Incline Plane Problem given mass, friction, 2 velocities

[TehDarkArchon]

Homework Statement

A solid mass weighing 50 kg slides down an incline plane with the coefficient of kinetic friction being 0.05. The velocity is measured to be 2.00 m/s and 5.00 m/s at two points 15 m apart. What are the A) Magnitude and direction of all forces action on the solid mass B) Acceleration of the mass and C) Angle the plane is inclined at?

Homework Equations

Fg = mg
Fn = mgcos(theta)
fs = (uk x Fn)
mgsin(theta)

F = ma

The Attempt at a Solution

So far I have the force of gravity (Fg) being mg = (50kg)(-9.81 m/s^2) but Fn = mgcos(theta), and since this is not given how would I go about calculating this? Also for part B, I was under the impression that since there is kinetic friction, using the kinematic equations would not work in this situation. Any help is much appreciated!

 

[tiny-tim]

Welcome to PF!

Hi TehDarkArchon! Welcome to PF!

(have a mu: µ anad a theta: θ and try using the X² tag just above the Reply box )

… for part B, I was under the impression that since there is kinetic friction, using the kinematic equations would not work in this situation.

All the forces are constant (including the friction), so the acceleration is constant, and the standard constant acceleration equations apply.

Use one of them to answer B first, then call the angle θ and answer A and C …

what do you get? ​

 

[TehDarkArchon]

Thank you very much for the prompt response, and sorry about not taking the time to get a good understanding of the formatting before posting =\ For B I used the equation v_f² = v_o² + 2ad, which in my case is rearranged to get (25 m/s - 4 m/s)/(2 x 15 m) giving me 0.700 m/s². I am confused about the angle though...should I use another kinematic equation and solve for time and then split the plane into horizontal and verticle components? It seems pretty complicated that way..

 

[tiny-tim]

Hi TehDarkArchon!

(just got up :zzz: …)

For B I used the equation v_f² = v_o² + 2ad, which in my case is rearranged to get (25 m/s - 4 m/s)/(2 x 15 m) giving me 0.700 m/s².

Yup!

Im confused about the angle though...should
I use another kinematic equation and solve for time and then split the plane into horizontal and verticle components? It seems pretty complicated that way..

Forget about horizontal and vertical …

in problems like this, use along-the-slope and perpendicular-to-the-slope instead!

There's zero acceleration perpendicular-to-the-slope, so that tells you what N is (as a function of θ), that gives you the friction force, and then you use F_total = ma along-the-slope, and solve for θ so that a = 0.7.