Penguin sliding down incline with friction: find the angle

[Any Help]

1.Question:

A penguin is going down a slide. The coefficient of kinetic friction between the penguin and the slide has a value of 0.77. It takes three times as long to slide down this slide as it would if the slide were frictionless. Find the angle of the slide.
2. My answer: I chose solving it using mechanical energies

Suppose it reaches ground state after covering distance d,

Equations of mechanical energy;

with friction:

Ek+Epg=Wf+Ek1+Epg1 Wf=-0.77.d.mg.cos(alfa)

mv^2/2+mg.d.sin(alfa)=-0.77dmgcos(alfa)+mV^2/2+mgh(final) divide by m (h final=0 taking ground state when it covers d)

v^2/2+gdsin(alfa)=-0.77gdcos(alfa)+V^2/2--------------------{1}

without friction: Ek+Epg=Ek1+Epg1 (Epg1=0)

mv^2/2+mg.3dsin(alfa)=mV^2/2 divide by m (V after cutting 3d without friction equal V after cutting 1d with friction)

v^2/2+3d.g.sin(alfa)=V^2/2----------------------------{2}

{2} - {1}:... tan(alfa)=0.77.g/2

that gives ALFA=75.155 degree Is it correct?

 

[Biker]

Ek+Epg=Wf+Ek1+Epg1 Wf=-0.77.d.mg.cos(alfa)

mv^2/2+mg.d.sin(alfa)=-0.77dmgcos(alfa)+mV^2/2+mgh(final) divide by m (h final=0 taking ground state when it covers d)

v^2/2+gdsin(alfa)=-0.77gdcos(alfa)+V^2/2--------------------{1}

without friction: Ek+Epg=Ek1+Epg1 (Epg1=0)

mv^2/2+mg.3dsin(alfa)=mV^2/2 divide by m (V after cutting 3d without friction equal V after cutting 1d with friction)

v^2/2+3d.g.sin(alfa)=V^2/2----------------------------{2}

{2} - {1}:... tan(alfa)=0.77.g/2

that gives ALFA=75.155 degree Is it correct?

There are multiple mistakes in your solution, Are you asked to solve this using energy conservation?
You can basically use equations of motion to solve this
It gave you an equation.
$3T_{time ~takes~ to ~slide ~without ~friction} = T_{time~ takes ~to ~slide~ with ~friction}$
Draw a FBD, identify the forces and acquire accelerations of the bodies.

Some algebra will give you the angle, Everytime you arrive at something post your work and we will be here :D

 

[Any Help]

There are multiple mistakes in your solution, Are you asked to solve this using energy conservation?
You can basically use equations of motion to solve this
It gave you an equation.
$3T_{time ~takes~ to ~slide ~without ~friction} = T_{time~ takes ~to ~slide~ with ~friction}$
Draw a FBD, identify the forces and acquire accelerations of the bodies.

Some algebra will give you the angle, Everytime you arrive at something post your work and we will be here :D

you mean i must find the time equation for both?

 

[Biker]

you mean i must find the time equation for both?

Yes :D
Use the equations of motion to find the time.

 

[Any Help]

then it will be with friction
-0.77gcos(alfa)+gsin(alfa)=af
without friction gsin(alfa)=a
delta x= v0t+0.5at^2
t=sqaur root (2.deltax/af) T=sqrrt(2.deltax/a)
3T=t
9T^2=t^2
9af=a
tan(alfa)=9x0.77/8 alfa=40.9
right?

 

[Biker]

then it will be with friction
-0.77gcos(alfa)+gsin(alfa)=af
without friction gsin(alfa)=a
delta x= v0t+0.5at^2
t=sqaur root (2.deltax/af) T=sqrrt(2.deltax/a)
3T=t
9T^2=t^2
9af=a
tan(alfa)=9x0.77/8 alfa=40.9
right?

Excellent work :).