Final answer:
To calculate the ideal speed to take a banked curve, you can use the formula: tan(θ) = (v^2)/( r * g), where θ is the angle of banking, v is the speed of the car, r is the radius of the curve, and g is the acceleration due to gravity.
Step-by-step explanation:
To analyze the situation, we can use the concept of banked curves and friction to find the speed at which a car can safely navigate the curve without sliding. The key formula for this scenario is the following:
tan(θ) = {v^2} / {g . r}
where:
- θ is the angle of banking,
- v is the speed of the car,
- g is the acceleration due to gravity (approximately (9.8 m/s^2),
- r is the radius of the curve.
Given:
- θ = 7.0^\circ,
- r = 900 m ,
- μ = 0.60 ) (coefficient of friction).
We also need to consider the frictional force, which can be calculated using the formula:
f_friction = μ . N
where N is the normal force. The normal force is given by N = m . g , where m is the mass of the car.
Let's go through the calculations step by step.
1. Calculate the tangent of the angle of banking θ:
tan(θ) = tan(7.0^\circ)
2. Calculate the speed v:
v = {g . r . tan(θ)}^1/2
3. Calculate the normal force N :
N = m . g
4. Calculate the frictional force f_friction:
f_friction = μ . N
Now, we need additional information about the mass of the car (\( m \)) to complete the calculation. If you provide the mass of the car, we can proceed with the numerical calculations.