Conservation of energy of a car problem

In summary, the question asks for the minimum speed needed at point B for a 200-kg roller coaster car to reach the top of the incline D without leaving the track. Using Newton's second law, the minimum speed can be found by setting the normal force at the top of the loop to be zero, resulting in a force from gravity alone equal to m.v^2/r. This can be solved for the speed needed at point B to be sufficient for the car to round the top of the loop at C. The radius of curvature at C is given as ρC = 25 m.
  • #1
myoplex11
45
0

Homework Statement


Determine the height h to the top of the incline D to which the 200-kg roller coaster car will reach, if it is launched at B with a speed just sufficient for it to round the top of the loop at C without leaving the track. The radius of curvature at C is
ρC = 25 m. I have attached a picture of this problem below.



Homework Equations


KE1+PE1=KE2+PE2


The Attempt at a Solution


.5mv1^2+mgh=.5mv^2+mgh
.5mv1^2=mgh
0.5v1^2=gh
 

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  • #2
… physics for "hug" is "force" …

myoplex11 said:

Homework Equations


KE1+PE1=KE2+PE2

The Attempt at a Solution


.5mv1^2+mgh=.5mv^2+mgh
.5mv1^2=mgh
0.5v1^2=gh

Your method would only give you the speed needed for the car to reach the top with zero speed.

The question requires the speed at the top to be so great that the car still "hugs the track".

Physics for "hug" is "force". :smile:

(Reminds me of: Principal "How is you mathematics?" Groucho Marx: "Sir, I speak it like a native!" :smile:)
So … what are the forces on the car at the top of the track? :smile:
 
  • #3
centipetal force and the normal force i still have no idea how to do this
 
  • #4
… the acceleration is always downward …

myoplex11 said:
centipetal force and the normal force i still have no idea how to do this

"Centipetal force" is not a force! :frown:

And you've missed out gravity …

The only two forces are gravity, and the normal force (the reaction force).

Those two forces determine the acceleration.

Paradoxically, they're both downward (at the top of the loop, C) … which means that the acceleration is always downward (centripetal)! :frown:

But that doesn't matter, because circular motion (at the top of the circle) requires downward acceleration! :smile:

This is geometry, not physics (and you can easily prove it using vectors) … an object with speed v in a circle or radius r has an acceleration of v^2/r towards the centre of the circle.

So, at C, you want gravity and the normal force together to equal m.v^2/r (Newtons' second law).

The question asks for the minimum case, which obviously must be when the normal force is zero: then the force from gravity alone equals mv^2/r.

And so … ? :smile:
 

1. How does the conservation of energy apply to a car problem?

The conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. In the case of a car, the chemical energy from the fuel is converted into mechanical energy to move the car forward. This energy is then transferred to the wheels, causing them to rotate and move the car.

2. Can the conservation of energy be used to calculate the speed of a car?

Yes, the conservation of energy can be used to calculate the speed of a car. By knowing the initial energy of the car (from the fuel) and the final energy (in the form of kinetic energy), the speed of the car can be calculated using the formula: KE = 1/2mv^2, where m is the mass of the car and v is the velocity (speed).

3. What factors can affect the conservation of energy in a car problem?

Several factors can affect the conservation of energy in a car problem, such as the type of fuel used, the efficiency of the engine, the weight and aerodynamics of the car, and external forces like friction and air resistance. Any inefficiencies in the conversion of energy can also affect the conservation of energy.

4. How does the conservation of energy relate to fuel efficiency in cars?

The conservation of energy is closely related to fuel efficiency in cars. The more efficient the conversion of chemical energy from fuel to mechanical energy, the less fuel is needed to move the car. This means that a car with good fuel efficiency is also conserving energy by minimizing any energy losses in the process.

5. Is the conservation of energy always applicable to cars?

Yes, the conservation of energy is always applicable to cars. However, it is important to note that while energy is always conserved, it can be converted into different forms and may not always be useful or efficient. For example, when a car brakes, the kinetic energy is converted into heat energy, which is not useful for moving the car forward. Therefore, while energy is conserved, it may not always be conserved in a useful or efficient way.

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