Conservation of Energy, Velocity, Ramp, Angle

In summary, the conversation is about calculating the velocity of a car on a ramp that leads to a perpendicular wall, and whether or not the angle of the ramp (θ) needs to be accounted for in the equation E = E'. The suggested solution is to use the equation mgh = 1/2 mv^2 and solve for v, taking into account the angle in the acceleration equation a = v'(t) = g sin(θ).
  • #1
mhz
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0

Homework Statement


This isn't really coursework or homework, but something I really want to confirm.

There is a ramp of height h on an angle θ that a car is placed on that leads to a wall perpendicular to the ground (looks like this: |∠). When calculating velocity of the car when it hits the wall using E = E', do I need to account for θ?

Every instinct I have says yes, but I want confirmation.


Homework Equations


E = E'


The Attempt at a Solution


E = E'
mgh = 1/2 mv^2

Solve for v .. doesn't really matter what it is.

Is the velocity of the car in a momentum equation (p = mv) equal to v or is it equal to v*cosθ?
 
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  • #2
You have to take the angle the acceleration parallel to the ramp is a = v'(t)= g sin(theta)

Integrate it to get the result.
 

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 or transformed from one form to another.

2. How does velocity affect energy conservation?

Velocity is a measure of an object's speed and direction. In terms of energy conservation, an object's velocity affects its kinetic energy, which is the energy an object possesses due to its motion. As an object's velocity increases, its kinetic energy also increases, and vice versa.

3. What role does a ramp play in energy conservation?

A ramp is a sloped surface that allows objects to move between different elevations. In terms of energy conservation, a ramp can be used to reduce the amount of work needed to move an object from a lower elevation to a higher elevation. This is because the ramp allows for a longer distance over which the object can move, reducing the amount of force required to overcome the change in elevation.

4. How does the angle of a ramp affect energy conservation?

The angle of a ramp can affect energy conservation in two ways. First, a steeper ramp (higher angle) will require more force to move an object up it, which means more energy is needed. Second, a steeper ramp will also result in an object moving a shorter distance to reach the same elevation, meaning less work is done and less energy is conserved.

5. How is energy conserved in a real-life scenario involving a ramp?

In a real-life scenario, energy conservation on a ramp can be seen in activities such as using a wheelchair ramp or pushing a cart up a hill. By using a ramp, less force is needed to move an object to a higher elevation, resulting in less energy being expended. This is why ramps are commonly used to make tasks easier for people with physical limitations or to transport heavy objects with less effort.

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