Final answer:
The maximum speed at which a car can turn on a bend without skidding can be found using the formula for centripetal force and the frictional force. Using the given coefficient of friction (0.4) and the radius of the bend (20 m), the maximum speed is calculated to be approximately 8.86 m/s.
Step-by-step explanation:
To find the maximum speed at which a car can turn on a bend without skidding, we utilize the centripetal force formula and the concept of frictional force. The centripetal force needed to keep the car on the bend is provided by the frictional force between the tires and the road. The frictional force can be calculated by multiplying the coefficient of friction by the normal force, which in this case is equal to the weight of the car (since we assume the road is flat and there is no banking).
The formula for centripetal force is Fc = mv2/r, where m is the mass of the car, v is the velocity, and r is the radius of the bend. The frictional force is Ff = μN, where μ is the coefficient of friction and N is the normal force. Setting these two forces equal to each other, we have mv2/r = μN. Since N = mg, we can substitute to get mv2/r = μ mg, and with mass on both sides of the equation, it cancels out. Thus we get v2 = μ gr, and taking the square root we find v = √(μ gr).
Given a radius r = 20 m and a coefficient of friction μ = 0.4, we calculate: v = √(0.4 * 9.81 * 20) giving v = √(78.48), which equals approximately 8.86 m/s. This is the maximum speed the car can handle on the bend without skidding.