Inclined Surface: Velocity and angle of incline

AI Thread Summary
The angle of incline directly affects the acceleration of a car moving down a slope due to gravitational potential energy (PE). As the angle increases, the component of gravitational force acting parallel to the incline increases, leading to greater acceleration. The relationship between height and the length of the incline can be expressed as h = length * sin(θ). The velocity of the car can be determined using the equation v = √(2gh), where g is the acceleration due to gravity. Understanding these relationships is crucial for solving problems related to motion on inclined planes.
Svensken
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Homework Statement



How is angle of incline related to the acceleration of the car moving down it?

I know how to find both the velocity and acceleration of a car moving down a track using the suvat equations. I don't understand the relationship between angle of incline, velocity and gravity.

Basically, how does increased gravitational PE affect velocity?

Homework Equations



mgh
2s/t=v

The Attempt at a Solution



I think it has something to do with cosine of the angle as well as 1/2mv^2

Thank you guys and Gals!
 
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Spit the weight of the car into components perpendicular to the plane and parallel to the plane.

Also, how would you find the height the car is at when you know the length of the incline?
 
i was thinking:

mgh turns into 1/2 mv^2 (i am neglecting friction)

rearranging gives
v = sqroot(2gh)

Since g is equal to acceleration due to gravity it becomes g =a*sin(angle)

Is this correct?
 
Svensken said:
i was thinking:

mgh turns into 1/2 mv^2 (i am neglecting friction)

rearranging gives
v = sqroot(2gh)

yes but say you only had the length of the incline and the angle θ, what would h in terms of that length and θ?

Svensken said:
Since g is equal to acceleration due to gravity it becomes g =a*sin(angle)

Is this correct?

This is correct for the car's acceleration parallel to the plane
 
rock.freak667 said:
what would h in terms of that length and θ?

i would assume that h= length*sinθ?

This is correct for the car's acceleration parallel to the plane

Parallel meaning moving down the plane?

Thanks mate!
 
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