Plot a linear graph mg (y-axis) vs average x (x-axis). Note: Do not use connecting points. Note: Copy of the graph must attach to the lab report. Step 2: Post the equation of line (in form of y = mx + b) on the plotting. Step 3: State the slope which is equals to the value of spring constant.
In regards to a lab about Hooke's Law:
- Why do you take measurements twice for Δx?
- According to Hooke’s law, you should expect to get the equation of line as: y = mx. Explain why you have a non-zero value for b.
- Does the mass of spring effect your result? Explain it clearly.
Background information:
Theory:
Part I: Hooke’s law
Whenever a restoring force is created due to displacement of a body from its mean position, the restoring force tries to bring the body back to the original (mean) position. If the restoring force is proportional to the displacement from the mean position, the resulting vibratory motion is called simple harmonic motion. A linear restoring force may be expressed mathematically by the equation
F = -k Δx (1)
where F = mhg which is the force (N), Δx (m) is the displacement from the equilibrium point, and k (N/m) is a proportionality constant which is called ‘Spring Constant’ of the spring. mh is the hanging mass. The minus sign expresses the restoring nature of the force by indicating that the direction of F is always opposite to the displacement Δx from equilibrium.
For vibratory motion we have the following definitions:
Amplitude, A: The maximum displacement from the equilibrium point on either side. (unit: m)
The following equations give the displacement, velocity and acceleration of the mass as a function of time:
Displacement:
Velocity:
Acceleration:
Two physical examples of this type of force are considered in the present experiment, the simple pendulum and the spring-mass system.
Plot a graph: F (= mg) vs Δx graph using Excel or other software. It should be a linear graph in the form of:
Y = mx + b
Post the equation of line on graph so you can get the slope of the graph.
From equation (1): This slope = k.
Procedure:
Part I:
- Use the electronic balance to obtain the combined mass of the spring and hanger
- Adjust the movable scale so that the bottom of the hanger is at the 0 cm position. Add a 50.0-g slotted mass (or possibly another mass increment depending on your spring) and observe the elongation x of the spring. Record x in m (meter). Repeat for the rest of the masses listed in the table (or adjusted masses for your spring stiffness
- For each added mass, determine the force F stretching the spring in N (newtons).
- Use Excel to plot the force vs the elongation and fit your data with a straight line.
Data: For Hooke’s Law
|
Hanging Mass(m) (kg) |
x1 (m) |
x2 (m) |
Avg of x (m) |
mg (N) |
|
0.07 |
0.097 |
0.097 |
0.097 |
0.6867 |
|
0.09 |
0.127 |
0.125 |
0.126 |
0.8829 |
|
0.11 |
0.155 |
0.155 |
0.155 |
1.0791 |
|
0.13 |
0.184 |
0.186 |
0.185 |
1.2753 |
|
0.15 |
0.214 |
0.216 |
0.215 |
1.4715 |
|
0.17 |
0.244 |
0.244 |
0.244 |
1.6677 |
|
0.19 |
0.271 |
0.272 |
0.2715 |
1.8639 |
|
0.21 |
0.3 |
0.3 |
0.3 |
2.0601 |
Calculations:
- Step1: Plot a linear graph mg (y-axis) vs average x (x-axis). Note: Do not use connecting points. Note: Copy of the graph must attach to the lab report.
- Step 2: Post the equation of line (in form of y = mx + b) on the plotting.
- Step 3: State the slope which is equals to the value of spring constant.
Result: Spring constant = 6.74
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