Measuring Acceleration Due to Gravity, g - SMU

Measuring Acceleration Due to Gravity, g

Introduction

y = y + v t + 12 a t f o oy We will use the formula

y 2, valid for constant acceleration, to calculate

the acceleration due to gravity, g, in Dallas. In the equation, y is the vertical distance the object

travels from its staring point, a is the acceleration, and t is the time for the object to fall.

y = 12 at2 Dropping an object from rest beginning at the origin we find that

.

a y t2 If is constant, then should be proportional to . Notice the equation is independent of the

object's mass.

In this free fall experiment, a steel ball is clamped into the spring loaded release mechanism. The ball is in series with the triggering circuit for the timing device. When the thumbscrew is loosened, the mechanism pops open, releasing the ball and starting the timing device. When the ball strikes the receptor pad, the top plate of the pad is forced against the metal base. This automatically stops the timing. The timing device displays the time it took for the ball to drop from the release mechanism to the pad.

Equipment

Free Fall Adapter

Photogate Timer

? ? Steel Ball Bearings [ (15.87 0.01) mm & (19.05 0.01) mm in diameter]

Two-meter stick Meter stick.

Procedure

Equipment Setup

Setup the Free Fall Adapter with the Photogate Timer and load the 15.87 mm ball bearing: The Ball Release Mechanism holds a steel ball between the Release Plate and the Contact Screw. The Dowel Pin is pushed into place to hold the Release Plate. A thumbscrew holds the dowel pin in place. A spring on the dowel pin pushes the release plate away from the ball when the thumbscrew is loosened.

1. Clamp the ball release mechanism to the vertical support rod at the desired height over the floor or table.

2. Loosen the thumbscrew slightly. 3. Insert the steel ball into the release mechanism between the contact screw and the hole

in the release plate. See B. Press the release plate against the ball to hold it in place. See C. 4. Press against the end of the dowel pin so the spring on the dowel pin is compressed and the ball is clamped between the hole in the release plate and the contact screw. See D. Tighten the thumbscrew. 5. Position the ball receptor pad directly under the ball. 6. Connect the Free Fall Adapter phone plug to the Photogate Timer and supply electrical power to the timer.

Data Collection

1. Set up the Free Fall Adapter as described above. Use the 15.87 mm diameter steel ball. 2. Set y, the height from which the ball drops, to approximately 2.0 meters. 3. Measure the distance from the bottom of the ball to the top of the receptor pad as accurately

as possible and record the distance with its associated uncertainty. 4. Measure and record the fall time with its associated uncertainty:

Turn on the timer and set it to GATE mode. Tap the receptor pad to reset the Free Fall Adapter electronics. Press the RESET button to reset the timer. Loosen the thumbscrew on the Free Fall Adapter to release the ball.

NOTE: The ball should hit in the center of the receptor pad. If not, reset the time,

reposition the pad, and try again.

Read the time on the digital display. This is the time it took for the ball to fall from the

release mechanism to the receptor pad.

y? ? y? t? ? t? 5. Repeat the measurements three more times and record your values. Calculate the averages

of the four trials with their uncetainties ie.

and

.

6. Set the vertical distance, y, to 1.60, 1.20, and 0.80 meters and repeat the data recording

steps for each new value of y. Be sure to measure the distance carefully.

7. Repeat the steps for the 19.05 mm diameter steel ball.

Analysis Questions

y? t? 1. For each height setting and each ball, calculate the average drop distance and fall time

y? t?2 y? with their associated uncertainties.

2. For each ball, plot a graph of versus , with as the dependent variable (y-axis). Include

g ? g a linear trend line with its regression equation. From the slope determine the acceleration

due to gravity for each ball. Was the free-fall acceleration (

) the same for each ball

within experimental limits?

3. What was the effect of the different ball masses on the free-fall acceleration values?

Explain

m/s2 ? m/s2 4. What role did the different starting ball heights play in the accelerations? Explain

5. Are these free-fall accelerations in agreement with the standard value 9.80

0.01

(that is, do the error ranges overlap)? See Taylor page 5 if you are confused.

6. Why did you measure the fall distances from the bottom of the ball to the ball receptor pad

and not to the top or middle? Explain.

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