The coefficient of static friction between a rubber tire and a wet road is 0.443.
a) On this surface, what is the maximum safe speed of a car going around a level, unbanked circular track of radius 250 meters?
b) How long would the car take to go once around the track at the maximum safe speed?
Help!!!!!
I agree in the fact that the frictional force is 0.443.
this friction coefficient force is vary interesting. gya
normal force is ... m g
frictional force is ... .443 m g
the frictional force equals the centripetal force
... .443 m g = m v^2 / r
... v^2 = .443 g r
solve for v
the circumference (for once around) is
... 2 π r
divide the circumference by the velocity to find the time
To find the maximum safe speed, we can use the concept of centripetal force. The centripetal force is provided by the static friction between the tire and the road, which prevents the car from sliding outwards. The formula for centripetal force is:
Fc = mv^2 / r
Where:
- Fc is the centripetal force
- m is the mass of the car
- v is the velocity of the car
- r is the radius of the circular track
In this case, we are given the coefficient of static friction (μs) between the tire and the wet road, which is 0.443. The static friction force is given by:
Fs = μs * N
Where:
- Fs is the static friction force
- N is the normal force (equal to the weight of the car)
Since the car is on an unbanked track:
N = m * g
Where:
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Combining these equations, the maximum safe speed can be calculated by equating the centripetal force and the static friction force:
mv^2 / r = μs * m * g
Canceling out the mass (m) on both sides, we get:
v^2 / r = μs * g
Rearranging the equation to solve for v:
v = sqrt(μs * g * r)
Let's calculate the value of the maximum safe speed:
a) Maximum safe speed:
μs = 0.443
g = 9.8 m/s^2
r = 250 meters
v = sqrt(0.443 * 9.8 * 250)
v = sqrt(1087.85)
v ≈ 32.98 m/s
Therefore, the maximum safe speed for the car on this surface is approximately 32.98 m/s.
To find the time taken to go once around the track at the maximum safe speed, we can use the formula for the circumference of a circle:
C = 2πr
The time taken can be calculated by dividing the circumference by the velocity:
b) Time taken to go once around:
C = 2π * r = 2π * 250
v = 32.98 m/s
t = C / v
t = (2π * 250) / 32.98
t ≈ 47.68 seconds
Therefore, the car would take approximately 47.68 seconds to go once around the track at the maximum safe speed.