# Kinematics and Dynamics Lab Experiments

Physics I · Principles of Laboratory Practice · https://tryals.app/learn/physics-i/kinematics-and-dynamics-lab-experiments

## Mechanics Experiments

Laboratory experiments test **kinematics** and **dynamics** against real data. The best experiments plot one variable against another to yield a straight line, where the slope or intercept reveals the physical quantity.

| Experiment | Measured | Key equation |
| --- | --- | --- |
| Free fall | $t$ vs $h$ | $h = \frac{1}{2}gt^{2}$ |
| Inclined plane | $a$ vs $\sin\theta$ | $a = g\sin\theta$ |
| Newton's 2nd Law | $a$ vs $F$ | $F = ma$ |
| Simple pendulum | $T$ vs $L$ | $T = 2\pi\sqrt{L/g}$ |
| Spring constant | $F$ vs $x$ | $F = kx$ |

## Pendulum & Best Practices

To measure **acceleration due to gravity** $g$ from a pendulum, rearrange the period formula to:

$$g = \frac{4\pi^2 L}{T^2}$$

Plot $T^{2}$ vs $L$; the slope is $4\pi^{2}/g$. For $L = 1.00$ m and $T = 2.006$ s, calculating gives $g = 9.81$ m/s$^2$.

**Practical tips**: Use **photogates** or video analysis. Measure **multiple periods** and divide ($T = t_{10}/10$) to reduce timing error by $10\times$.

**Common pitfall**: Change one variable at a time. Varying mass and force together to save time produces untangible data.

## Practice questions

5 of this lesson's 14 practice questions, with answers. The full set is in the app.

### 1. In a free-fall experiment, air resistance can always be neglected regardless of the object's shape or speed.

**Answer:** False

**Why:** Air resistance depends on speed, shape, and cross-sectional area; it is only negligible for dense, compact objects at low speeds.

Page: https://tryals.app/practice/physics-i/kinematics-and-dynamics-lab-experiments/in-a-free-fall-experiment-air-resistance-can-always-be-neglected

### 2. Complete the statement with the correct term.

**Answer:** The period of a simple pendulum depends on its **length** and the local gravitational acceleration g.

**Why:** $T = 2\pi\sqrt{L/g}$; the period depends on length L and g, not on mass or amplitude (for small angles).

Page: https://tryals.app/practice/physics-i/kinematics-and-dynamics-lab-experiments/complete-the-statement-with-the-correct-term

### 3. A kinematics experiment gives $g = 9.2$ m/s² rather than 9.81. What should be checked before concluding the measurement is simply imprecise?

A. Whether more decimal places were available from the instruments
B. Whether the accepted value of $g$ is correct for that laboratory
C. Whether the deviation is one-sided across every trial
D. Whether the experiment was performed at the same temperature as the standard

**Answer:** C. Whether the deviation is one-sided across every trial

**Why:** Scatter goes both ways; bias does not. A consistently low $g$ is a clue about the apparatus, and treating it as noise discards the most informative thing in the data.

Page: https://tryals.app/practice/physics-i/kinematics-and-dynamics-lab-experiments/a-kinematics-experiment-gives-g-9-2-m-s-rather-than-9-81-what

### 4. Which modifications improve the accuracy of a pendulum experiment?

A. Timing many oscillations and dividing by the count
B. Timing a single swing for each measurement
C. Using a very heavy bob to reduce air resistance effects
D. Using a small amplitude (< 10°)

**Answer:** A. Timing many oscillations and dividing by the count; C. Using a very heavy bob to reduce air resistance effects; D. Using a small amplitude (< 10°)

**Why:** Timing many swings reduces timing error; small angles ensure the small-angle approximation holds.

Page: https://tryals.app/practice/physics-i/kinematics-and-dynamics-lab-experiments/which-modifications-improve-the-accuracy-of-a-pendulum-experiment

### 5. Design the experiment: verify that $F = ma$ using a cart on a low-friction track. Order the steps.

**Answer:**

1. Level the track and measure the cart’s mass
2. Apply a known force with a calibrated hanging weight
3. Record position vs. time with the motion sensor
4. Extract acceleration from a fit to the position data
5. Repeat across several forces and plot F against a
6. Check that the plot is a line whose slope equals the mass

**Why:** The verification is the final plot: if F vs. a is straight with slope m, Newton wins on this track. Notice the architecture, one variable deliberately varied, one measured, everything else clamped. That is experimental design in a single sentence.

Page: https://tryals.app/practice/physics-i/kinematics-and-dynamics-lab-experiments/design-the-experiment-verify-that-f-ma-using-a-cart-on-a