Finding the Distance a Mass Travels Up an Incline with Friction

[mrshappy0]

Homework Statement

Hey all! I was given a multi-step problem and solved everything but the last step. Okay so, a mass on a frictionless plane by a string at an angle theta for a distance until it reaches an incline that has friction and is parallel to the string. The problem asks to find the distance that the mass will travel up the incline.

Homework Equations

Δk=Wnet

The Attempt at a Solution

I already know the initial velocity that the mass is moving when it begins to climb the incline.
So I assume I would use this formula:
-v_i²mass/2=(T-f_k-mg)H and just solve for H. Does this sound right?

 

[anathema]

Hi there,

Great job on solving most of the problem! Your approach using the work-energy theorem is correct. However, you may need to consider the initial kinetic energy of the mass as well, as it will contribute to the final height it reaches on the incline.

The equation you have written should be:

ΔK = Wnet

Where ΔK is the change in kinetic energy, and Wnet is the net work done on the mass. Since the mass starts with an initial velocity, it will have some initial kinetic energy. This initial kinetic energy will be converted into potential energy as the mass climbs the incline.

So, the equation should be:

Kf - Ki = Wnet

Where Kf is the final kinetic energy (which will be zero since the mass comes to a stop at the top of the incline), and Ki is the initial kinetic energy. Wnet is the net work done on the mass, which is equal to the work done by the tension force (T), the friction force (fk), and the weight force (mg).

So, the equation becomes:

0 - (1/2)mv_i^2 = Td + fkH + mgh

Where d is the distance the mass travels along the incline, and H is the height it reaches. You can solve for H using this equation, and don't forget to include the initial kinetic energy term.

I hope this helps! Let me know if you have any other questions. Keep up the good work!