What is the deceleration on an incline?

In summary, King is asking how he can calculate the deceleration of an object that begins to go up an incline of angle X. He uses potential energy and kinetic energy to calculate the object's length up the incline and finds that it is about 7.55 millimeters.
  • #1
KingNothing
882
4
Hey all, I have a question. How can I calculate the deceleration of an object that begins to go up an incline of angle X? See there are a lot of problems like this. One of mine for example involves an object entering an incline of 25 degrees at 0.25 m/s, and I need to calculate how far it goes up the incline.
 
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  • #2
KingNothing,

Draw a diagram of the incline and the object. What direction would a force have to be in order to decelerate the object? Draw vectors for the forces acting on the object. Which one(s) of these could contribute to decelerating the object?
 
  • #3
I have...I get gravity coming from the top, force normal going perpendicular to the hypotenuse side...and that's all (there is no friction in this problem).
 
  • #4
If there is no friction, the force normal to the hypotenuse is irrelevant. The force is the component of force ALONG the hypotenuse. That would be -mg sin(theta) where theta is the angle the slope makes with the horizontal.
 
  • #5
I think I got this one wrong...instead of force equations, I used energy equations...

If the speed is .25 m/s when it enters the incline, then I set potential energy equal to kinetic energy...
[tex].5m(.25^2)=mgh[/tex]
[tex].5*.25^2=9.8h[/tex]

or about 3.2 millimeters, which would be the vertical component of the incline, so...
[tex]l=\frac{.5*.25^2}{9.8*sin25}[/tex] or about 7.55 millimeters.

I did use that method, at one point...if you do that, and use a mass of 1 kg for simplicity, you get d=.5(9.8*sin25)(.25/(9.8*sin25))^2 or the same answer.
 
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  • #6
Hi,

The equation for the length up the incline is correct (I didn't check the numbers, but I assume they're ok too.). The only thing I would suggest is that you not use a single variable for more than one thing. You use h to mean height off of the ground in your first equation and then you use h to mean length along the incline in your last equation. I was able to follow what you did, but you're liable to confuse yourself and others if you do things like that. You've got 26 letters, capital and lower case, all the greek alphabet, and all the subscripts you want to make up new variable names; it's worth it to do so.
 
  • #7
jamesrc said:
Hi,

The equation for the length up the incline is correct (I didn't check the numbers, but I assume they're ok too.). The only thing I would suggest is that you not use a single variable for more than one thing. You use h to mean height off of the ground in your first equation and then you use h to mean length along the incline in your last equation. I was able to follow what you did, but you're liable to confuse yourself and others if you do things like that. You've got 26 letters, capital and lower case, all the greek alphabet, and all the subscripts you want to make up new variable names; it's worth it to do so.

Whoops, that was a mistake with the last h. I usually do use pretty decent/legitbble notation.
 
  • #8
OK. Didn't mean to get on a soapbox there; mistakes happen.
 
  • #9
It's all good:). Thanks James.
 

1. What is deceleration on an incline?

Deceleration on an incline refers to the decrease in speed or velocity of an object that is moving along an incline or slope. This is due to the opposing force of gravity acting on the object.

2. How is deceleration on an incline calculated?

The deceleration on an incline can be calculated using the formula a = gsinθ, where a is the deceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline.

3. Does the mass of the object affect deceleration on an incline?

Yes, the mass of the object does affect the deceleration on an incline. Objects with a larger mass will experience a greater deceleration compared to objects with a smaller mass.

4. What factors can influence deceleration on an incline?

Apart from the mass of the object, other factors that can influence deceleration on an incline include the angle of the incline, the coefficient of friction between the object and the surface of the incline, and any additional forces acting on the object.

5. How can deceleration on an incline be useful in real-life situations?

Deceleration on an incline is a common occurrence in various real-life situations, such as driving on a hilly road or riding a rollercoaster. Understanding and calculating deceleration on an incline can help in designing safer roads and amusement park rides, as well as in analyzing the performance of vehicles and sports equipment on inclined surfaces.

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