My physics optional extra work: This would be helpful so I can compare the solutions here as I do the work by myself. Question:
A car enters a circular flat curve with a radius of curvature of 0.20 km with a maximum speed of 135 km/h. If the friction between the road and the car's tires can supply a centripetal acceleration, what is the static coefficient of friction?
This would be helpful so I can compare the solutions here as I do the work by myself
right, >wink wink<
Looks like a homework dump to me.
To find the coefficient of static friction, we first need to understand the concept of centripetal acceleration and its relationship with friction.
Centripetal acceleration is the acceleration that keeps an object moving in a circular path. It is always directed towards the center of the circle. For an object moving in a circular path at a constant speed, the centripetal acceleration is given by the formula:
a = (v^2) / r
where "a" is the centripetal acceleration, "v" is the velocity, and "r" is the radius of curvature.
In this question, we are given the maximum speed of the car, which is 135 km/h. To find the centripetal acceleration, we need to convert this speed to meters per second (m/s):
v = (135 km/h) × (1000 m/1 km) × (1 h/3600 s) = 37.5 m/s
We are also given the radius of curvature, which is 0.20 km. Again, we need to convert this to meters:
r = 0.20 km × (1000 m/1 km) = 200 m
Now, we can plug these values into the formula for centripetal acceleration:
a = (37.5^2) / 200 = 7.03125 m/s^2
Next, we need to relate the centripetal acceleration to the force of friction. The force of friction is given by:
f = μN
where "f" is the force of friction, "μ" is the coefficient of friction, and "N" is the normal force.
In this case, the normal force is equal to the weight of the car, since it is moving on a flat surface. The weight can be calculated using the formula:
w = mg
where "w" is the weight, "m" is the mass, and "g" is the acceleration due to gravity.
However, the mass of the car is not mentioned in the question. So, we only need to find the coefficient of static friction, which is a dimensionless quantity and does not depend on mass. Therefore, we can avoid calculating the mass and directly find the coefficient of static friction.
To calculate the normal force, we can use the formula:
N = mg
Now, we can substitute the value of normal force and the calculated centripetal acceleration into the equation for friction:
f = μN = μmg
Since the friction between the road and the car's tires can supply the centripetal acceleration, we have:
f = ma = μmg
Solving for μ, we get:
μ = a / g
Let's calculate the coefficient of static friction using the given values:
μ = 7.03125 m/s^2 / 9.81 m/s^2 ≈ 0.716
Therefore, the static coefficient of friction between the car's tires and the road is approximately 0.716.