Answer:
To calculate the maximum angular velocity at which the car can travel around the curve, we need to consider the centripetal force acting on the car. The centripetal force is provided by the friction force between the tires and the road surface.
The maximum friction force can be calculated using the formula:
Friction force = coefficient of friction * normal force
The normal force is equal to the weight of the car and the driver combined, since it acts perpendicular to the surface. The total weight is the sum of the weight of the car and the weight of the driver.
Total weight = weight of car + weight of driver
Using the given values:
Weight of car = 45 kg
Weight of driver = 70 kg
Total weight = 45 kg + 70 kg = 115 kg
Now, we can calculate the maximum friction force:
Friction force = 0.2 * 115 kg * 9.8 m/s^2 (acceleration due to gravity)
Friction force = 22.54 N
The centripetal force required for the car to travel around the curve is equal to the friction force.
Centripetal force = Friction force = 22.54 N
The centripetal force is also equal to the mass of the car and driver multiplied by the centripetal acceleration:
Centripetal force = (mass of car + mass of driver) * (angular velocity)^2 * radius
Substituting the values:
22.54 N = (45 kg + 70 kg) * (angular velocity)^2 * 42 m
Simplifying the equation:
22.54 N = 115 kg * (angular velocity)^2 * 42 m
Rearranging the equation to solve for angular velocity:
(angular velocity)^2 = 22.54 N / (115 kg * 42 m)
angular velocity = √(22.54 N / (115 kg * 42 m))
Calculating the value:
angular velocity = √(0.000378)
angular velocity ≈ 0.019 m/s
Therefore, the maximum angular velocity at which the car can travel round the curve is approximately 0.019 m/s.
Step-by-step explanation: