a) calculate the acceleration of a 0.55-m-diameter car tire while the car is traveling at a constant speed of 25m/sec.
b) compare this with acceleration experienced by a jet car tire of diameter 1.0m when setting a land speed record of 310m/sec
To calculate the acceleration of a car tire, we need to use the formula:
Acceleration = V^2 / R
Where:
- V is the velocity/speed of the car in meters per second (m/s), and
- R is the radius of the car tire in meters (m).
a) To calculate the acceleration of a 0.55-m diameter car tire while the car is traveling at a constant speed of 25 m/s:
First, we need to find the radius (R) of the car tire. The radius of a tire is half of its diameter.
Radius (R) = Diameter / 2
R = 0.55 m / 2
R = 0.275 m
Now, we can substitute the values in the formula:
Acceleration = (25 m/s)^2 / 0.275 meters
Acceleration = 625 m^2/s^2 / 0.275 meters
Acceleration = 2272.73 m^2/s^2
Hence, the acceleration of the car tire is approximately 2272.73 m^2/s^2.
b) To compare this with the acceleration experienced by a jet car tire of diameter 1.0 m when setting a land speed record of 310 m/s:
Similarly, first, we need to find the radius (R) of the jet car tire.
Radius (R) = Diameter / 2
R = 1.0 m / 2
R = 0.5 m
Now, we can substitute the values in the formula:
Acceleration = (310 m/s)^2 / 0.5 meters
Acceleration = 96100 m^2/s^2 / 0.5 meters
Acceleration = 192200 m^2/s^2
Hence, the acceleration of the jet car tire is approximately 192200 m^2/s^2.
Comparing the two accelerations:
- The car tire has an acceleration of approximately 2272.73 m^2/s^2.
- The jet car tire has an acceleration of approximately 192200 m^2/s^2.
Therefore, the jet car tire experiences a significantly greater acceleration compared to the car tire.