Here is the problem and answers. how do i reach the answer?
A car at the Indianapolis-500 accelerates uniformly from the pit area, going from rest to 325 km/h in a semicircular arc with a radius of 198 m.
Determine the tangential acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration.
6.55m/s2
Determine the radial acceleration of the car at this time.
20.6m/s2
If the curve were flat, what would the coefficient of static friction have to be between the tires and the roadbed to provide this acceleration with no slipping or skidding?
2.2
tangentialacceleration:
vf^2=Vi^2+2ad where d is half the turn, or PI*198/2 Be certain to convert Vf to m/s
radial acceleration= V^2/r where V is in m/s.
Force=m*v^2/r
mu*mg=m v^2/r
solve for mu.
If this question is Webassign related, you may have to 1/2 the answers you plug into the textbox, like I did.
Bub Pursley describes it correctly.
To reach the answer, you need to understand the concepts of tangential acceleration, radial acceleration, and the coefficient of static friction.
1. To determine the tangential acceleration of the car when it is halfway through the turn, you can use the formula for tangential acceleration:
a = v^2 / r
where:
a = tangential acceleration
v = velocity of the car
r = radius of the arc
In this case, the car is going from rest to 325 km/h, so you need to convert the velocity to m/s:
v = 325 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 90.28 m/s
The radius of the arc is given as 198 m.
Now you can plug these values into the formula:
a = (90.28 m/s)^2 / 198 m = 41.03 m/s^2
Therefore, the tangential acceleration of the car when it is halfway through the turn is 41.03 m/s^2.
2. To determine the radial acceleration of the car at this time, you can use the formula for radial acceleration in uniform circular motion:
ar = v^2 / r
Using the same values as before:
ar = (90.28 m/s)^2 / 198 m = 41.03 m/s^2
Therefore, the radial acceleration of the car at this time is 41.03 m/s^2.
3. If the curve were flat, the coefficient of static friction (µ) between the tires and the roadbed can be determined using the formula:
µ = ar / g
where:
µ = coefficient of static friction
ar = radial acceleration
g = acceleration due to gravity (approximately 9.8 m/s^2)
Using the radial acceleration from the previous calculation:
µ = 41.03 m/s^2 / 9.8 m/s^2 = 4.18
Therefore, if the curve were flat, the coefficient of static friction between the tires and the roadbed would have to be approximately 4.18.