Voltage Probe Force Voltage Probe Force LabLab

by Kevin Bell and Christopher by Kevin Bell and Christopher NieldNield

The ProblemThe Problem

Determine the force with which a Determine the force with which a tennis racket acts on a tennis tennis racket acts on a tennis ball.ball.

The ExperimentThe Experiment

To calculate force, it is necessary To calculate force, it is necessary to determine the time duration to determine the time duration during which the ball and racket during which the ball and racket are in contact (are in contact (ΔΔt) and the and t) and the and the change in velocity during this the change in velocity during this time (time (ΔΔv)v)

The ExperimentThe Experiment

ΔΔv could be measured with v could be measured with photogates, but to keep our lab photogates, but to keep our lab simple we calculated the change simple we calculated the change based on the height from which based on the height from which the ball was dropped and the ball was dropped and assuming no air resistance and assuming no air resistance and perfect elasticity.perfect elasticity.

The ExperimentThe Experiment

Measuring Measuring ΔΔt is more difficult.t is more difficult. To do this, we considered the To do this, we considered the

possibility of using a setup in possibility of using a setup in which the ball would complete an which the ball would complete an electrical circuit while in contact electrical circuit while in contact with the racket that could with the racket that could potentially activate and potentially activate and deactivate the timer.deactivate the timer.

The SetupThe Setup

Instead of a jury-Instead of a jury-rigged timer rigged timer setup, however, setup, however, we found that the we found that the Vernier voltage Vernier voltage probe was probe was capable of highly capable of highly precise precise measurements of measurements of voltage against voltage against time.time.

The LabThe Lab

We wrapped a We wrapped a tennis ball with tennis ball with uninsulated uninsulated copper wire to copper wire to make it conduct make it conduct electricity.electricity.

The SetupThe Setup

We then laced We then laced more wire more wire through the through the strings of the strings of the tennis racket.tennis racket.

The SetupThe Setup

We then attached We then attached the racket wires to the racket wires to a battery and the a battery and the voltage probe, voltage probe, such that the wire such that the wire on the ball on the ball completed the completed the circuit and circuit and registered as a registered as a voltage spike.voltage spike.

The SetupThe Setup

The ball wrapped in wireThe ball wrapped in wire

The SetupThe Setup

Alligator clips attached to the wire on the racket, the Alligator clips attached to the wire on the racket, the voltage probe electrodes, and the batteryvoltage probe electrodes, and the battery

The SetupThe Setup

The ball completing the circuitThe ball completing the circuit The ball must be massed The ball must be massed for later analysisfor later analysis

The SetupThe Setup

C-clamps were used for stability.C-clamps were used for stability.

Another clamp is used to hold the ball and Another clamp is used to hold the ball and drop it consistently.drop it consistently.

The ExperimentThe Experiment

A quick twist drops the A quick twist drops the ball without added forceball without added force

From there, it drops to the From there, it drops to the tennis racket setuptennis racket setup

The ExperimentThe Experiment

The contact time of the ball and racket can The contact time of the ball and racket can clearly be seen in the voltage spike.clearly be seen in the voltage spike.

The Data AnalysisThe Data Analysis

Average contact time (Average contact time (ΔΔt): 0.00975st): 0.00975s Ball mass (m): 0.05943kgBall mass (m): 0.05943kg Calculated acceleration Calculated acceleration

(a):-769.0m/s(a):-769.0m/s22

By Newton’s Second Law, By Newton’s Second Law,

F=ma=(0.05943kg)(-769.0m/sF=ma=(0.05943kg)(-769.0m/s22))

≈≈--45.7N45.7N

Acceleration Calculations