How to solve/ work this problem? If a curve with a radius of 88m is perfectly banked for a car traveling 75 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95km/h?
This is similar to a problem I answered Sunday.
http://www.jiskha.com/display.cgi?id=1298220599
In this case you have to use friction to avoid slipping away from the center of the turn, not towards it. There sill be a sign change.
See if you can figure it out. I have to get some sleep.
I get what you were doing, but I still need help on how to work this one, like step by step.
To solve this problem, we need to analyze the forces acting on the car as it travels along the banked curve. The three main forces involved are:
1. The gravitational force (mg), directed vertically downward.
2. The normal force (N), perpendicular to the surface of the road.
3. The frictional force (f), acting horizontally towards the center of the curve.
The angle of the banking (θ) is not provided, so we need to calculate it first using the given information. The angle of banking is related to the radius (r) and the acceleration due to gravity (g) by the equation:
θ = atan(v² / (r * g))
where:
θ is the angle of banking,
v is the velocity of the car, and
r is the radius of the curve.
Let's plug in the given values:
v = 75 km/h = 20.83 m/s
r = 88 m
g = 9.8 m/s²
θ = atan((20.83)² / (88 * 9.8))
Using a scientific calculator, the angle of banking is approximately 34.84 degrees. Now we can move on to finding the coefficient of static friction.
The frictional force can be calculated using the equation:
f = μs * N
where:
f is the frictional force,
μs is the coefficient of static friction, and
N is the normal force.
In this case, the normal force is equal to the gravitational force acting downwards (mg), multiplied by the cosine of the angle of banking:
N = mg * cos(θ)
Let's calculate the normal force:
N = (m * g) * cos(34.84)
To continue solving the problem, we need to know the mass (m) of the car.