Calculating Total Time for an Inclined Plane Motion Problem

[anubis01]

Homework Statement

A block of wood is projected up an inclined plane with initial speed v₀. If the inclination of the plane is 30⁰ and the coefficient of sliding friction u_k=0.1, find the total time for the block to return to the point of projection.

Homework Equations

f_A=u_kN
N=mgcosθ

The Attempt at a Solution

To be honest I'm not sure where to start with this. I'm just asking for a bit of
guidance on how to start the question.

 

[TVP45]

Can you set it up if there is no friction involved? Have you made a FBD?

 

[anubis01]

I'm not sure about setting it up without involving friction but I have made a FBD diagram.

 

[TVP45]

What can you tell about the initial conditions parallel to the incline?

 

[anubis01]

Oh I solved the problem (a good nights sleep does wonders apparently), thank you for the help though.

 

[LazyMan]

Can you tell me how you did it? I am really stuck on this problem

 

[anubis01]

The most important thing about the question is setting up the FBD once you get that the rest is simple. You need to analyze the system in two steps, the first one being up hill and the second downhill.

You should be able to first find the acceleration uphill, which can then be used to determine the time going up the incline , kinematic equations will be helpful in this regard. You can then use the information to find the time going down the incline.

 

[LazyMan]

Okay, I will give it a shot and if I still have troubles do you mind if I post back on here and you could help me out? Thanks!