Question

Franklin is driving some test laps at Daytona. The track has a radius of 300 m and is tilted at 30 degrees at the turns. The car has a mass of 700 kg.

1. How fast can he drive in m/s if there is no friction?
2. How fast can he go if she doubled the mass of the car?
3. If his tires had a coefficient of friction of 0.40 and there was friction, how fast could he go in m/s?
4. What angle in degrees should the track be tilted at, if he only plans to drive at 25 m/s with no friction?

Answer 1

we can use the centripetal force formula: Franklin can drive at a maximum speed of approximately 52 m/s with no friction.

Step-by-step explanation:

To find the maximum speed Franklin can drive with no friction, we can use the centripetal force formula:

F = m × ac

Where F is the friction force, m is the mass of the car, and ac is the centripetal acceleration. Since there is no friction, F = 0, so we have:

0 = m × ac

ac = 0

The centripetal acceleration is given by the formula:

ac = r × ω2

Where r is the radius of the track and ω is the angular velocity. Since the track is tilted at 30 degrees at the turns, the normal force cancels out the gravitational force, so we can use the formula for the gravitational force:

Fg = m × g

Where Fg is the gravitational force, m is the mass of the car, and g is the acceleration due to gravity, which is approximately 9.8 m/s². Setting this equal to the centripetal force, we get:

m × g = m × ac

Simplifying and solving for ω, we get:

ω = √(g/r)

Substituting the values given, we have:

ω = √(9.8/300) ≈ 0.173 rad/s

Finally, to find the maximum speed, we can multiply the angular velocity by the radius:

v = r × ω = 300 × 0.173 ≈ 52 m/s

Therefore, Franklin can drive at a maximum speed of approximately 52 m/s with no friction.