How Does the Angle Affect the Height and Speed of a Toy Car on a Track?

• Supremetheking
In summary, when the car is released from rest, it has a height at point A (vA = 0), but after it leaves the track and reaches the highest point in its trajectory, it will have a different height because of the angle ϴ above the horizontal.
Supremetheking

1. Homework Statement

A toy car coasts along he curved track shown above. The car has initial speed vA when it is at point A at the top of the track, and the car leaves the track at point B with speed vB at an angle ϴ above the horizontal. Assume that the energy losses due to friction is negligible.
(a) Suppose the toy car is released from rest at point A (vA = 0).
i. After the car leaves the track and reaches the highest point in its trajectory it will be at a different height than it was at point A. Briefly explain why this is so. ii. Determine the speed of the car when it is at the highest point in its trajectory after leaving the track, in terms of vB and ϴ. Briefly explain how you arrived at your answer.
(b) Suppose the toy car is given an initial push so that it has nonzero speed at point A. Determine the speed vA of the car at point A such that the highest point in its trajectory after leaving the track is the same as its height at point A. Express your answer in terms of vB and ϴ. Explain how you arrived at your answer.

Homework Equations

Conservation of Energy

The Attempt at a Solution

I was able to find the speed of the highest point of the car after leaving the track, but part 1a, I think that the angle would affect it, but I don't know how. For part c I don't know how to make it consist of only Vb and theta.

Supremetheking said:
part 1a, I think that the angle would affect it,
Yes, it would. In fact, the question is not quite correct. There is an angle at which it would regain the same height.
Supremetheking said:
For part c I don't know how to make it consist of only Vb and theta.

Supremetheking
Oh for part c, i got now after using the conservation of energy. I made a mistake while solving it before, which led me to not have Vb and theta only.
Part a, I got it too now, since only 90 degrees would allow it to be the same height, but since the angle in the picture doesn't show 90 degrees, but a angle of theta, we know that it won't reach the same height, since the vertical PE is converted to horizontal KE.
Thanks for helping!

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transferred from one form to another. This means that the total amount of energy in a closed system remains constant.

2. How is conservation of energy related to AP Physics?

Conservation of energy is a fundamental principle in AP Physics, as it applies to all types of energy, including mechanical, thermal, electrical, and nuclear energy. It is used to analyze and solve problems related to energy transformations and the motion of objects.

3. Can you give an example of an AP Physics question on conservation of energy?

Sure! One example could be a question asking you to calculate the final velocity of a rollercoaster car at the bottom of a hill, given its initial velocity and the height of the hill. This question would require you to use the conservation of energy principle to determine the potential and kinetic energy of the car at different points in its motion.

4. What are some key formulas related to conservation of energy in AP Physics?

Some key formulas include:
- The work-energy theorem: W = ΔK = Kf - Ki
- The gravitational potential energy formula: PE = mgh
- The kinetic energy formula: KE = 1/2mv^2
- The conservation of energy formula (for a closed system): ΔE = ΔK + ΔU = 0
- The law of conservation of energy: Ei = Ef
Note: E represents total energy, K represents kinetic energy, U represents potential energy, m represents mass, g represents acceleration due to gravity, h represents height, and v represents velocity.

5. How can I apply the concept of conservation of energy in real life?

Conservation of energy is a fundamental principle that can be seen in everyday life. For example, when you turn on a light switch, electrical energy is converted into light and heat energy. You can also apply this concept when calculating the efficiency of devices, such as a car or a light bulb, by comparing the input (energy in) to the output (energy out).

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