Question

The Indianapolis Motor Speedway has four banked curves, each of which forms a quarter of a circle. Suppose a race car speeds along one of these curves with a constant tangential speed of 75.0 m/s. Neglecting the effects due to the banking of the curve, the centripetal acceleration on the car is 22.0 m/s2. What is the radius of the curve?

Answer 1

The radius of the curve can be determined using the formula for centripetal acceleration, which is given by v^2/r. Substituting the given values, we get r = (75.0 m/s)^2/22.0 m/s^2.

Step-by-step explanation:

The radius of the curve can be determined using the formula for centripetal acceleration, which is given by:

ac = v2/r

Where ac is the centripetal acceleration, v is the tangential speed, and r is the radius of the curve. Rearranging the formula, we have:

r = v2/ac

Substituting the given values, we get:

r = (75.0 m/s)2/22.0 m/s2

Answer 2

r = 255.68 m

Step-by-step explanation:

When a body moves in a circular path, an acceleration, due to constant change in its direction, is developed, known as centripetal acceleration. The centripetal acceleration acts towards the center of the circular path. The formula to calculate the centripetal acceleration is given as follows:

ac = v²/r

where,

ac = centripetal acceleration = 22 m/s²

v = tangential speed = 75 m/s

r = radius of curve = ?

Therefore,

22 m/s² = (75 m/s)²/r

r = (75 m/s)²/(22 m/s²)

r = 255.68 m