Investigating Projectile Motion with an Air Hockey Table

[firebug]

the lab involves an air hockey tab set up on a slight angle (one side is raised by a textbook) and the puck is pushed in such a way as to create what looks like a parabolic shape on the paper with carbon markings. The point is to determine if the motion is a projectile motion. So far, my group has calculating the velocity in the x- direction, but we're stumped as how to find acceleration in the y-direction, due to the fact that the table is on a slight slant. the force of friction is negilible against the puck and the table because of the force of air (hence the name air hockey). What i want is some idea of how to calculate the acceleratation due to gravity. a formula or steps would be nice... we can take it from there. thanks.

 

[zwtipp05]

Using the angle of the table, set up a free body diagram and look at how you can rearrange the vectors for Normal Force and Gravity to find the acceleration along the table.

 

[firebug]

mmmhmmm... thought so. but to find the angle of the table you would use the height of the table + book and the lenght, then the heigh from the table to the airtable top?

 

[andrevdh]

From your explanation of the setup I gather that you have a recorded paper with markings of the puck position at constant time intervals.To prove that the y-acceleration of the puck was constant you need to draw a graph of the y-velocity of the graph as a function of time. If the gradient of such a graph is constant then you have proved that the acceleration is constant. This can be calculated from
$$\overline{v_y}=\frac{\Delta y}{\Delta t}$$
The calculated y-velocities will be in the middle of the time intervals, since they are average values. If you do not have the time interval value you need to first draw the y-displacement vs time graph and then calculate the gradient of such graph in between the data points and use these gradients for the y-velocities.

 

[firebug]

the time displacement between each track (recording of position of puck) is 30 ms...if that helps...

 

[andrevdh]

To calculate the average y-velocity component of the puck for the second time interval:
$$\overline {v_{y2}}=\frac{\Delta y2}{0.030}$$
This is the average y-velocity of the puck at a time in the middle of the interval. Also note that
$$\Delta y$$
is positive in this case. When the puck is gowing down this quantity will be negative giving a negative y-velocity component!

 

[firebug]

yup... figured that.