Normal force - object sliding with velocity

[mybrohshi5]

Homework Statement

A small rock with mass 0.22 kg is released from rest at point A, which is at the top edge of a large, hemispherical bowl with radius R = 0.60 m (the figure ). Assume that the size of the rock is small compared to R, so that the rock can be treated as a particle, and assume that the rock slides rather than rolls. The absolute value of the work done by friction on the rock, when it moves from point A to point B at the bottom of the bowl, is 0.25 J.

http://session.masteringphysics.com/problemAsset/1000053271/8/YF-07-25.jpg

Just as the rock reaches point B, what is the normal force on it due to the bottom of the bowl?

Homework Equations

The Attempt at a Solution

I know that its not just the mass times gravity like the normal force usually is because it has a velocity of 3.08 m/s.

I am just not sure how to use this and find the normal force :(

Any suggestions?

Thank you

 

[kuruman]

Can you find the speed of the rock when it reaches bottom?
Once you have that, draw a free body diagram.

 

[mybrohshi5]

I found the speed at the bottom. it is 3.08 m/s

I drew a FBD when the rock is at the bottom of the bowl.

I have the normal force perpendicular to the surface.

I have the force of gravity perp. to the surface but in the downward direction

I have velocity to the right

i have the force of friction to the left

Does that sound right?

not sure what to do from here though

 

[kuruman]

That sounds right. Now answer these two questions:
What is the sum of all the vertical forces?
What is the acceleration in the vertical direction?

 

[mybrohshi5]

OK i have two thoughts on those two questions. I am over thinking this and confusing myself :(

the sum of the vertical forces should equal zero.
OR
the sum of the vertical forces should equal mass times acceleration


the acceleration in the vertical direction is just the acceleration due to gravity
OR
the acceleration in the vertical direction is just zero

 

[kuruman]

OK i have two thoughts on those two questions. I am over thinking this and confusing myself :(

the sum of the vertical forces should equal zero.
OR
the sum of the vertical forces should equal mass times acceleration

the acceleration in the vertical direction is just the acceleration due to gravity
OR
the acceleration in the vertical direction is just zero

Instantaneously, the mass is moving in a circle at the bottom of the bowl. This means that its velocity is changing direction, therefore it is accelerating.

Therefore the sum of the vertical forces is mass times acceleration. Find an expression for the sum of the vertical forces and an expression for the acceleration (don't forget that the mass is going around in a circle) and set them equal.

Sorry, I have to sign off now.

 

[mybrohshi5]

So for my equation i have...

Normal force - force of gravity = m(a)

Can anyone help me from here? i am really lost :(

 

[kuruman]

What is the acceleration a for an object that is going around in a circle? Put that in your expression and find the normal force.

 

[mybrohshi5]

acceleration for an object going around in a circle is a=(4pi^2R)/T^2 correct?

so then to find time would i use v = d/t ?

Just a quick question on top of this.

Since i am finding the sum of the vertical forces wouldn't I use the acceleration in the vertical direction?

And can you tell me how you knew the object was "Instantaneously, the mass is moving in a circle at the bottom of the bowl"?

Thanks for the help

 

[kuruman]

acceleration for an object going around in a circle is a=(4pi^2R)/T^2 correct?

Strictly speaking your expression for the acceleration is correct, but I would use a = v²/R because v is already known.

so then to find time would i use v = d/t ?

This expression is valid only when the acceleration is zero. Not the case here.

Since i am finding the sum of the vertical forces wouldn't I use the acceleration in the vertical direction?

That is what you should use.

And can you tell me how you knew the object was "Instantaneously, the mass is moving in a circle at the bottom of the bowl"?

Look at the picture you posted. The mass is in a bowl that looks like the inside of a spherical shell cut in half. At any point along its path, the mass is going around a circle, the center of which is the center of the shell.

Thanks for the help

You are welcome.