use for part c and d, but I have to combine the mass of both the bucket and glass?