If the coefficient of friction between the tires of a car and the road is 0.101, what is the minimum stopping distance of a car traveling at 78.4 km/hr?
To find the minimum stopping distance of a car, we need to calculate the distance it takes for the car to decelerate from its initial speed to zero. The key factor in calculating this stopping distance is the coefficient of friction between the car's tires and the road.
Here's the step-by-step process to calculate the minimum stopping distance:
Step 1: Convert the car's speed from km/hr to m/s.
Given that the car is traveling at 78.4 km/hr, we need to convert this to m/s. To convert km/hr to m/s, we divide the speed by 3.6, since there are 3.6 seconds in an hour.
78.4 km/hr ÷ 3.6 = 21.778 m/s
Step 2: Calculate the deceleration of the car.
Deceleration is the rate at which the car slows down. To find the deceleration, we can use the formula:
Deceleration = (Final Velocity - Initial Velocity) / Time
Since the final velocity is zero (the car comes to a stop), and the initial velocity is 21.778 m/s (from Step 1), we can simplify this to:
Deceleration = - Initial Velocity / Time
Deceleration = - 21.778 m/s / Time
Step 3: Use the coefficient of friction to determine the normal force.
The normal force is the force exerted by the road on the car, perpendicular to the surface. The coefficient of friction relates this force to the force of friction. The formula for friction force is:
Friction force = Coefficient of friction * Normal force
Step 4: Use the deceleration to find the normal force.
The normal force can be calculated using the formula:
Normal force = Mass of the car * Acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s². We can solve for the mass of the car from the given information.
Step 5: Calculate the stopping distance using the deceleration and the car's speed.
The stopping distance can be calculated using the formula:
Stopping distance = (Initial Velocity²) / (2 * Deceleration)
Let's plug in the numbers and calculate the minimum stopping distance:
Step 1: Initial Velocity = 21.778 m/s
Step 2: Deceleration = - 21.778 m/s / Time
Unfortunately, we don't know the time it takes for the car to stop. However, we can use the concept of the coefficient of friction to determine the maximum deceleration by using the formula:
Deceleration = - (Coefficient of friction * Acceleration due to gravity)
Deceleration = - (0.101 * 9.8 m/s²)
Step 3: The normal force can be calculated using the formula:
Normal force = Mass of the car * Acceleration due to gravity
Since the mass of the car is not given in the question, we are unable to proceed further without this information.
Therefore, the question cannot be answered without knowing the mass of the car.