Driving in your car with a constant speed of 12 , you encounter a bump in the road that has a circular cross-section, as indicated in the figure .

If the radius of curvature of the bump is 35 , find the apparent weight of a 70- person in your car as you pass over the top of the bump.

To find the apparent weight of the person, we first need to determine the forces acting on them.

1. The weight of the person exerted downward due to gravity, which can be calculated using the formula:
Weight = mass * gravity
where the mass is 70 kg (person) and gravity is approximately 9.8 m/s^2.

Weight = 70 kg * 9.8 m/s^2
Weight = 686 N

2. The normal force exerted by the bump on the person. At the top of the bump, the normal force is equal to the apparent weight.

Since the person is experiencing circular motion, a centripetal force is acting on them. This force is provided by the normal force.

Centripetal force = mass * centripetal acceleration
where the centripetal acceleration can be calculated using the formula:
centripetal acceleration = (velocity^2) / radius of curvature

Centripetal acceleration = (12 m/sec)^2 / 35 m
Centripetal acceleration = (144 m^2/s^2) / 35 m
Centripetal acceleration = 4.114 m/s^2

Therefore, the normal force or apparent weight can be calculated using the formula:
Centripetal force = mass * centripetal acceleration

Apparent weight = 70 kg * 4.114 m/s^2
Apparent weight = 288 N

Therefore, the apparent weight of the person in the car as they pass over the top of the bump is 288 N.

To find the apparent weight of a person in the car as it passes over the top of the bump, we can start by considering the forces acting on the person at that moment.

1. First, let's analyze the forces acting on the person when the car is on a flat road with no bumps. These forces include:
- Weight (mg), where m is the mass of the person and g is the acceleration due to gravity.
- Normal force (N), which is the force exerted by the ground on the person, perpendicular to the surface.

2. When the car encounters the bump, the normal force changes because the road is no longer flat. At the top of the bump, the normal force will be different due to the curvature of the road.

3. Let's consider the forces when the car is at the top of the bump. The forces acting on the person include:
- Weight (mg), as before.
- Normal force (N), which will be different due to the curvature of the bump.
- Apparent weight (N_app), which is the weight experienced by the person at the top of the bump.

4. The apparent weight can be calculated using the equation:
N_app = N + mg,
where N is the normal force at the top of the bump.

5. To find the normal force at the top of the bump, we can use the concept of centripetal force. At the top of the bump, the normal force provides the centripetal force to keep the car moving in a circular path.
The formula for centripetal force is given by:
F_c = m * (v^2 / r),
where F_c is the centripetal force, m is the mass of the car, v is the velocity of the car, and r is the radius of curvature of the bump.

6. Since the car is moving at a constant speed of 12, the velocity (v) is 12.

7. We can use the centripetal force equation to find the normal force (N) at the top of the bump:
N = F_c - mg.

8. Substitute the values of m, v, r, and g into the equation:
N = (m * (v^2 / r)) - mg.

9. Finally, substitute the given values of m (70 kg), v (12 m/s), r (35 m), and g (9.8 m/s^2) to calculate the apparent weight (N_app).