What is the distance moved up the plane (friction problem)

[aps0324]

A particle P of mass 3 kg is projected up the line of greatest slope of a plane inclined at an angle of 50° to the horizontal. The coefficient of friction between P and the plane is 0.5. The intiial speed of P is 9 m/s.

ii) Find the frictional force acting on P

ii) What distance moved up the plane by P until its velocity becomes zero.

Homework Equations

f = μ x N where N is the normal

N = m x g x cos(50)

The Attempt at a Solution

i)

N = m x g x cos(50) = 19.28 N

f = 0.5 x 19.28 = 9.64 N


ii) Here I do not know what to do. I thought I could take -5 m/s^2 as a deceleration by using :

f = μ x N

m x a = 0.5 x m x g

a = 5 m/s^2

and then using SUVAT equations but this is wrong since I do not get the answer shown in my book..

Please help!

Thank you!

 

[tiny-tim]

ii) What distance moved up the plane by P until its velocity becomes zero.

Hi aps0324!

Use the work-energy theorem … change in energy = https://www.physicsforums.com/library.php?do=view_item&itemid=75"

 

[aps0324]

I did think of that..but shouldn't friction still be taken into account? Because I did the following :

1/2 x m x v^2 = mgh

h = v^2 (2g) = 4.05 where v = 9 m/s and g = 10

and then in order to find the hypotenuse i used

Hypotenuse = 4.05 / sin(50)

But this gives me 5.28 m and the answer is 3.72 m

 

[tiny-tim]

I did think of that..but shouldn't friction still be taken into account

Friction is taken into account, in the https://www.physicsforums.com/library.php?do=view_item&itemid=75" …

work done = force times distance.