- #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.