Grade: Grade 11 Subject: Science Unit: Physics Lesson: 3 of 6 SAT: ProblemSolving+DataAnalysis ACT: Science

Investigation Lab

Learn

Scientific investigation is at the heart of physics. In this lesson, you will design and conduct experiments to explore the relationships between motion, force, and energy that you learned in previous lessons.

The Scientific Method in Physics

Physics investigations follow a structured approach:

  1. Identify the Question: What phenomenon are you trying to understand or measure?
  2. Form a Hypothesis: Make a testable prediction based on physics principles.
  3. Design the Experiment: Identify variables (independent, dependent, controlled) and procedures.
  4. Collect Data: Take multiple measurements and record observations systematically.
  5. Analyze Results: Use graphs, calculations, and statistical methods to interpret data.
  6. Draw Conclusions: Evaluate whether the data supports or refutes your hypothesis.

Identifying Variables

In any physics experiment, you must clearly define:

  • Independent Variable: The factor you deliberately change (e.g., height of a ramp, mass of an object)
  • Dependent Variable: The factor you measure as a result (e.g., velocity, acceleration, time)
  • Controlled Variables: Factors you keep constant to ensure a fair test (e.g., surface material, room temperature)

Measurement and Uncertainty

All measurements have uncertainty. When recording data:

  • Use appropriate significant figures based on your measuring instrument
  • Take multiple trials to account for random error
  • Calculate the mean and standard deviation of your measurements
  • Report results with uncertainty: value +/- uncertainty (units)

Sample Investigation: Conservation of Energy on an Inclined Plane

Question: Does the gravitational potential energy at the top of a ramp equal the kinetic energy at the bottom?

Hypothesis: If energy is conserved, then PE at top = KE at bottom (minus friction losses).

Variables:

  • Independent: Height of ramp
  • Dependent: Velocity at bottom of ramp
  • Controlled: Mass of cart, surface of ramp, release point

Examples

Example 1: Calculating Expected Velocity

Problem: A 0.5 kg cart is released from rest at a height of 0.8 m on a frictionless ramp. What is the expected velocity at the bottom?

Solution:

Using conservation of energy: PE = KE

mgh = (1/2)mv^2

gh = (1/2)v^2

v = sqrt(2gh) = sqrt(2 x 9.8 x 0.8) = sqrt(15.68) = 3.96 m/s

Example 2: Analyzing Experimental Error

Problem: In an experiment, a student measured the velocity at the bottom as 3.5 m/s instead of the expected 3.96 m/s. Calculate the percent error.

Solution:

Percent Error = |Experimental - Theoretical| / Theoretical x 100%

Percent Error = |3.5 - 3.96| / 3.96 x 100% = 11.6%

This suggests energy was lost to friction.

Example 3: Calculating Uncertainty

Problem: A student measures the time for a cart to travel down a ramp in 5 trials: 2.31 s, 2.28 s, 2.35 s, 2.30 s, 2.26 s. What is the mean and uncertainty?

Solution:

Mean = (2.31 + 2.28 + 2.35 + 2.30 + 2.26) / 5 = 2.30 s

Range = 2.35 - 2.26 = 0.09 s

Uncertainty = Range / 2 = 0.045 s (round to 0.05 s)

Result: t = 2.30 +/- 0.05 s

Practice

Complete these practice problems to reinforce your understanding of physics investigations.

1. A student wants to test how the mass of a pendulum bob affects its period. Identify the independent variable, dependent variable, and two controlled variables.

2. In a projectile motion experiment, a ball is launched horizontally from a table 1.2 m high. Using g = 9.8 m/s^2, calculate how long the ball is in the air before hitting the ground.

3. A student measures the acceleration of a cart as 1.8, 2.1, 1.9, 2.0, and 2.2 m/s^2 in five trials. Calculate the mean acceleration and the percent uncertainty.

4. Explain why it is important to take multiple measurements in a physics experiment instead of relying on a single trial.

5. A theoretical calculation predicts a ball will reach a velocity of 5.0 m/s at the bottom of a ramp. The experimental measurement is 4.6 m/s. Calculate the percent error and suggest one source of this discrepancy.

6. Design an experiment to test Newton's Second Law (F = ma). Describe what equipment you would need, your procedure, and how you would analyze the data.

7. A stopwatch has a precision of 0.01 seconds. If a student measures a time of 3.45 seconds, how should this measurement be reported with uncertainty?

8. In an experiment on momentum conservation, two carts collide. Cart A (mass 0.5 kg, velocity 2.0 m/s) collides with stationary Cart B (mass 0.5 kg). After collision, both carts move together. Calculate the expected final velocity using conservation of momentum.

9. A student's data shows a linear relationship between force and acceleration. If the slope of the best-fit line is 2.5 kg, what does this value represent in the context of Newton's Second Law?

10. Describe the difference between systematic error and random error. Give one example of each in a physics experiment measuring the period of a pendulum.

Check Your Understanding

Answer these questions to test your knowledge of physics investigations.

Question 1: Which variable is deliberately changed by the experimenter?

A) Dependent variable
B) Independent variable
C) Controlled variable
D) Random variable

Question 2: A student calculates a theoretical value of 12.0 m/s but measures 11.4 m/s experimentally. The percent error is:

A) 0.5%
B) 5.0%
C) 5.3%
D) 6.0%

Question 3: Why is it important to keep controlled variables constant during an experiment?

Next Steps

  • Review the scientific method and ensure you can apply it to new investigations
  • Practice calculating percent error and uncertainty in measurements
  • Move on to the next lesson: Data and Graphs