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Free Fall STUDENT

Lab Partners: OTHER STUDENT, OTHEROTHER STUDENT DATE

Individual Formal Lab Report

Purpose

The purpose of this lab experiment was to measure the acceleration due to gravity of a free falling object within the lab.

Equipment

1) Free fall apparatus 2) Ruler (accurate to ½ mm) 3) White tape

Procedure

1) Set up the free fall apparatus. 2) Secure tape to the free fall apparatus so that current jumps occur along the apparatus as the object falls, marking the tape at the various spark points. 3) Turn off current to the apparatus before 4) measuring the distances between the periodic current jumps.

Data

Measured Displacement (Δx in cm ±1cm)

Time (t in s) Calculated Velocity (v in cm/s ±3cm/s)

Δx1 = 3.0 t1 = 0.03 v1 = 90

Δx2 = 4.1 t2 = 0.07 v2 = 123

Δx3 = 5.2 t3 = 0.10 v3 = 156

Δx4 = 6.3 t4 = 0.13 v4 = 189

Δx5 = 7.4 t5 = 0.17 v5 = 222

Δx6 = 8.4 t6 = 0.20 v6 = 252

Δx7 = 9.5 t7 = 0.23 v7 = 285

Δx8 = 10.6 t8 = 0.27 v8 = 318

Δx9 = 11.7 t9 = 0.30 v9 = 351

Δx10 = 26.6 t10 = 0.37 v10 = 399

Δx11 = 15.0 t11 = 0.40 v11 = 450

Δx12 = 16.2 t12 = 0.43 v12 = 486

Analysis

Calculating Instantaneous Velocity v = Δxx / t

Example: v1 = Δx1 / t1 = 3.0cm / 0.03s = 90 cm/s

Propagation of error for velocity Err. = √( (σv/σx * Δx)² + (σv/σt*Δt)² ) = √( (1/30 * 0.1)² + 0² ) = 3cm/s

Linear Regression Analysis v(t) = (m * t) + b

m = n(Σ(tn * vn)) - (Σtn * Σvn) / n(Σtn²) – (Σtn)² = 970 b = Σvn - mΣtn / n = 58

where Σ(tn * vn) = (t1 * v1) + (t2 * v2) + ... + (tn * vn) Σtn = t1 + t2 + ... + tn

Σvn = v1 + v2 + ... + vn Σtn² = t1² + t2² + ... + tn²

v(t) = (970cm/s² * t) + 58cm/s v = (a * t) + vi

where a = acceleration due to gravity

a = 970cm/s² or 9.70m/s²

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

100

200

300

400

500

600

f(x) = 970.15 x + 58.47

Velocity vs Time

Velocity (cm/s)

Linear (Velocity (cm/s))

Discussion

%error = ( |9.70m/s² - 9.7945m/s²| / 9.7945m/s² ) x100% = ( 0.0945m/s² / 9.7945m/s² ) x100% = 1.0%

In this particular experiment there are multiple sources of error. For one, the pulse machine cannot be expected to fire at precisely 1/30th of a second every second. In fact for measurement Δx10 it missed a pulse. This was compensated for by doubling the amount of time taken to cover the displacement to 1/15th of a second. Second, the arcs that mark the tape do not occur in a precisely linear fashion because electricity does not arc in a precisely linear way, which would have caused the markings that were measured to be slightly off. Also, air resistance was not taken into account during the calculations, which surely slowed the free falling object. Had the experiment been done in a vacuum and with a more reliable current pulse machine, I suspect the results would have improved.

Conclusion

In this experiment we measured acceleration due to gravity within the lab to be 9.70m/s², which is 1% below the standard value.