Force and Motion - Car going over a hill

In summary: The speed is such that the car just barely stays on the hill.In summary, the problem involves a stuntman driving a car over the top of a hill with a circular cross section. The greatest speed at which he can drive without the car leaving the road is when the centripetal force provided by gravity is equal to the centrifugal force, which is calculated using the formula Fc = mv^2/R. Solving for the speed gives the answer of Fg = mg = mv^2/R.
  • #1

Homework Statement


In Figure 6-58, a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 211 m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?


Homework Equations


Ac = mv^2/R
fnet = ma


The Attempt at a Solution


I honestly have no idea how to tackle this problem. Help?
 
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  • #2
It is circular motion. Recall that a "centripetal force" is required to hold an object in circular motion. You must use that formula and be aware of what force is providing the centripetal force. That force will become too small when the speed gets too high. Set them equal and solve for the speed.
 
  • #3
Delphi51 said:
It is circular motion. Recall that a "centripetal force" is required to hold an object in circular motion. You must use that formula and be aware of what force is providing the centripetal force. That force will become too small when the speed gets too high. Set them equal and solve for the speed.

I don't understand. First of all, the force causing the motion is the car itself moving up the hill. If the formula you're talking about is Fc = mv^2/R, then I don't see how the force will become small when the speed is high. They are directly proportional so the force would increase as the speed increases. Please clarify... thanks =)

edit: got the answer, Fg is the force = mg = mv^2/R
 
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  • #4
Congrats! Yes, gravity provides the centripetal force right at the top of the hill.
 

1. What is the relationship between force and motion when a car goes over a hill?

Force and motion are closely related when a car goes over a hill. The car's motion is determined by the force of gravity pulling it downwards and the force of the engine pushing it forward.

2. How does the weight of the car affect its motion when going over a hill?

The weight of the car plays a significant role in its motion when going over a hill. The heavier the car, the greater the force of gravity pulling it downwards, which can affect the speed and acceleration of the car.

3. What is the role of friction in a car's motion when going over a hill?

Friction plays a crucial role in a car's motion when going over a hill. Friction between the car's tires and the road surface helps to keep the car from slipping or sliding as it goes up and down the hill.

4. How does the slope of the hill affect the car's motion?

The slope of the hill can greatly influence the car's motion. The steeper the slope, the greater the force of gravity pulling the car down the hill, which can lead to a faster and more intense motion. On the other hand, a gentler slope will result in a slower and smoother motion.

5. What is the role of inertia in a car going over a hill?

Inertia is the tendency of an object to resist changes in its state of motion. When a car goes over a hill, its inertia can affect how it moves. The car's momentum and speed before going over the hill will determine how it will continue to move over the hill. Inertia also plays a role in the car's ability to maintain its motion as it goes up and down the hill.

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