Martian Sports: Investigating Newton’s Second Law

Performance Expectation: HS-PS2-1 Disciplinary Core Idea: PS2.A: Forces and Motion Science and Engineering Practice: Analyzing and Interpreting Data Crosscutting Concept: Cause and Effect

The Phenomenon: The Red Planet Field Goal

It is the year 2085. The Interplanetary Athletics League (IAL) is holding its inaugural championship on Mars. During a pre-game practice, an Earth-born kicker tries to boot a field goal using the same force they use back home. To their surprise, the ball stays in the air for nearly three times as long and travels much further than expected.

Initial Question: Why does the same “kick” result in such a different motion on Mars? Is it because the ball is lighter, or is something else causing it to accelerate differently?

Part 1: Predictive Sandbox

Open the Projectile Motion Simulation. Before gathering data, use the Gravity (g) slider to compare Earth (9.8 m/s²) and Mars (3.7 m/s²).

1. Set the Launch Velocity to 15 m/s and Angle to 45°.
2. Launch the ball on Earth ($g = 9.8$) and observe the path.
3. Predict: If you switch to Mars ($g = 3.7$), how will the “Total Velocity” vector (green arrow) change over time compared to Earth? Will it shrink faster or slower as it moves upward? Explain your reasoning.

Part 2: Designing the Investigation

To prove Newton’s Second Law ($F_{net} = m \cdot a$), we need to see how a change in Net Force affects Acceleration. In this simulation, the only force acting on the ball in flight is gravity.

Proposal: We will test three different “Planets” (Gravity settings) to see if the resulting acceleration matches the Force applied.

Part 3: Data Collection & Analysis

For each environment below, launch the ball with $v_0 = 20$ m/s and $Angle = 60^\circ$. Use the Record Data button to capture at least 3 points during the ascent (while the ball is still going up).

Trial A: Earth (g = 9.8)

1. Record $t_1$, $t_2$, and the corresponding $v_y$ (vertical velocity) values.
2. Calculate the vertical acceleration: $a_y = \frac{v_{y2} - v_{y1}}{t_2 - t_1}$
3. Result: $a_y =$ ____ m/s²

Trial B: Mars (g = 3.7)

1. Repeat the process.
2. Result: $a_y =$ ____ m/s²

Horizontal Check:

Look at the $v_x$ column in your recorded data for any of the trials.

• Does $v_x$ change over time? ____
• If acceleration is caused by a Net Force ($a = F/m$), what does this tell you about the horizontal force acting on the ball in this simulation?

Part 4: The “Target” Challenge

An astronaut habitat is located exactly 50 meters away on the Martian surface ($g=3.7$).

1. Using your knowledge of how lower gravity “slows down” the vertical acceleration, try to hit the center of the 50m mark.
2. What Launch Velocity and Angle did you use?
3. Why was it easier to hit a distant target on Mars than it would be on Earth with the same equipment?

Part 5: Synthesis (CER)

Claim: Describe the mathematical relationship between the net force acting on the projectile and its acceleration.

Evidence: Use the $a_y$ values you calculated in Part 3 and compare them to the $g$ settings you used. Mention what happened to $v_x$ when no force was present.

Reasoning: Explain how your data supports Newton’s Second Law. How does the “pull of the planet” act as the $F_{net}$ in this system, and why does a smaller $g$ result in a “floatier” flight?