Relationship Between Acceleration on a ramp and Acceleration due to gravity

[ScienceSinger]

Homework Statement

We performed a lab to find an experimental value of gravity. I used a ramp with a height of 0.08 m, and the ramp was 1 m long. The ramp made an angel of approximately 4.59 degrees with the horizontal. We used software to calculate velocity with respect to time and position with respect to time graphs. Using the formula for our position over time graph which was displayed on the graph as Ax^2+Bx+C, with an A value of 0.2236, which I have assumed for units to ad up is our acceleration value. Now, we need to use some kind of formula to find the relationship between a_ramp and g.

Homework Equations

x=x₀+v_it+at²
ma=mg
a=g/(sin(angle))
v=d/t
Einitial=Efinal

The Attempt at a Solution

I thought that ma=mg would make a=g/(sin(angle)) but this is incorrect...
Our TA put up something on the board that looked like this:
a=g#
where # is supposedly the fraction of kinetic energy caused by linear instead of rotational motion,
but I have no idea why that is true. I even did the whole energy conservation equation, keeping in mind that vi =0, but I cannot derive any sort of equation to show that this whole a=g# thing is true. Any advice would be helpful; I feel I'm missing some key concept here and my TA refused to talk to me further to allow me to understand.

 

[Doc Al]

Read up on inclined planes: Inclined Planes

 

[ScienceSinger]

Read up on inclined planes: Inclined Planes

Hi, could you explain why the formula appears to be F=mgsin(angle)? I don't understand from the reading why the sin(angle) is on that side of the equation... Is that just a formula that I should know or is my trigonometry wrong?

 

[NascentOxygen]

I thought that [...] would make a=g/(sin(angle)) but this is incorrect...

Hi SS. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Show the diagram you drew that led you to this equation.

If the slope was very gentle, this equation of yours would produce huge accelerations along the slope.

 

[HalfLostAndSearching]

First of all, it is important to note that the acceleration on a ramp is not the same as the acceleration due to gravity. The acceleration on a ramp, also known as the ramp's acceleration, is the acceleration of an object as it moves down the ramp. This is affected by factors such as the angle and length of the ramp, as well as any friction present.

On the other hand, the acceleration due to gravity, denoted as "g", is a constant value that represents the acceleration of an object due to the gravitational force of the Earth. This value is approximately 9.8 m/s^2 on Earth.

Now, to address the relationship between the two, we can use the equation ma=mg, where m is the mass of the object. This equation states that the force (ma) causing the ramp's acceleration is equal to the force (mg) of gravity acting on the object. This means that the ramp's acceleration is directly proportional to the acceleration due to gravity.

In terms of the formula your TA wrote on the board, a=g#, the "#" represents a dimensionless number that takes into account the effects of rotational motion on the ramp's acceleration. This means that the ramp's acceleration is not solely dependent on the acceleration due to gravity, but also on the rotational motion of the ramp itself.

In conclusion, the relationship between the ramp's acceleration and the acceleration due to gravity is that the ramp's acceleration is directly proportional to the acceleration due to gravity, but also takes into account the effects of rotational motion on the ramp.