- #1

ericcy

- 19

- 1

- 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 long), find

b) the acceleration of the cyclist if all sources of friction yield an effective coefficient of fricition of 0.11(solved this, answer is 0.1554m/s^2, this provides context for next question)

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

- Relevant Equations
- Fgx=Sin(theta)mg

Fgy-Cos(theta)mg

ma=Fnet

Ei=Ef

Because the friction is the same in both parts, the calculated acceleration from (b) should be the same for (c)

I knew I could find Vf, and thought I could do it with an energy equation

Ei=Ef

mgh=1/2mv^2

gh=1/2v^2

(2)9.81(1.5)=1/2v^2(2)

(square root)29.43=(square root)v^2

v= 5.424

Then kinematics to determine the time

Vf=Vi+at

5.424/1.554=0.1554t/1.554

t=34.9s

Pretty sure that this should work, but maybe it won't for inclined planes? I'm not sure. It could be that I didn't include the actual energy lost from friction (ff=1.0706)? I was thinking that I could also do it by using the hypotenuse of the triangle formed (12M) as distance for another kinematics equation, but why won't the other method work that I showed above?

The textbook answer is 12s

Sorry for the bunch of questions recently, I have a unit test tomorrow and just want to make sure I understand everything. Thanks guys.

I knew I could find Vf, and thought I could do it with an energy equation

Ei=Ef

mgh=1/2mv^2

gh=1/2v^2

(2)9.81(1.5)=1/2v^2(2)

(square root)29.43=(square root)v^2

v= 5.424

Then kinematics to determine the time

Vf=Vi+at

5.424/1.554=0.1554t/1.554

t=34.9s

Pretty sure that this should work, but maybe it won't for inclined planes? I'm not sure. It could be that I didn't include the actual energy lost from friction (ff=1.0706)? I was thinking that I could also do it by using the hypotenuse of the triangle formed (12M) as distance for another kinematics equation, but why won't the other method work that I showed above?

The textbook answer is 12s

Sorry for the bunch of questions recently, I have a unit test tomorrow and just want to make sure I understand everything. Thanks guys.