Conservation of Energy, Velocity, Ramp, Angle

AI Thread Summary
When calculating the velocity of a car hitting a wall after descending a ramp, the angle θ must be considered due to its effect on acceleration. The conservation of energy equation E = E' indicates that gravitational potential energy (mgh) converts into kinetic energy (1/2 mv^2). The velocity of the car should be calculated as v = sqrt(2gh), but the component of velocity parallel to the wall is affected by the angle, leading to v*cos(θ) for momentum calculations. The acceleration down the ramp is influenced by gravity, specifically a = g sin(θ). Therefore, both energy conservation and the ramp's angle are crucial for accurate velocity determination.
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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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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.
 
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