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Kinetics of a Particle (car and wind resistance)?
A car of mass m is traveling at a slow velocity v0. If it is subjected to the drag resistance of the wind, which is proportional to its velocity, i.e., FD = kv, determine the distance and the time the car will travel before its velocity becomes 0.5v0. Assume no other frictional forces act on the car.
I got the answer.
S denotes an integral.
For the x-direction: -Fd=m(dv/dt)
-kv=m(dv/dt)
(-k/m)S[0,t]dt=S[v0,v](dv/v)
(-k/m)t=ln(v/v0)
set v=0.5v0: t=(m/k)ln(2)
t=0.693(m/k)
-------------------------------------------
(-kv)=m(vdv/dx)
-kvdx=mvdv
-S[0,x]kdx=mvdv
-S[0,x]kdx=S[v0,v]mdv
-kx=m(v-v0)
At v=0.5v0
x=(m/k)(0.5v0)
x=0.5(mv0/k)
S denotes an integral.
For the x-direction: -Fd=m(dv/dt)
-kv=m(dv/dt)
(-k/m)S[0,t]dt=S[v0,v](dv/v)
(-k/m)t=ln(v/v0)
set v=0.5v0: t=(m/k)ln(2)
t=0.693(m/k)
-------------------------------------------
(-kv)=m(vdv/dx)
-kvdx=mvdv
-S[0,x]kdx=mvdv
-S[0,x]kdx=S[v0,v]mdv
-kx=m(v-v0)
At v=0.5v0
x=(m/k)(0.5v0)
x=0.5(mv0/k)
3 Answers
- 8 years agoFavorite Answer
a = FD / m = -kv / m
(v0/2)^2 - v0^2 = 2a*s = (-2kv/m)*s
so distance travelled is s = -(3v0^2/4) * -m/(2kv) = 3*v*m/(8k)
v0/2 = v0 - a*t = v0 - (kv/m)*t
so time is t = -v0/2 * -m/(kv) = m*v0 / 2kv
but unfortunately acceleration a is not constant because v starts at v0 and drops to v0/2 ...
I'll keep thinking :)
- shoeLv 45 years ago
If we use 2d of wheels for producing the present the resistants led to via the magnets which u try 2 convert the present will decelerate the motor vehicle... so merely they are connecting the engine to battery to offer modern.... we cant fix a extensive wind mill interior the motor vehicle to make the main of wind resistance... so the two are almost imposible
- kasabLv 78 years ago
I have kept your question under watch, and went about it once without getting a convincing answer.
This is a difficult case of a variable acceleration, and none of the conventional formulas for motion can apply. Therefore, the solution offered by Dr. Watkin... can not be right.
I see that you just announced that you got the answer 4 minutes ago.
Please present it, if you care.
