⚙️Calculating Normal Force in Circular Motion: 🏞️ Hill and Valley Explained

In this video, we learn about the forces acting on a driver of a car moving at a constant speed over a circular hill and into a valley. We will calculate the normal force exerted on the driver by the car seat at the bottom of the valley. The driver has a mass of 70 kg, and it is given that at the top of the hill, the normal force is zero. Additionally, the radius of curvature remains the same for both the hill and the valley.

At the top of the hill, the normal force (Fn) from the seat on the driver is zero. This implies that the only force acting on the driver is their weight (mg), which provides the centripetal force needed for circular motion.
At the bottom of the valley, two forces act on the driver:
The gravitational force (mg) acting downwards.
The normal force (Fn) from the seat acting upwards.
Applying Newton's Second Law:

At the Top of the Hill:
The relevant forces are the gravitational force (mg) and the centripetal force (Fc).
According to Newton's second law, the equation is:
Fn - mg = -Fc
Given that Fn = 0 at the top of the hill, the equation simplifies to:
Fc = mg
This shows that the centripetal force is entirely provided by the driver's weight, confirming that the speed is such that Fc = 70 kg * 9.8 m/s² = 686 N.

At the Bottom of the Valley:
The forces acting are the gravitational force (mg) downwards and the normal force (Fn) upwards. Here, the centripetal force (Fc) is directed upwards.
Using Newton's second law, the equation becomes:
Fn - mg = Fc
Rearranging to solve for the normal force (Fn):
Fn = mg + Fc
Substituting the known values:
Fn = 70 kg * 9.8 m/s² + 686 N = 686 N + 686 N = 1372 N

Through this analysis, we find that the normal force on the driver at the bottom of the valley is 1372 N, indicating that the driver experiences a force twice their weight. This lesson provides a clear example of applying Newton's laws to real-world circular motion scenarios.

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Key Moments
00:00 Introduction - Problem Setup
(Describing the car's motion over a hill and into a valley)

01:00 Forces at the Top of the Hill
(Analyzing forces and applying Newton's second law)

02:32 Forces at the Bottom of the Valley
(Calculating the normal force using centripetal force)