Energy with nonconservative forces

[maniacp08]

A 3.0kg slides along a horizontal surface with a speed of 7.0m/s.
After sliding a distance of 2.0m, the block makes a transition to a ramp inclined at an angle of 40 degrees to the horizontal. The coefficient of kinetic friction between the block and the surfaces is .30.

Find
a) the speed of the block when it reaches the ramp
b)the distance the block slides along the inclined surface before coming momentarilly at rest(neglect any energy dissipated along the transition curve)

For part A I used
External Work = change in potential energy + change in kinetic energy + change in thermal energy

External work = 0
change in potential energy = 0

so it becomes
0 = change in kinetic energy + change in thermal energy

change in kinetic energy = 1/2 m Vf^2 - 1/2 m Vi^2
change in thermal energy = Uk * FN * displacement = Uk * m * g * 2
I plug in the numbers and I solve for Vf?

For Part B:
I can use the same equation but this time I am solving for height.
External Work = change in potential energy + change in kinetic energy + change in thermal energy

External Work = 0
change in potential energy = -mgh
change in kinetic energy = -1/2 m Vi^2
change in thermal energy = Uk * FN * displacement = Uk * m * g * 2

Solve for the height it reaches, then use trig to find the distance/hypotenuse.

Are these approaches correct? Thanks for helping.

 

[Irid]

Yes, sure, the energy conservation is a good approach. Good luck!

 

[baba89]

Yes, your approaches are correct. For part A, you can use the conservation of energy principle to find the final speed of the block when it reaches the ramp. As you have correctly identified, the external work done on the block is zero, so the total mechanical energy (kinetic + potential) is conserved. Therefore, you can set the initial kinetic energy (1/2 m Vi^2) equal to the final kinetic energy (1/2 m Vf^2) and solve for Vf.

For part B, you can use the same approach to find the height the block reaches on the ramp. Once you have the height, you can use trigonometry to find the distance the block slides along the inclined surface before coming to a momentary rest. This distance will be equal to the hypotenuse of the triangle formed by the inclined surface and the horizontal surface.