A 640-kg racing car completes one lap in 14.3 s around a circular track with a radius of 45.0 m. The car moves at constant speed.
(a) What is the acceleration of the car?
m/s2
(b) What force must the track exert on the tires to produce this acceleration?
a = v^2/r where v = 2 pi r/14.3
F = m a = 640 a
To find the answers to these questions, we need to use some basic equations related to circular motion.
(a) The acceleration of an object moving in a circular path can be calculated using the formula:
a = v^2 / r
where a is the acceleration, v is the velocity, and r is the radius.
In this case, we are given the radius of the track (r = 45.0 m) and the time it takes to complete one lap (t = 14.3 s). To find the velocity, we need to first calculate the circumference of the track using the formula:
C = 2 * π * r
Substituting the values, we have:
C = 2 * 3.14 * 45.0 = 282.6 m
The velocity of the car can be found by dividing the distance traveled (C) by the time taken (t):
v = C / t = 282.6 / 14.3 = 19.76 m/s
Now we can find the acceleration by substituting the values into the equation:
a = v^2 / r = (19.76)^2 / 45.0 = 8.6256 m/s^2
Therefore, the acceleration of the car is approximately 8.63 m/s^2.
(b) To find the force exerted by the track on the tires, we can use Newton's second law of motion, which states that force (F) equals mass (m) times acceleration (a):
F = m * a
In this case, we are given the mass of the car (m = 640 kg) and the acceleration (a = 8.63 m/s^2). Substituting these values into the equation:
F = 640 * 8.63 = 5539.2 N
Therefore, the force that the track must exert on the tires to produce this acceleration is approximately 5539.2 N.