A 605-kg racing car completes one lap in 14.3 s around a circular track with a radius of 40.0 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?
Correction:
b. F = ma = 605*1.23 = 743.6 N.
a. C = pi*2r = 3.14 * 80 = 251.3 m = The
Circumference.
V = 251.3m/14.3s = 17.6 m/s.
a = (V-Vo)/t.
a = (17.6-0)/14.3 = 1.23 m/s^2.
b. F = ma = 60s * 1.23 = 743.6 N.
(a) To find the acceleration of the car, we can use the formula for centripetal acceleration:
\[a = \frac{v^2}{r}\]
Where:
a is the acceleration,
v is the velocity, and
r is the radius.
Since the car moves at a constant speed, the velocity remains constant throughout the lap. We can calculate the velocity using the formula for the circumference of a circle:
\[v = \frac{2 \pi r}{t}\]
Where:
v is the velocity,
r is the radius, and
t is the time.
Substituting the given values:
r = 40.0 m
t = 14.3 s
\[v = \frac{2 \pi \cdot 40.0}{14.3}\]
\[v \approx 88.89 \, \text{m/s}\]
Now, we can calculate the acceleration:
\[a = \frac{(88.89)^2}{40.0}\]
\[a \approx 196.9 \, \text{m/s}^2\]
Therefore, the acceleration of the car is approximately 196.9 m/s^2.
(b) To find the force exerted by the track on the tires, we can use Newton's second law of motion:
\[F = m \cdot a\]
Where:
F is the force,
m is the mass, and
a is the acceleration.
Substituting the given values:
m = 605 kg
a = 196.9 m/s^2
\[F = 605 \cdot 196.9\]
\[F \approx 119,264.5 \, \text{N}\]
Therefore, the force exerted by the track on the tires to produce this acceleration is approximately 119,264.5 N.
To find the acceleration of the car, we can use the formula for centripetal acceleration, which is given by:
a = (v^2) / r
where:
a = acceleration
v = velocity
r = radius
(a) Firstly, to find the velocity of the car, we need to calculate the distance covered in one lap and divide it by the time taken. The distance covered in one lap is equal to the circumference of the circular track, which is given by:
circumference = 2 * π * r
So, the velocity of the car is:
v = (2 * π * r) / t
Substituting the given values:
r = 40.0 m and t = 14.3 s
v = (2 * π * 40.0) / 14.3
Calculate the value of v.
Once we have the velocity, we can calculate the acceleration using the centripetal acceleration formula:
a = (v^2) / r
Substitute the calculated value of v and the given value of r to find the acceleration. Calculate the value of a.
(b) To find the force that the track must exert on the tires to produce this acceleration, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
F = m * a
Substitute the given value of the mass (605 kg) and the calculated value of the acceleration (from part a) to find the force. Calculate the value of F.