Hookes Law

7. EXPERIMENT M7: HOOKE’S LAW OBJECTIVES

In this experiment, you can learn about the oscillation period and frequency, harmonic oscillation, the spring constant, constant, and Hook’s law. law. Finally the oscillation period of a spring is measured and the spring constant is determined.

THEORY

A simple kind of oscillation occurs when the restoring force

is directly proportional

to the displace displacement ment from from equilibrium equilibrium . This happens happens if the spring spring (Fig. (Fig. 7.1) obeys Hooke’s Hooke’s law. Hooke's Law gives the relationship between the force applied to an unstretched spring and the amount the spring is stretched: (7.1) where

is the spring (or force) constant.

Figure 7.1 Stretching a spring from elongation

x  0

to elongation x  1.

Using the Newton’s second law of motion Eq. (7.1) becomes

(7.2.a)

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or 

.

(7.2.b)

This equation is the differential equation of simple harmonic motion. The wave function of Eq. (7.2) describes the displacements of mass: (7.3.a) or  (7.3.b) where

is the amplitude and

phase angle.

One can calculate the period of the motion using the angular frequency

for 

small amplitude:

.

(7.4)

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EXPERIMENTAL PROCEDURE Part I 1. Make the initial reading (or zero reading) as zero with no mass suspended (Fig. 7.2).

Figure 7.2 Experimental set-up of Hooke’s law.

2. Suspend the mass

and record the elongation caused by the weight of its mass

. Record the measurements on table 7.1. 3. While the first mass is still suspended, add the other masses one by one onto the

 previous one and repeat step 2 for the new loads respectively and record them on the table 7.1. 4. Plot a graph of the weight

versus the elongation

in graph 7.1.

5. Determine the slope of the graph that gives the spring constant

.

Part II 6. Suspend the mass

. R elease the mass with small amplitude and using a counter 

(chronometer) measure the time for 10 periods (3 times). Repeat the measurement for  . Record the measurements on table 7.2. 7. Calculate the spring constant from the Eq. (7.4) for each measurement and record it on

the table 7.2. 8. Calculate the average of the spring constant for both loading mass using arithmetic mean

(see appendix). Record the spring constant that is found from the slope of graph 7.1 and find percentage error (see appendix). Record it on the table 7.2. Compare the values and explain the results. 50

LABORATORY REPORT: CALCULATIONS AND GRAPHS

 Name Faculty number Date Instructor name

: _______________________  : _______________________  : _______________________  : _______________________ Instructor’s signature: ____________ 

These blanks must be written in pen (not pencil).

Table 7.1 Hooke’s law calculations.

0.070 0.120 0.170 0.220 0.270 Show your work here:

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Graph 7.1 The weight

W  versus

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the elongation x.

Table 7.2 Calculation of the spring constant.

Trial 1 Trial 2 Trial 3

Show your work here:

Explain the results:

BIBLIOGRAPHY

[1] Mechanics Laboratory (LMF217) Manual, http://en.isikun.edu.tr/download/m5.pdf. [2] University Physics with Modern Physics with MasteringPhysics™, 12/E, Hugh D. Young and Roger A. Freedman, 2008. [3] Physics Laboratory Experiments, Hooke’s law 1.3.01-01.

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