Final answer:
Friction is needed to keep a car from sliding toward the inside of a banked curve. The ideal speed can be calculated using the formula tan θ = (v²) / (r * g). The minimum coefficient of friction can be found using the formula f = m * g * tan θ.
Step-by-step explanation:
When a car takes a banked curve at a speed less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve. To calculate the ideal speed to take a 100 m radius curve banked at 15.0°, we can use the formula:
tan θ = (v²) / (r * g)
Where:
- θ is the angle of the banked curve
- v is the speed of the car
- r is the radius of the curve
- g is the acceleration due to gravity
To find the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h, we can use the formula:
f = m * g * tan θ
Where:
- f is the force of friction
- m is the mass of the car
- g is the acceleration due to gravity
- θ is the angle of the banked curve