Finding the Angle for 25m/s Glider Velocity on Tilted Track

[hellothere123]

Homework Statement

i have an air track glider on a track that is tilted. the distance between the initial position and the photogate that measures the time it takes for the glider to pass the photogate in 0.001s is .5m I need to find the angle theta that will give me 25m/s (the max measurable velocity) at the photogate. in case it helps, the flag width is .025m.

Homework Equations

v^2 = vi^2 + 2ax
a=gsin(theta)

my problem is you cannot arcsin a number greater than 1. because the glider is at rest then i let it go, i need to find the angle that will get the glider to travel at 25 m/s by the time it gets to the photogate. however, this doesn't seem possible because if it were in free fall.. to fall at 25m/s, it would need 31.887m to travel, which we do not have on this track.

however it should be possible or maybe i am missing something, because the next question asks, if the angle exceeds this critical angle, the calculations provide an inaccurate value of g and i need to know why. any help is greatly appreciated.

 

[jbsteele]

The Attempt at a Solutionv^2 = vi^2 + 2ax25^2 = 0 + 2a(.5)a=250 m/s^2a=gsin(theta)250= gsin(theta)g=250/sin(theta)tan(theta)= 250/g theta= tan-1(250/g)

 

[nlightner]

Firstly, it is important to note that the equations provided are for motion under constant acceleration, which may not be the case for your setup. The glider may experience a different type of motion, such as uniform circular motion, as it moves along the tilted track. This could explain why the equations are not giving you the expected results.

To accurately determine the angle theta that will give you 25m/s at the photogate, you will need to use the equations of motion for the specific type of motion that the glider is experiencing. This may involve taking into account the curvature of the track and the forces acting on the glider.

Furthermore, it may not be possible to achieve a velocity of 25m/s at the photogate if the glider is starting from rest and only has a distance of 0.5m to accelerate. This would require an acceleration of 1000 m/s^2, which is not realistic. It is important to consider the limitations of your setup and the laws of physics when setting up an experiment.

In regards to the next question about the critical angle, it is possible that the calculations for the acceleration due to gravity may be inaccurate if the angle exceeds a certain value. This could be due to the assumptions made in the equations or the limitations of the setup. It is important to carefully analyze the experimental setup and the equations being used to determine the accuracy of the results.

In summary, to accurately determine the angle theta that will give you 25m/s at the photogate, you will need to use the appropriate equations for the type of motion being experienced. It is also important to consider the limitations of the setup and the accuracy of the calculations in order to make accurate conclusions from the experiment.