Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross-section.
If the radius of curvature of the bump is 35 m, find the apparent weight of a 63-kg person in your car as you pass over the top of the bump.
63 kg*(g - V^2/R) (in Newtons)
To find the apparent weight of the person as you pass over the bump, you need to consider the forces acting on the person.
When you are driving over the bump, there are two main forces acting on the person: the gravitational force (weight) and the normal force.
1. Gravitational force (Weight):
The weight of the person can be calculated using the formula: weight = mass x gravity, where the mass is given as 63 kg and the acceleration due to gravity is approximately 9.8 m/s². Therefore, the weight of the person is calculated as: weight = 63 kg x 9.8 m/s² = 617.4 N.
2. Normal force:
The normal force is the force exerted by a surface perpendicular to the object in contact with it. In this case, as the car passes over the top of the bump, the normal force will be directed downward and will be equal to the apparent weight of the person.
The normal force can be calculated using the centripetal force acting on the car as it goes around the circular cross-section of the bump.
The centripetal force is given by the formula: centripetal force = mass x (velocity² / radius), where the mass is the person's mass (63 kg), the velocity is the constant driving speed (12 m/s), and the radius is the radius of curvature of the bump (35 m).
centripetal force = 63 kg x (12 m/s)² / 35 m = 259.2 N.
Since the normal force is equal to the centripetal force, the apparent weight of the person as you pass over the top of the bump is 259.2 N.
Therefore, the apparent weight of the person is 259.2 N.