Question about thermal energy due to friction

[iheartpink]

Brief summary: There is a block that travels down and frictionless curved ramp from A to B and it slides from B to C where the kinetic friction coefficient is 0.25
Question: Determine the thermal energy produced as the block slides from B to C

My question:
I know for gravitational/vertical problems the equation would be change of kinetic energy plus the change of gravitation potential energy plus the force of friction*displacement = 0. Since nothing is falling and the displacement is purely horizontal, I am not sure what equation to use to solve this part of the problem

 

[Doc Al]

If B to C is purely horizontal, then the change in gravitational PE will be zero. But here all you need to do is calculate the work done against friction (if you are given enough information to calculate it directly)--all of it goes to to thermal energy.

 

[iheartpink]

Okay...
I know that the work done by friction will be the normal force*friction coefficient*displacement which will be 9.8*.25*3= 7.35
is that thermal energy produced?

Next it asks for the velocity at point C. is that velocity figured from the work-energy principle? If i know the initial velocity is the velocity at point C (the end of the horizontal stretch) given by change in kinetic energy + change in potential + thermal energy = 0? if so I solved for the velocity and was given a negative number. A negative number doesn't make since if the movement is in the positive x direction, so I'm confused.

 

[Doc Al]

I know that the work done by friction will be the normal force*friction coefficient*displacement which will be 9.8*.25*3= 7.35
is that thermal energy produced?

That's the correct relationship: Work done against friction = $\mu N s$. But what's the mass of the object? (1 kg?) The displacement from B to C? (3 m?)

Next it asks for the velocity at point C. is that velocity figured from the work-energy principle? If i know the initial velocity is the velocity at point C (the end of the horizontal stretch) given by change in kinetic energy + change in potential + thermal energy = 0?

The velocity at point C would be the final velocity, wouldn't it? But that's the right idea: energy conservation.

if so I solved for the velocity and was given a negative number.

That doesn't make sense. Please state the full problem and describe how you solved for the velocity. (You should be solving for the final KE of the block, then using that to calculate the final velocity.)

 

[iheartpink]

the problem says to consider the track. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.0 m long with a coefficient of kinetic friction = 0.25. The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at point A. After sliding on the track , it compressed the spring by 0.20m. Determine (a) the velocity of the block at point B, (b) the thermal energy produced as the block slides from B to C, (c) the velocity of the block at point C

to solve for the velocity at point B:
I solved for the arclength and found that it was 3.14 m with the central angle of 90 degrees. O then used the formula velocity squared equals the square root of 2*g*y. i plugged in 3.14 m for the y value and solved the velocity to be 7.845 m/s.

 

[iheartpink]

well. i discovered one mistake: there is no need to find arc length. the y displacement is just the radius, which is two. but i still calculated a negative value for velocity sqaured

 

[Doc Al]

Please describe how you did that calculation.