b) if the fly was just hanging out before and sticks to the windshield, it's change in momentum is:
deltap = mfly * v
a) Per Newton's 3rd law, same answer
c) To first order, you can divide the change in momentum mcar * deltavcar by the change in momentum from one fly.
number of flies = mcar * deltavcar / (mfly * v)
---as others have noted, each fly delivers less and less impulse as the car slows down. But the car doesn't slow down much, and I take the word %26quot;approximately%26quot; in the question to be license to ignore the issue and just divide the total impulse you want by the impulse of one fly smacking at full speed.Fly hitting windshield!?
Depends on whether or not the collision is elastic or inelastic.Fly hitting windshield!?
I'd put the brake on after about 10 flies hit one after another...Fly hitting windshield!?
There would have to be a solid wall of flies several feet thick to even start to slow down the car. It's too disgusting to think about.Fly hitting windshield!?
not only does the fly see its own *** just before it dies, it sees the asses of all the other flies too.
conservation of momentum
Mcar * Vcar = Mfly*Vfly
you know Mcar, Mfly, Vfly is 12km/h since it goes from stationary to the car's speed. find the change in Vcar.
the answer to b has to be the same as a due to conservation of momentum
for c, Mcar is the same (unless, you're counting the added mass of the flies on the car) Vcar is 1km/h change. Vfly is 120km/h, solve for Mfly which is the mass of flies needed. I guess this is just an approximation since Mcar and Vfly are always changing, but it's close enoughFly hitting windshield!?
You should check my math on this:
The writer of the question likely means for the fly to be squashed and stick, so assume it is inelastic.
M1=mass of car
V1= speed of car before collision
V2= speed of car after collision
m=mass of fly
Total momentum before collision
M1V1= 1100Kg*120Km/hr
Total momentum after collision
(M1+m)V2= 1100.0002kg*V2
Set these equal
1100Kg*120Km/hr = 1100.0002kg*V2
V2 = 1100*120/1100.0002 Km/hr
Momentum of Car after collision
1100(1100*120/1100.0002)
Change in momentum of Car
1100Kg*120Km/hr - 1100Kg(1100*120Km/hr/1100.0002)=
1100.0002*(1100Kg*120Km/hr/1100.0002) -1100Kg(1100*120Km/hr/1100.0002)=
.0002*(1100Kg*120Km/hr/1100.0002)
Momentum of fly after
.0002 kg *(1100*120/1100.0002 Km/hr)
Change in momentum of fly
0 - .0002 kg *(1100*120/1100.0002 Km/hr)=
-.0002 kg *(1100*120/1100.0002 Km/hr)
This is the same magnitude as the change for the car.
b) Could be trickier. It is tempting to assume linear thinking that since
one fly casused the speed to drop from 120 to 119.99997818 that each fly
will cause the same drop in speed.
But this is not so if each fly squashes and sticks to the car.
In this case the mass of the moving object will be growing with each collision.
You could just repeat the problem above incrementally increasing the starting mass and decreasing the final speed until you get to 1 km/hr
But it is easier to go from the beginning to the end in one step
M1=mass of car
V1= speed of car before any collision
V2= speed of car after all collisions
m=mass of one fly
n=number of flies
Total Monmentum Before any collisions
M1*V1 = 1100Kg*120Km/hr
Total Monmentum After all collisions
(M1 +n*m)V2= (1100 +n*.0002)*1 kgkm/h
Set these equal
M1*V1 =(M1 +n*m)V2
1100Kg*120Km/hr=(1100 +n*.0002)*1 kgkm/h
1100*120=1100 + .0002*n
n=654500000 flies
