Acceleration and Freefall

Procedure

Part 1

We will use the formula y_f = y_o + v_oy t + ½ a_y t², valid for constant acceleration, to calculate the acceleration due to gravity, g, in Dallas.

Supply electrical power to the timer.
Load the ball bearing in the clamp at the top of the Behr freefall apparatus. It is critical that you perform this operation gently so that you do not alter the height of the clamp from one trial to the next.
Measure the height from the ball bearing to the timer pad on the floor using the two-meter stick. Do this more than once.
Reset the timer.
Release the ball bearing. The timer will begin counting thousandths of a second, and will stop when the ball bearing strikes the pad on the floor. Record the freefall time.
Reload the ball bearing, reset the timer, and repeat for several trials.

Part 2

We will use the pair of simultaneous equations

y_f = y_o + v_oy t + ½ a_y t²

x_f = x_o + v_ox t

to calculate the muzzle velocity of a projectile (the speed at which the projectile emerges from the gun).

Level the spring cannon using the built-in bubble level. Adjust the height of the legs by turning the feet.
Use the C-clamp to attach the gun base rigidly to the lab bench. This will prevent recoil of the gun. Ensure that the base is still level even after the C-clamp is attached.
Load the projectile into the spring cannon.
Align the edge of the spring cannon with the edge of the table.
Test fire the cannon and observe approximately where the projectile strikes the floor.
Use masking tape to attach a piece of white paper to the floor near that location.
Place (do not tape) a sheet of carbon paper shiny side down on top of the white paper.
Reload and realign the spring cannon. Fire several shots.
Do not remove the white paper from the floor before you have taken the horizontal distance measurements from the ball bearing to the marks.
For the uncertainty in horizontal distance, x, use the standard deviation of the mean (SDOM). See Taylor section 4.4 if you are confused.
Measure the height of the projectile from the floor.
You may use your own value of g and g from Part 1 if it is reasonable, or you may use the standard 9.80 m/s² ± 0.01 m/s².

Error analysis

Part 1

Find the free-fall acceleration and its propagated error: g ± g.
Is your free-fall acceleration in agreement with the standard value 9.80 m/s² ± 0.01 m/s² (that is, do the error ranges overlap)? See Taylor page 5 if you are confused.
Should you measure the height from the top, middle, or bottom of the ball bearing to the timer pad on the floor? Why?
Identify at least two sources of statistical error.
Identify at least two sources of systematic error.

Part 2

Find the muzzle velocity of the projectile and its propagated error: v ± v. Do not find the time t or the error on the time t. Time is not a measured quantity; eliminate time as a variable before propagting (as you did on the prelab).
Should you measure the horizontal distance with the gun spring compressed or uncompressed? Why?
Should you measure the height from the top, middle, or bottom of the ball bearing to the ground? Why?
Identify at least two sources of statistical error.
Identify at least two sources of systematic error.

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