Report For PHYS1110: Describe The Physics Behind Everyday Li ✓ Solved

Report for PHYS1110: describe the physics behind an everyday

Report for PHYS1110: describe the physics behind an everyday phenomenon of interest by constructing an investigation that demonstrates the physics.

You will plan a brief post in your group discussion forum including your Aim, a short method, and the independent and dependent variables and any constants.

The final report should explain the relevant physical principles with equations and include a practical investigation using basic equipment.

Choose a topic such as bouncing balls, oscillations on springs, the greenhouse effect, boats sailing into the wind, or another tutor-approved topic.

Focus on the physics rather than chemistry or biology.

The investigation should be specific, accessible with common equipment, and clearly relate to everyday life.

Paper For Above Instructions

Introduction

Understanding everyday phenomena through simple experiments is a cornerstone of physics education. The bouncing ball is a classic illustration of energy conversion and dissipative processes. The aim here is to quantify energy loss upon impact with different surfaces, using the coefficient of restitution, e, as a measure of collision elasticity. This approach connects classroom physics to everyday experience, showing how seemingly ordinary events reveal fundamental physical ideas (Halliday, Resnick, & Walker, 2018).

Theoretical background

When a ball drops vertically and collides with a surface, its velocity just before impact, v_i, is redirected upward with a magnitude v_f = e·v_i, where e is the coefficient of restitution. A perfectly elastic collision would have e = 1, while a completely inelastic collision would have e ≈ 0. The rebound height h_r relative to the drop height h_d is related by h_r/h_d = e^2, so e = sqrt(h_r/h_d) for a vertical drop with negligible air resistance. This relationship derives from energy and momentum considerations for a collision and provides a practical means to quantify elasticity (Halliday, Resnick, & Walker, 2018; HyperPhysics, n.d.).

In real-world situations, energy loss arises from deformation of the ball and surface, internal friction, heat generation, and air drag. Surface properties, such as hardness and roughness, also influence how much energy is dissipated during impact. The simple relationship e = sqrt(h_r/h_d) allows a clear, measurable link between observable rebound height and the underlying physics of the collision (Britannica, n.d.; NASA, n.d.).

Methods and variables

Independent variable: surface type (for example, wood vs. tile).

Dependent variable: rebound height (or rebound velocity, from which e can be inferred).

Controlled variables: drop height h_d, ball type/material, ambient conditions, and alignment of the ball with respect to the surface.

Procedure (proposed): Use a rubber ball of known diameter and mass. Drop the ball from a fixed height h_d that is easy to reproduce (e.g., 1.0 m) onto two surface types. Measure the rebound height h_r using a ruler or by analyzing video frames from a smartphone camera placed perpendicular to the surface. Repeat each trial multiple times to obtain an average h_r for each surface. Compute e for each surface with e = sqrt(h_r/h_d).

Equipment should be simple: a ball, a ruler or measuring tape, a stable support for consistent drop height, and a smartphone (optional) to record the drop for height analysis. This aligns with the constraint that the investigation be doable with common equipment and still illustrate the key physics (Halliday et al., 2018; HyperPhysics, n.d.).

Data and calculations (example data)

Suppose the drop height is h_d = 1.00 m. For surface A (wood), measured rebound heights across five trials yield h_r values of about 0.64–0.66 m, averaging h_r ≈ 0.65 m. For surface B (tile), h_r values are about 0.36–0.40 m, averaging h_r ≈ 0.38 m. Using e = sqrt(h_r/h_d): surface A gives e ≈ sqrt(0.65) ≈ 0.81; surface B gives e ≈ sqrt(0.38) ≈ 0.62. These numbers illustrate how surface properties influence collision elasticity and energy retention (Serway & Jewett, 2013; Young & Freedman, 2014).

If you account for measurement uncertainty, calculate standard deviations for h_r and propagate to e to obtain an uncertainty in e. Repeating trials reduces random error and clarifies the difference between surfaces. The general trend should show higher e on harder, smoother surfaces and lower e on softer or rougher surfaces due to increased energy dissipation (Britannica, n.d.; NASA, n.d.).

Analysis and interpretation

From the theoretical viewpoint, e is a measure of the elasticity of the collision: the fraction of velocity retained after impact. Since h_r/h_d = e^2, a larger e means less energy is dissipated during contact. The energy loss fraction is 1 − e^2, which corresponds to the portion of the ball’s mechanical energy converted to heat, deformation, and other non-recoverable forms (Feynman, 1964; Halliday et al., 2018).

Discrepancies between measured e values and idealized predictions can arise from several sources: air resistance during the fall and rise (negligible at 1 m but not zero), misalignment of the drop (angle of impact), surface contaminants (dust or moisture), and timing/height measurement errors. An improved experiment could use a high-speed camera or a motion-tracking app to more precisely determine h_r and h_d, or use a ball with a more uniform elastic response to minimize variability (HyperPhysics, n.d.; Britannica, n.d.).

Uncertainties and improvements

Uncertainties can be quantified by repeating measurements on each surface and calculating the standard deviation of h_r. Propagating uncertainty to e via partial derivatives yields δe ≈ (1/(2√(h_r h_d))) δh_r, highlighting that precise height measurements are crucial for accurate e values. Improvements include calibrating the drop height apparatus, using a single surface area to avoid edge effects, and controlling environmental conditions such as humidity and temperature that can affect material properties (Beiser, 2013; Halliday et al., 2018).

Conclusion

The bouncing-ball experiment provides a clear, hands-on illustration of energy dissipation and collision elasticity. By measuring rebound heights on different surfaces and applying the relation e = sqrt(h_r/h_d), students connect observable outcomes to fundamental physics principles: conservation of energy, momentum exchange at impact, and the role of material properties in real-world damping. The exercise demonstrates how everyday experiences reflect deeper theoretical concepts and how careful measurements can quantify the physics of common phenomena (Serway & Jewett, 2013; Knight, 2006).

Discussion of broader relevance

Similar energy-dissipation ideas appear in a range of everyday contexts, from sports science (how court surfaces affect bounce) to engineering (designing materials with specific damping properties). Understanding restitution coefficients helps explain why some surfaces are preferred in sport flooring, why sports equipment behaves differently in different environments, and how energy management is achieved in engineering systems. The conceptual framework also connects to introductory topics in classical mechanics and thermodynamics, reinforcing that physics provides quantifiable explanations for everyday experiences (Feynman, 1964; Britannica, n.d.).

References

  1. Halliday, D., Resnick, R., & Walker, J. (2018). Fundamentals of Physics (11th ed.). Wiley.
  2. Serway, R. A., & Jewett, J. W. (2013). Physics for Scientists and Engineers (9th ed.). Cengage.
  3. Young, H. D., & Freedman, R. A. (2014). University Physics with Modern Physics (14th ed.). Pearson.
  4. Giancoli, D. (2014). Physics: Principles with Applications (7th ed.). Pearson.
  5. Knight, R. D. (2006). Physics for Scientists and Engineers: A Strategic Approach (2nd ed.). Pearson.
  6. HyperPhysics. (n.d.). Coefficient of Restitution. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/restitution.html
  7. Britannica. (n.d.). Coefficient of restitution. Retrieved from https://www.britannica.com/science/coefficient-of-restitution
  8. NASA. (n.d.). Drag. Retrieved from https://www.grc.nasa.gov/www/k-12/airplane/drag1.html
  9. Feynman, R. P. (1964). The Feynman Lectures on Physics, Vol. I. Addison-Wesley.
  10. Britannica. (n.d.). Air resistance. Retrieved from https://www.britannica.com/science/air-resistance

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