Finding the Spring Constant (k) and Gravity (g) using Hooke’s Law and the Laws of Simple Harmonic Motion

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Finding the Spring Constant (k) and Gravity (g) using Hooke's Law and the Laws of Simple Harmonic Motion

Aim: In this investigation I will calculate an estimate for the spring constant of a certain spring. To do this I will use Hooke's Law -

F = k e

I will then use the laws of simple harmonic motion to get a better estimate and compare the two results. The equation that I will use is below:

T = 2?

Plan: To use Hooke's Law to calculate k I will need to find the extension of the spring when a certain force is hanging from it.

To use the simple harmonic motion formula I will need to time the period (T) of the oscillations of the spring when a certain mass is hanging from it.

To calculate gravity (g) I will need the square of the period (T2) and the extension of the spring for each mass as I will be using the following formula:

T2 = 4 ?2 e

g

which is derived as follows:

T2 = 4 ?2 m

k

F = m g

F = k e

k e = m g

k = m g

e

T2 = 4 ?2 m e

m g

T2 = 4 ?2 e

g

Equipment List

. Clamp and Stand

2. 10gram weights

3. Ruler - accurate ? 0.5mm

4. Stopwatch - accurate ? 0.005 seconds

5. Digital scientific scales - accurate ? 0.005g

6. Spring

7. Marker

8. Safety Glasses

9. Gloves

Procedure

. Set up the equipment as below:

2.

Safety - Put on safety glasses and gloves as the spring could snap as we put more weight onto it.

3. Place first weight on scales and record mass in the table under mass. (mass must be in kilograms. All results should be recorded to 3 d.p.)

4. Place mass on end of spring

5. Measure the extension using the ruler, record in table.

6. Place marker 1 cm under the bottom of the mass using another clamp
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7. Pull mass down to the marker, start stopwatch as you release, each time the mass reaches the marker count 1 oscillation, after 20 stop stopwatch. Divide time by 20 ( to get the period. All results should be recorded to 3 d.p.) and record in the table.

8. Place next mass on scales and record mass in the table (Note - when adding a mass to the table, the value should be added to the previous mass. See table below for example).

9. Complete steps 4, 5, 6 and 7 for 6 weights.

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