Question

driving in your car with a constant speed of 12m/s you can encounter a hill in the road with a radius curvature of 110m if you have a mass of 80 kg what is the fastest speed at which you go down without losing the contact with ground

Answer 1

The fastest speed at which you can go down the hill without losing contact with the ground is approximately 33.17 m/s.

Step-by-step explanation:

To determine the fastest speed at which you can go down a hill without losing contact with the ground, we need to consider the balance between the gravitational force and the centripetal force. The centripetal force is provided by the normal force exerted by the ground on the car at the top of the hill.

At the top of the hill, the net force acting on the car is the difference between the gravitational force and the centripetal force:

Net Force = Gravity force - Centripetal force

For the car to remain in contact with the ground, the net force must be greater than or equal to zero.

At the top of the hill, the normal force is equal to the car's weight:

Normal force = mass × acceleration due to gravity

Since the normal force provides the centripetal force, the normal force can also be expressed as:

Normal force = mass × centripetal acceleration

Therefore, we have:

mass × centripetal acceleration = mass × acceleration due to gravity

Dividing both sides of the equation by mass, we find:

centripetal acceleration = acceleration due to gravity

Thus, the fastest speed at which you can go down the hill without losing contact with the ground is when the centripetal acceleration is equal to the acceleration due to gravity. In other words, the car will remain in contact with the ground as long as the centripetal acceleration (v^2/r) is equal to 9.8 m/s^2 (acceleration due to gravity).

Therefore, we have:

(v^2) / r = 9.8

Solving for v, the fastest speed, we get:

v = sqrt(9.8×r)

Plugging in the values given in the question, we have:

v = sqrt(9.8×110)

v ≈ 33.17 m/s