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wallpaper
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Consider the system of a cart rolling down an inclined plane.
Is the acceleration constant? Why?
Is the acceleration constant? Why?
Is Acceleration Constant on an Inclined Plane?
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In summary, the acceleration of a cart rolling down an inclined plane is constant, assuming no resistances and a constant angle of incline. The acceleration is equal to the sine of the angle to the horizontal made by the incline. The degree of tilt affects the acceleration by changing the angle, but the acceleration remains constant as long as the angle and gravity are constant. This can be calculated using basic trigonometry, with the acceleration equal to g*sin(theta) where theta is the angle of the incline.
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Mentallic
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Yes the acceleration is constant assuming no resistances and the incline is at a constant angle.
The acceleration vector of the cart is equal to the sine of the angle to the horizontal made by the incline. Since the angle and gravity are constant, the acceleration of the cart is also constant.
My reasoning as to why may only be intuitive though.
The acceleration vector of the cart is equal to the sine of the angle to the horizontal made by the incline. Since the angle and gravity are constant, the acceleration of the cart is also constant.
My reasoning as to why may only be intuitive though.
- #3
wallpaper
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Ooh thanks. I have another question though, how does the degree of the tilt affect the acceleration?
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Troels
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wallpaper said:
Like it was said:
Mentallic said:
- #5
Mentallic
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wallpaper said:
I'll be a little more clear here
What you need to do is draw a diagram of the situation, labelling the angle [tex]\theta[/tex] and the gravity acceleration vector (pointed directly towards the floor with a value of 9.8ms-2 if this scenario is on Earth's surface).
Now, what you need to find is the acceleration vector of the cart. This is simply the hypotenuse of your right-angled triangle that you were able to illustrate with the vectors. Since you have the angle, the opposite side and the hypotenuse; the relationship is:
[tex]sin\theta=\frac{opp}{hyp}[/tex]
[tex]sin\theta=\frac{g}{a_f}[/tex]
where:
af being the accleration of the cart
g=acceleration due to gravity
Therefore, [tex]a_f=\frac{g}{sin\theta}[/tex]
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nasu
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The acceleration is
g*sin(theta)
where theta is the angle of the incline.
This is assuming no friction, of course.
If it were g/sin(theta) you'll get infinite acceleration on a horizontal plane...
g*sin(theta)
where theta is the angle of the incline.
This is assuming no friction, of course.
If it were g/sin(theta) you'll get infinite acceleration on a horizontal plane...
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- #7
Mentallic
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Yes your logical thinking sounds much more correct. However, this simple trigonometry is confusing me because I can't get that result. Can anyone spot my mistake?
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Doc Al
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What you are trying to find is the component of g parallel to the incline, so g should be the hypotenuse of your triangle.Mentallic said:
FAQ: Is Acceleration Constant on an Inclined Plane?
What is acceleration?
Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction.
How is acceleration measured?
Acceleration is typically measured in units of meters per second squared (m/s^2) or feet per second squared (ft/s^2). It can be calculated by dividing the change in an object's velocity by the time it takes for that change to occur.
What does constant acceleration mean?
Constant acceleration means that the rate of change of an object's velocity remains the same over time. This means that the object's acceleration does not vary and its velocity is changing by the same amount in each unit of time.
Can acceleration be both positive and negative?
Yes, acceleration can be both positive and negative. A positive acceleration means that the object is speeding up, while a negative acceleration means that it is slowing down. The sign of acceleration depends on the direction of the object's motion.
Is the acceleration of a falling object constant?
In a vacuum, the acceleration of a falling object is constant. This acceleration is known as the acceleration due to gravity and has a value of approximately 9.8 m/s^2. However, in the real world, air resistance and other factors can affect the acceleration of a falling object, making it non-constant.