# Time & Angle: My Science Fair Project

• xdanizzlex
In summary, the equation you can use to predict the time it takes for a ball to roll down an inclined plane is t = √(2d/gsinA), where t is time, d is distance, g is acceleration due to gravity, and A is the angle of the incline. You can use this equation by finding the velocity using energy conservation or by using the formula d=1/2at^2, depending on the information you are given. Make sure to account for friction if it is present.
xdanizzlex
I am doing my Science Fair project on Inclined Planes. My experiment mainly revolves around the ANGLE of the inclined plane determining the TIME it takes a ball to roll down the plane. I was wondering it I kept all of the other variables the same (length of the plane, weight of the ball) and only manipulated the angle of the plane, what the equation would be used to predict the time. I researched all that I could in books and online but everything I found gave me all of these complex equations that didn't have to do with angle (or at least I think they didn't). Any help would be appreciated, thanks!

xdanizzlex said:
I am doing my Science Fair project on Inclined Planes. My experiment mainly revolves around the ANGLE of the inclined plane determining the TIME it takes a ball to roll down the plane. I was wondering it I kept all of the other variables the same (length of the plane, weight of the ball) and only manipulated the angle of the plane, what the equation would be used to predict the time. I researched all that I could in books and online but everything I found gave me all of these complex equations that didn't have to do with angle (or at least I think they didn't). Any help would be appreciated, thanks!

If I understood, you are trying to find a function t(A), where A is the angle of the incline. Well, you can use energy conservation to find the velocity of the object on the bottom of the incline, expressed in terms of A. Further on, you should plug that velocity into the kinematic equation of velocity of the object, which is v(t) = g*sinA*t. You can now easily express the time t as a function of the angle A. I hope that helped.

Well, you can use energy conservation to find the velocity of the object on the bottom of the incline, expressed in terms of A.

So basically this means find velocity right? Why do I have to find the velocity when it's at the bottom of the incline (aka the end of it). How do I use energy conservation to find it? Sorry if my questions irritate you because I;m still really new to physics =(

xdanizzlex said:
So basically this means find velocity right? Why do I have to find the velocity when it's at the bottom of the incline (aka the end of it). How do I use energy conservation to find it? Sorry if my questions irritate you because I;m still really new to physics =(

Use the fact that the potential energy of the object at the top of the incline equals the kinetic energy at the bottom (since kinetic energy at the top equals zero, as does potential energy at the bottom). You can find the velocity from this equation.

You could also avoid energy all together and use d=1/2at^2. The acceleration is still gsinA. So time would be sqrt(2d/gsinA). Youll come up with the same thing either way, except this formula depends on the length of the ramp, not the vertical height. If youre angle is changing, your height will be changing too, so this is probably better than energy

would using these formulas work and are they correct?:

distance = .5* A * T^2 or rearranged as t= square root of (distance/.5*A)

and

mass*gravity*Sin of the angle - friction = mass*acceleration

I can use the second one to find the acceleration because I am given the mass and can solve for the sin of the angle, and then plug it into the first one and then solve for time?

xdanizzlex said:
would using these formulas work and are they correct?:

distance = .5* A * T^2 or rearranged as t= square root of (distance/.5*A)

and

mass*gravity*Sin of the angle - friction = mass*acceleration

I can use the second one to find the acceleration because I am given the mass and can solve for the sin of the angle, and then plug it into the first one and then solve for time?

You didn't mention anything about friction. But if you are given a frictional force/coefficient of kinetic friction, you can use the second one to find the acceleration. The method turdferguson suggested should work just fine, too, if you're not given any frictional force.

## 1. What is the purpose of your science fair project on Time & Angle?

The purpose of my science fair project on Time & Angle is to investigate the relationship between time and angle, and how changes in one affect the other. This project aims to demonstrate the concept of time and angle in a visual and tangible way.

## 2. How did you conduct your experiment for this project?

For this project, I used a protractor to measure angles and a clock to measure time. I conducted several experiments by changing the angle and recording the corresponding time it took for an object to travel a set distance at that angle. I repeated this process multiple times and took an average to ensure accuracy.

## 3. What were your findings from this project?

My findings showed that as the angle increases, the time it takes for an object to travel a set distance also increases. This relationship follows a direct proportion, meaning that as one variable increases, the other also increases in a linear fashion.

## 4. How does this project relate to real-world applications?

This project has real-world applications in fields such as physics, engineering, and mathematics. Understanding the relationship between time and angle is crucial in designing structures and machines, as well as in solving equations and problems involving angles and time.

## 5. What was the most challenging part of your project?

The most challenging part of my project was collecting accurate data and ensuring consistency in my experiments. It required precision and attention to detail to measure angles and time accurately, as even small errors could significantly affect the results. However, with careful planning and multiple trials, I was able to overcome this challenge and obtain reliable data for my project.

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