A block of mass going down an incline plane with friction

[chiCEstudent]

Homework Statement

A block of mass m = 15.0kg starts from rest and slides down an incline plane with slope angle theta = 45 degrees for a distance d₁. It then reaches the flat surface and travels for a distance d₂, where it comes to rest. The coefficient of kinetic friction between the block and all surfaces is the same everywhere with a value of uk = 0.200

Write the Newton's Laws equations of motion and solve for acceleration of the block on the incline plane. Do the same for the block's motion on the flat region. (the question also asks for free body diagrams but I know how to do this)

Given d₁ = 2 meters, find d₂, the distance the block travels on the flat surface before coming to a rest.

Homework Equations

Newton's Laws equations? This is the part I don't know

The Attempt at a Solution

I am not sure what equations I need to use...


Thanks for the help in advance! If anyone can provide the equations I think I can take it from there... thanks!

 

[mgb_phys]

Try conservation of energy

 

[jhae2.718]

For a conservative force, $0=W_{net}={\Delta}U+{\Delta}K+F_ks$,
where ${\Delta}U=mgh_f-mgh_i$ and ${\Delta}K=\frac{mv_f^2}{2}-\frac{mv_0^2}{2}$. $F_ks$ is the force of kinetic friction times the displacement.

You should then be able to use that and constant acceleration equations to solve the problem.

 

[chiCEstudent]

Ok... I am trying the equations, but I'm not sure which values to plug in where. I know gravity has a -9.8m/s² acceleration, but I don't think this value applies since its on an incline of 45 degrees. I remember something about finding the vector components using sine and cosine... If someone can give me another push in the right direction I would really appreciate it

 

[Jebus_Chris]

Fnet=ma

The block is moving down the ramp with a constant acceleration because of gravity and friction(draw a picture of the forces to find the net force and therefore the acceleration). When it reaches the flat part it has constant acceleration based only upon friction.
You can use kinematics equations to find the speeds and distances once you find the acceleration.