Ball rolling down an inclined plane

In summary, the conversation discusses a math problem involving a ball rolling down an inclined plane and the equation used to calculate the distance traveled. The speaker wants to predict the distance after 2 days and asks about the assumptions and strengths and limitations of the model. They mention that the model may not work once the ball reaches terminal velocity and may need help due to their lack of knowledge in physics.
  • #1
i_need_help
I have this math problem for school that I need help with

A ball is rolling down an inclined plane. The equation I have is y = .165x^2 + .997x + .845 where y is the distance traveled and x is the time taken

I want to predict the distance it has rolled in 2 days, which I can do

but what sort of assumptions would i have to make?

and what are the strengths and limitations for the model?
for example, a limitation is that when it reaches terminal velocity the model won't work anymore because the model expects the speed to keep increasing

i don't know anything about physics so i need help
 
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  • #2
Here's what I believe you need:

That equation is if the ball rolls at a constant acceleration. You need assume that it would have constant acceleration, so what would prevent the ball from from going at a constant acceleration?

Not sure about the limitations, though.
 
  • #3


I would first like to commend you for seeking help and taking the time to understand the problem. It shows a great curiosity and dedication to learning.

To answer your question, there are a few assumptions we can make in order to use the given equation to predict the distance traveled by the ball in 2 days.

Firstly, we can assume that the ball is rolling down the inclined plane without any external forces acting on it, such as friction or air resistance. This would ensure that the acceleration remains constant and the equation can accurately predict the distance traveled.

Secondly, we can assume that the ball is rolling in a straight line down the inclined plane, without any changes in direction. This would ensure that the equation, which is based on the concept of motion in a straight line, remains applicable.

Lastly, we can assume that the initial conditions (such as the initial height and velocity of the ball) remain constant throughout the 2 days.

As for the strengths and limitations of the model, you have already mentioned a limitation which is the assumption of constant acceleration. In reality, the acceleration of the ball would change as it reaches terminal velocity.

Another limitation could be the assumption of a perfect inclined plane with no imperfections or irregularities. In real life, there may be small bumps or grooves on the surface of the inclined plane which could affect the motion of the ball.

However, a strength of the model is that it provides a simple and easy-to-use equation to predict the distance traveled by the ball. It also takes into account the effect of time on the distance traveled, which is a key factor in any motion.

In conclusion, while the given equation can provide a good estimate for the distance traveled by the ball, it is important to keep in mind the limitations and assumptions made in the model. Understanding these limitations can help us make more accurate predictions and improve our understanding of the physical world. I hope this helps!
 

1. What is the relationship between the angle of the inclined plane and the speed of the rolling ball?

The steeper the angle of the inclined plane, the faster the ball will roll down. This is because the ball experiences a greater gravitational force and less resistance as the angle increases, causing it to accelerate.

2. How does the mass of the ball affect its speed when rolling down an inclined plane?

The mass of the ball does not affect its speed when rolling down an inclined plane, as long as air resistance and friction are negligible. This is because all objects, regardless of mass, experience the same acceleration due to gravity.

3. What is the significance of the coefficient of friction in a ball rolling down an inclined plane?

The coefficient of friction is a measure of the resistance between two surfaces in contact. In the case of a ball rolling down an inclined plane, a higher coefficient of friction between the ball and the surface will cause the ball to roll slower due to increased resistance.

4. How does the height of the inclined plane affect the potential energy of the ball?

The higher the inclined plane, the greater the potential energy of the ball. This is because potential energy is directly proportional to height, and as the ball rolls down the inclined plane, its potential energy is converted into kinetic energy.

5. Can the shape of the ball affect its speed when rolling down an inclined plane?

The shape of the ball can affect its speed when rolling down an inclined plane if air resistance is not negligible. A more streamlined shape will experience less air resistance and roll faster compared to a less streamlined shape.

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