How many times as large a centripetal acceleration is required of a car rounding a curve at 45.1 MPH as for one rounding the same curve at 10.8 MPH? That is, what is the ratio of the centripetal acceleration required for the faster car to the same for the slower car?
To find the ratio of the centripetal acceleration required for the faster car to the slower car, we need to first understand the relationship between centripetal acceleration and speed.
The centripetal acceleration (a) can be calculated using the formula:
a = v^2 / r
where v is the velocity and r is the radius of the curve.
We are given the velocities for both cars: 45.1 MPH for the faster car and 10.8 MPH for the slower car. We need to convert these velocities to meters per second (m/s) for the equation to work.
1 MPH is equal to 0.447 m/s.
So, the faster car's velocity would be (45.1 MPH) * (0.447 m/s / 1 MPH) = 20.14 m/s.
The slower car's velocity would be (10.8 MPH) * (0.447 m/s / 1 MPH) = 4.83 m/s.
Next, we need to understand that the radius of the curve is not given in the question. Without the radius, we cannot directly calculate the centripetal acceleration. Therefore, we cannot accurately determine the ratio between the centripetal accelerations for the two cars.
To find the ratio, we would need additional information, such as the radius of the curve or any other relevant data. Without that information, we are unable to calculate the answer.