# HELP physics prove question

1. Nov 3, 2008

### Kudo Shinichi

HELP!!!physics prove question

1. The problem statement, all variables and given/known data
A boy is seated on the top of a hemispherical mound of ice. He is given a very small push and starts sliding down the ice surface, assumed to be fricitionless. show that he leaves the ice at a point who height is 2R/3

3. The attempt at a solution
I don't really know how to do this question. However, I know that the normal force disappears as he leaves the ice.

2. Nov 3, 2008

### tiny-tim

Hi Kudo Shinichi!

Hint: calculate his speed at an angle θ, then caclulate the normal force.

3. Nov 3, 2008

### Kudo Shinichi

Re: HELP!!!physics prove question

x-direction:
v_0=v_0*cosθ
then use V_f=V_0+at
y-direction:
V_0=V_0*sinθ
then use V_f=V_0+at
but I have some many unknown variables...
Normal force=mg
also, How can i relate the speed to the normal force since F_n=mg

4. Nov 3, 2008

### tiny-tim

Nooo … that equation (and the other two kinematic equations) only work if a is constant … which will only happen in free-fall, or on a slope.

This is a sphere, not a slope.

Hint: use conservation of energy.

5. Nov 3, 2008

### Kudo Shinichi

Re: HELP!!!physics prove question

Do you mean conservation of momentum and conservation of kinetic energy?
P=P'
m1v1+m2v2=m1v1'+m2v2'

KE=KE'
1/2m1v1^2+1/2m2v2^2=1/2m1(v1')^2+1/2m2(v2')^2
Since the initial velocity is equal to 0
therefore,
m1v1'=-m2v2'
1/2m1(v1')^2=-1/2m2(v2')^2
we don't know the mass of the boy, how can we find out the velocity...also you said find out the velocity by using angles, but i didn't need to use any angle on the above equations. I still don't really understand how to relate the velocity to the normal force, because normal force is equal to mg and both variables are nothing to do with velocity.

6. Nov 4, 2008

### tiny-tim

conservation of momentum (m1v1+m2v2=m1v1'+m2v2') and conservation of energy are entirely different things

conservation of momentum will not work on a curved surface.
conservation of kinetic energy does not exist

it's conservation of energy … that's total energy, not just kinetic energy:

KE + PE = constant
this is obviously the wrong equation … whatever is m2?

Try again.

7. Nov 4, 2008

### Kudo Shinichi

Re: HELP!!!physics prove question

Total mechanical energy=PE+KE
PE+KE=0
PE=-KE
mgh=-1/2mv^2
m(9.8)(2R/3)=-1/2mv^2
m cancels out
v^2=9.8(2R/3)(-2)
v=sqrt(9.8*(2R/3)*-2)

I think this is the velocity that i need to find
and we know that the normal force =0 when the both is at the h=2R/3, but how do we relate the velocity to the normal force and how do we show that the boy leaves at height=2R/3

8. Nov 4, 2008

### tiny-tim

Use Newton's second law in the radial (normal) direction.

9. Nov 4, 2008

### Kudo Shinichi

Re: HELP!!!physics prove question

Total mechanical energy=PE+KE
PE+KE=0
PE=-KE
mgh=-1/2mv^2
m(9.8)(2R/3)=-1/2mv^2
m cancels out
v^2=9.8(2R/3)(-2)
v=sqrt(9.8*(2R/3)*-2)

f=m*dv/dt
f=m*d(sqrt(9.8*(2R/3)*-2))/dt

this is the force we got
sorry, but I still don't get how can we prove that the boy starts from 2R/3 by using the force we got from above.

10. Nov 4, 2008

### tiny-tim

No!!

fnet = ma.

(a only = dv/dt if the motion is in a straight line … this is along a curve)

What is fnet?

11. Nov 4, 2008

### Kudo Shinichi

Re: HELP!!!physics prove question

F_net is the net force, which is also stands for all the forces we applied.
F_net=F_1+F_2+F_3+....
F_net=ma
in this case a is equal to v because
a=v(T2)-v(T1)
and the initial velocity in the problem is zero
therefore a= v-0 a=v a=v=sqrt(9.8*(2R/3)*-2)

F_net=m*v=m*sqrt(9.8*(2R/3)*-2)
= sqrt(-13.1R)*m

12. Nov 5, 2008

### tiny-tim

So what are F_1 F_2 and F_3?

13. Nov 5, 2008

### Kudo Shinichi

Re: HELP!!!physics prove question

F_1=ma_1
F_2=ma_2
F_3=ma_3