Work of kinetic friction on block in vertical circle

[galaticman]

Homework Statement

1. Homework Statement
A block of mass 0.015kg enters the bottom of a circular, vertical track with a radius R = 0.3m at an initial velocity of 4/ms. If the block loses contact with the track at an angle of 130 degrees, what is Wk, the work done by kinetic friction?

Homework Equations

F=ma
W_tot= W_mg+W_N+W_Fk=1/2*mv_f²-1/2*mv_i²

The Attempt at a Solution

So far I have that W_mg=-mg*(Rcos50+R)=-0.072447J and that W_N=0 J
The only part that I am having trouble with is finding vf right before that block leaves the track. Any help would be appreciated!

EDIT: I am not sure how to go about relating F=ma=mv²/R without knowing what the friction force is ie. f_k

 

[PeterO]

Homework Statement

1. Homework Statement
A block of mass 0.015kg enters the bottom of a circular, vertical track with a radius R = 0.3m at an initial velocity of 4/ms. If the block loses contact with the track at an angle of 130 degrees, what is Wk, the work done by kinetic friction?

Homework Equations

F=ma
W_tot= W_mg+W_N+W_Fk=1/2*mv_f²-1/2*mv_i²

The Attempt at a Solution

So far I have that W_mg=-mg*(Rcos50+R)=-0.072447J and that W_N=0 J
The only part that I am having trouble with is finding vf right before that block leaves the track. Any help would be appreciated!

EDIT: I am not sure how to go about relating F=ma=mv²/R without knowing what the friction force is ie. f_k

Read the thread about 6 down, made by GGDK

 

[PhanthomJay]

When the block loses contact with the track, the normal force is 0. So only the radial component of the weight force contributes to the centripetal acceleration at that point.

 

[galaticman]

Read the thread about 6 down, made by GGDK

When the block loses contact with the track, the normal force is 0. So only the radial component of the weight force contributes to the centripetal acceleration at that point.

So if I am understanding this correctly would that mean that:
1. F_xmg=mv²/R
2. mg*sin40=mv²/R
3. v_f=√(R*9.8*sin40)
4. v_f=1.3747m/s

AND would that also mean that the mass of the block did not matter for V_f

 

[PhanthomJay]

So if I am understanding this correctly would that mean that:
1. F_xmg=mv²/R
2. mg*sin40=mv²/R
3. v_f=√(R*9.8*sin40)
4. v_f=1.3747m/s

yes

AND would that also mean that the mass of the block did not matter for V_f

Well, it cancels out, but if the mass was higher, the block would not travel 130 degrees, it would travel less since there is more friction force .. So it does matter, even though you don't need to know it to solve this problem.

I see that per PeterO, help is already being provided in a separate post from another OP. I might just add that instead of using W_t = \Delta KE,
which is OK to use, you might want to use the alternate form of the Work-Energy Theorem , W_{nc} = \Delta PE + \Delta KE,
where since the normal force does no work and since gravity is not a non-conservative force, then W_{nc} = W_{friction}

 

[galaticman]

thanks so much! I understand the entire problem completely now! you were a huge help