Experiment 4

Page 1

Course and Academic Information

• Institution: School of Medicine and Health Sciences
• Department: Department of Basic Sciences
• Course Code: BMPY110
• Course Title: Medical Physics Laboratory Worksheet
• Instructor: Mr. Siliya
• Experiment Identification: EXPERIMENT 4: ELASTIC POTENTIAL ENERGY (SHM)

Experimental Objective

• Aim: To determine the elastic potential energy of the spring.

Apparatus Required

• Helical spring
• Retort stand with clamp
• Mass hanger and slotted masses
• Meter rule
• Pointer (optional)

Theoretical Foundation

When an elastic material is deformed, it stores energy as elastic potential energy $U$, defined by the formula:

$U = \frac{1}{2} k x^2$

Where:

• $U$ is the energy measured in joules ($J$).
• $k$ is the stiffness of the spring, known as the spring constant, measured in Newtons per meter ($N\,m^{-1}$).
• $x$ is the extension of the spring measured in meters ($m$).

Medical Applications of Elastic Energy Storage

1. Tendons and ligaments: Store energy during locomotion and release it to improve biological movement efficiency.
2. Arterial walls: Expand during systole and recoil during diastole, aiding continuous blood flow.
3. Lung tissue: Provides restoring force during exhalation.

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Medical Applications of Elastic Energy Storage (Continued)

4. Prosthetic limbs: Use integrated springs to store and return energy during the gait cycle.

Experimental Procedure

1. Set up the apparatus by suspending the helical spring vertically from the retort stand clamp.
2. Measure and record the initial length of the spring without any load attached ($[1\text{ mark}]$).
3. Add a known mass (e.g., $50\,g$) to the mass hanger.
4. Measure the new length of the spring under load ($[1\text{ mark}]$).
5. Calculate the extension $x$ ($[2\text{ marks}]$).
6. Repeat by adding more masses in equal increments.
7. Record all measurements and calculated readings in a structured table ($[12\text{ marks}]$).

Page 3

Data Collection Table Structure

Data is tabulated under the following required standard columns and mass values:

Table Columns:

• Mass ($g$)
• Force ($N$)
• Length ($m$)
• Extension ($m$)
• Energy ($J$)

Prescribed Mass Increments:

• $50\,g$
• $100\,g$
• $150\,g$
• $200\,g$
• $250\,g$

Governing Equations for Calculations

• Force Calculation:

$F = m g$

• Spring Constant Calculation:

$k = \frac{F}{x}$

Data Analysis and Graphical Determination

8. Plot a graph of Force ($F$) against Extension ($x$). The slope of this line determines the spring constant $k$ ($[8\text{ marks}]$).
9. Use the graph to calculate the elastic potential energy of the spring by computing the total area under the force-extension graph ($[4\text{ marks}]$). 1