Is the particle still moving at point C?

[riseofphoenix]

A 1.8 x 10²-g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R = 37.0 cm (figure below).

(a) Calculate its gravitational potential energy at A relative to B.

Energy of system at point A: PE_A + KE_A
E_A: PE_A + KE_A
E_A: PE_A + 0
E_A: PE_A

So,

PE_{gravitational} = mgh
PE_{gravitational} = (0.18)(9.81)(0.37)
PE_{gravitational} = 0.653

Got this one correct...

(b) Calculate its kinetic energy at B.

Energy of system at point B: PE_B + KE_B
E_B: PE_B + KE_B
E_B: mg(0) + KE_B ***height is 0 at point B, so PE = 0***
E_B: KE_B

The solution says that KE_B = mgR
Howwww?! Isn't it supposed to be (1/2)mv²?
Please help!

 

[riseofphoenix]

A 1.8 x 10²-g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R = 37.0 cm (figure below).

(a) Calculate its gravitational potential energy at A relative to B.

Energy of system at point A: PE_A + KE_A
E_A: PE_A + KE_A
E_A: PE_A + 0
E_A: PE_A

So,

PE_{gravitational} = mgh
PE_{gravitational} = (0.18)(9.81)(0.37)
PE_{gravitational} = 0.653

Got this one correct...

(b) Calculate its kinetic energy at B.

Energy of system at point B: PE_B + KE_B
E_B: PE_B + KE_B
E_B: mg(0) + KE_B ***height is 0 at point B, so PE = 0***
E_B: KE_B

The solution says that KE_B = mgR
How?? Isn't it supposed to be (1/2)mv²?
Please help!

 

[TSny]

How does the total energy at B compare to the total energy at A?

 

[phinds]

Is anyone even online?

yes ...

 

[riseofphoenix]

How does the total energy at B compare to the total energy at A?

I have no idea! That's why I'm asking...

PE_A + KE_A = PE_B + KE_B

?

 

[TSny]

Have you covered the law of conservation of mechanical energy?

 

[riseofphoenix]

Well kind of...

But my teacher never really elaborated on it enough.

 

[TSny]

Total mechanical energy is conserved in a problem like this because there is no friction to convert some of the mechanical energy into heat energy. You actually set up the equation that expresses this idea when you wrote:

PE_A + KE_A = PE_B + KE_B

So, apply this equation to your problem and see what it gives you for the KE at B.

 

[riseofphoenix]

Total mechanical energy is conserved in a problem like this because there is no friction to convert some of the mechanical energy into heat energy. You actually set up the equation that expresses this idea when you wrote:


So, apply this equation to your problem and see what it gives you for the KE at B.

PE_A + 0 = 0 + KE_B
PE_A = KE_B
mgR = KE_B
(0.18)(9.81)(0.37) = KE_B
0.635 = KE_B

Is that right?

 

[TSny]

Yes, that's right.

I noticed that you posted this question a second time because you had not received an answer within an hour of your first post. We ask that you not do that. Sometimes it just takes a while for someone to respond to your question. Please read https://www.physicsforums.com/showpost.php?p=4021232&postcount=4

especially the part "How long did you wait for a reply". Thanks.

 

[riseofphoenix]

What about part d though?

(d) Calculate its potential energy at C relative to B.

I did...

PE_B + KE_B = PE_C + KE_C
0 + KE_B = PE_C + 0
KE_B = PE_C
(1/2)mv² = PE_C

But after I plugged in all the values and got PE_C = 0.651, it said it was wrong!

So is it supposed to be:

PE_B + KE_B = PE_C + KE_C
PE_B + 0 = PE_C + 0
mgh = PE_C
mg(2R/3) = PE_C

Is that right??

 

[riseofphoenix]

Yes, that's right.

I noticed that you posted this question a second time because you had not received an answer within a hour of your first post. We ask that you not do that. Sometimes it just takes a while for someone to respond to your question. Please read https://www.physicsforums.com/showpost.php?p=4021232&postcount=4

especially the part "How long did you wait for a reply". Thanks.

Ohhh ok!

 

[haruspex]

How will its total (KE+PE) at B compare with that at A?

 

[cepheid]

Duplicate threads merged.

 

[TSny]

What about part d though?

(d) Calculate its potential energy at C relative to B.

The potential energy at C relative to B just means to calculate PE_C - PE_B. You won't need to use the idea of conservation of energy to do that. Just use the formula for PE.

[EDIT: Maybe a better way to say it would be that the potential energy at C relative to B means to find the potential energy at C using h as the height measued from point B.]

 

[TSny]

What about part d though?

PE_B + KE_B = PE_C + KE_C
0 + KE_B = PE_C + 0
KE_B = PE_C
(1/2)mv² = PE_C

But after I plugged in all the values and got PE_C = 0.651, it said it was wrong!

The reason you didn't get the right answer was because you assumed the KE at C is zero. But it isn't. The particle is still sliding upward at that point.