Relationship Between Acceleration on a ramp and Acceleration due to gravity

AI Thread Summary
The discussion revolves around determining the relationship between the acceleration of an object on a ramp and the acceleration due to gravity. The lab involved measuring the ramp's height and angle to calculate acceleration using position and velocity graphs. A misunderstanding arose regarding the formula a = g/sin(angle), with participants questioning its validity and the role of kinetic energy in the context of linear versus rotational motion. Clarification was sought on why the sine function appears in the force equation F = mgsin(angle), indicating confusion about trigonometric principles in physics. Overall, the conversation highlights the complexities of applying theoretical concepts to experimental data in physics.
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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+vit+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.
 
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Doc Al said:
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?
 
ScienceSinger said:

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.
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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