# Speed of Toy Car on Curved Track: Exploring Kinetic Energy

• Michele Nunes
In summary, the toy car coasts along the curved track, losing negligible energy due to friction. At the highest point in its trajectory, the car has a vertical speed of VB and a horizontal speed of θ.
Michele Nunes

## Homework Statement

A toy car coasts along the curved track shown. 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 energy loss due to friction is negligible.

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.

## The Attempt at a Solution

Okay so conceptually I think I understand how to do the problem. At point A, all potential energy, at point B, almost all kinetic energy. Then when the car leaves point B, energy is lost due to the downward force of the car's weight, so I want to find the work done by the car's weight and then subtract that from the original amount of energy the car possessed and then go from there. But in terms of how this plays out in the actual equations, I have no idea. I'm not sure where to start in terms of the setting equations equal to each other and how exactly to set that up.

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Michele Nunes said:
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.

If this is all you need to find then there's no need for considerations of energy, work or whatever goes on at the curved track. It is simply a projectile motion question. What is the speed of a projectile at its highest point? Think in terms of the vertical and horizontal speeds

JeremyG said:
If this is all you need to find then there's no need for considerations of energy, work or whatever goes on at the curved track. It is simply a projectile motion question. What is the speed of a projectile at its highest point? Think in terms of the vertical and horizontal speeds
But how would I do that if I don't know any other variable? Like I don't know time or acceleration or displacement so how would I get the speed only in terms of VB and θ?

1. For projectile motion, neglecting air resistance, the horizontal component of the velocity remains constant. The only force acting on the projectile during this parabolic motion is its own weight, in the vertical direction.

2. At its highest point, what is its vertical and horizontal speed? You do not need time, acceleration nor displacement to come up with an expression of the velocity at the highest point.

Michele Nunes
JeremyG said:
1. For projectile motion, neglecting air resistance, the horizontal component of the velocity remains constant. The only force acting on the projectile during this parabolic motion is its own weight, in the vertical direction.

2. At its highest point, what is its vertical and horizontal speed? You do not need time, acceleration nor displacement to come up with an expression of the velocity at the highest point.
Oh yes okay, I was definitely over thinking this, thank you!

No problem! Glad to help! :)

## 1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass and velocity of the object.

## 2. How does the speed of a toy car on a curved track affect its kinetic energy?

The speed of a toy car on a curved track directly affects its kinetic energy. As the car moves faster, its kinetic energy increases, and as it slows down, its kinetic energy decreases.

## 3. Why is it important to explore the kinetic energy of a toy car on a curved track?

Exploring the kinetic energy of a toy car on a curved track allows us to understand the relationship between speed and energy and how it affects the movement of objects. It also helps us to understand the principles of physics and how they apply to real-world scenarios.

## 4. How can we calculate the kinetic energy of a toy car on a curved track?

The kinetic energy of a toy car on a curved track can be calculated by using the equation KE = 1/2 * m * v^2, where KE is kinetic energy, m is the mass of the car, and v is its velocity.

## 5. What factors can affect the speed of a toy car on a curved track?

The speed of a toy car on a curved track can be affected by various factors, including the mass of the car, the shape and angle of the track, the surface friction, and any additional forces acting on the car, such as air resistance or gravity.

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