A 640-kg racing car completes one lap in 14.3 s around a circular track with a radius of 55.0 m. The car moves at constant speed.(a) What is the acceleration of the car?(b) What force must the track exert on the tires to produce this acceleration?
v=2πR/t = …
a= a(n) =mv²/R
F=ma
(a) To find the acceleration of the car, we can use the equation for centripetal acceleration:
a = v^2 / r
Where:
a = acceleration
v = velocity
r = radius of the circular track
Given that the car moves at a constant speed, we can find the velocity using the formula:
v = 2πr / t
Where:
π = pi (approximately 3.14)
r = radius of the circular track
t = time taken to complete one lap
Plugging in the given values, we have:
v = 2 * 3.14 * 55.0 / 14.3
v ≈ 13.823 m/s
Now we can calculate the acceleration:
a = (13.823)^2 / 55.0
a ≈ 3.4549 m/s^2
Therefore, the acceleration of the car is approximately 3.4549 m/s^2.
(b) To find the force exerted by the track on the tires, we can use Newton's second law of motion:
F = m * a
Where:
F = force
m = mass
a = acceleration
Given that the mass of the car is 640 kg, and the acceleration is approximately 3.4549 m/s^2, we can calculate the force:
F = 640 * 3.4549
F ≈ 2211.936 N
Therefore, the track must exert a force of approximately 2211.936 Newtons on the tires to produce this acceleration.
To find the acceleration of the car, we can use the formula:
Acceleration (a) = v^2 / r
Where:
v = Velocity (speed) of the car
r = Radius of the circular track
Given that the car completes one lap in 14.3 seconds, we need to find the velocity (v) to calculate the acceleration (a).
To find the velocity, we can use the formula:
v = 2πr / t
Where:
t = Time taken to complete one lap
Let's calculate the velocity first:
v = (2 x π x 55.0 m) / 14.3 s
v ≈ 24.293 m/s
Now, we can substitute this value of velocity into the acceleration formula:
a = (24.293 m/s)^2 / 55.0 m
a ≈ 10.678 m/s^2
So, the acceleration of the car is approximately 10.678 m/s^2.
Now, to find the force exerted by the track on the tires, we can use the formula:
Force (F) = mass (m) x acceleration (a)
Given that the mass of the car is 640 kg and the acceleration is 10.678 m/s^2, we can calculate the force exerted by the track:
F = 640 kg x 10.678 m/s^2
F ≈ 6827.52 N
Therefore, the force that the track must exert on the tires to produce this acceleration is approximately 6827.52 Newtons.