# Incline plane question

1. Jul 13, 2008

### HelloMotto

1. The problem statement, all variables and given/known data

Starting from rest, a cyclist coasts down the starting ramp at a professional biking track. If the ramp has the minimum legal dimensions(1.5 m high and 12m lomg) find
a) the acceleration of the cyclist ignoring friction

b) the acceleration of the cyclist if all sources of friction yield an effective coefficient of friction = .11

c)time taken to reach the bottom of the ramp, if friction acts as in (b)

2. Relevant equations

My concern is the part a.
V1= 0
v2= ?
a=?
m=?
d=12m

I cant use Newton's 2nd law to find the a because the mass is not given nor the force.
I looked at all kinematic equation and none of them works as well...so how do i approach solving this problem?

2. Jul 13, 2008

### aniketp

The mass does not matter here.... It may get cancelled in the equations itself.
Also try and upload a figure of the problem.

3. Jul 13, 2008

### HelloMotto

no figure was given in the question

4. Jul 13, 2008

### LowlyPion

You know the height of the starting point 1.5m and you know the length of the starting ramp 12m and you know the value of gravity. 9.8m/s^2. You should be able to develop what the value of the constant acceleration is on the cycle shouldn't you?

5. Jul 13, 2008

### HelloMotto

i dont get it...how?

6. Jul 13, 2008

### elessariitkgp

Firstly the dimensions of the ramp give the angle of inclination of the ramp. If the height is $$\var H$$ and the length of the ramp be $$\var L$$, then $$tan\vartheta=\frac{\var H}{\var L}$$
The particle model can be used here.
Let the mass of the particle be $$\var m$$
Then observing the equilibrium perpendicular to the ramp,
$$\var N = \var mg cos \vartheta$$
and along the ramp
$$mg sin \theta - \mu mg cos\theta = ma$$
$$a=g sin \theta - \mu g cos\theta$$

which is independent of $$m$$

7. Jul 13, 2008