A 1562.4-kg sports car (including driver) crosses the rounded top of a hill (radius = 99.14 m) at 19.03 m/s. Determine (a) the normal force exerted by the road on the car.
Physics Explained: Normal Force on a Car at the Top of a Hill
To determine the normal force acting on a car at the top of a rounded hill, we use the concept of circular motion and apply Newton’s Second Law. When a car moves over the top of a hill, the only forces acting vertically are:
- Weight (W) of the car acting downward
- Normal Force (N) from the road acting upward
Given Values
Mass of car, m = 1562.4 kg
Speed, v = 19.03 m/s
Radius of curvature, r = 99.14 m
Acceleration due to gravity, g = 9.8 m/s²
Step 1: Understand the Net Force at the Top of the Hill
At the top of the hill, the net force is the centripetal force that keeps the car moving in a circular path. This force is provided by the difference between the car’s weight and the normal force.
⇒ Fnet = mg – N
Step 2: Apply Centripetal Force Equation
So combining both:
Step 3: Solve for Normal Force (N)
Step 4: Plug in the Values
N = (1562.4 × 9.8) – (1562.4 × 19.03² / 99.14)
Calculate each term:
- mg = 1562.4 × 9.8 = 15,318.52 N
- m × v² / r = 1562.4 × (19.03² / 99.14) = 1562.4 × (362.14 / 99.14) = 1562.4 × 3.652 ≈ 5,704.49 N
Final Calculation
Answer: The normal force exerted by the road on the car is approximately 9,614 N.
Note: If the car goes too fast over a hill, the normal force could become zero, meaning the car would momentarily lose contact with the ground (i.e., go airborne).