Acceleration on an Incline Plane: Solving for Unknowns

[HelloMotto]

Homework Statement

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)

Homework Equations

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

I can't 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?

 

[aniketp]

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

 

[HelloMotto]

no figure was given in the question

 

[LowlyPion]

Homework Statement

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)

Homework Equations

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

I can't 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?

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?

 

[HelloMotto]

i don't get it...how?

 

[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 $$m$$

 

[HelloMotto]

thank you. is the answer
1.2 m/s^2 for part a and .13m/s^2 in part b?