A car is negotiating a curve of radius 100 m at a speed of 15 m/s. What is the m
Practice Questions
Q1
A car is negotiating a curve of radius 100 m at a speed of 15 m/s. What is the minimum coefficient of friction required to prevent the car from skidding?
0.15
0.25
0.30
0.35
Questions & Step-by-Step Solutions
A car is negotiating a curve of radius 100 m at a speed of 15 m/s. What is the minimum coefficient of friction required to prevent the car from skidding?
Correct Answer: 0.23
Step 1: Identify the given values. The radius of the curve (r) is 100 meters, the speed of the car (v) is 15 meters per second, and the acceleration due to gravity (g) is approximately 9.8 meters per second squared.
Step 2: Understand that the car needs a frictional force to keep it from skidding while going around the curve. This frictional force can be expressed as the product of the coefficient of friction (μ), the mass of the car (m), and the acceleration due to gravity (g).
Step 3: The centripetal acceleration (a_c) required to keep the car moving in a circle is given by the formula a_c = v² / r. Plug in the values: a_c = (15 m/s)² / (100 m).
Step 4: Calculate the centripetal acceleration: a_c = 225 m²/s² / 100 m = 2.25 m/s².
Step 5: Set up the equation for the frictional force: μmg = ma_c. Since mass (m) appears on both sides, we can simplify it to μg = a_c.
Step 6: Rearrange the equation to solve for the coefficient of friction (μ): μ = a_c / g.
Step 7: Substitute the values into the equation: μ = 2.25 m/s² / 9.8 m/s².
Step 8: Calculate the coefficient of friction: μ ≈ 0.229, which we can round to approximately 0.23.
Centripetal Acceleration – The acceleration required to keep an object moving in a circular path, calculated as a_c = v²/r.
Frictional Force – The force that opposes the motion of the car, which must be sufficient to provide the necessary centripetal force.
Coefficient of Friction – A dimensionless scalar value that represents the frictional force between two bodies in contact.
