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Relationship Between Acceleration &
Mass (2078-666) 2030
Rationale
A mousetrap racer (MTR) is a spring-powered vehicle that uses elastic potential energy to revolve the axle and accelerate the car forward. The relationship between its mass and acceleration, when propelled with a constant driving force on a horizontal surface, demonstrates Newton's laws of motion. Newton's first law of motion, an object will remain at rest unless acted upon by an external force, correlates with the constant driving force and the MTR. (Encyclopedia Britannica 1998). The external force, the mousetrap assumed to exert a constant force in Newtons, powers the car causing motion from rest. Newton's second law states that force is equal to mass times acceleration which is indirectly proportional when rearranged to force divided by mass equals acceleration (The Physics Classroom 2021). Figure 1: Formula of Newton's 2nd Law revealing force is equal to mass multiplied by acceleration. Figure 2: Newton’s 2nd law rearranged to show acceleration is indirectly proportional to force, divided by mass. Newton's third law states that every action has an equal and opposite reaction, so when a pulling force propels the car, the reactive force is friction, assumed to be constant, and air resistance assumed to be negligible (Hall 2022). Figure 3: A free-body diagram of the forces acting upon the car which include:
- Gravity pulling the car down at 9.8m/s*2,
- Upthrust is the equal and opposite reactive force,
- Rolling friction is assumed to be constant as the horizontal surface is,
- Pulling force caused by elastic potential energy. Minimalising the mass reduces inertia and to maximises grip is essential to the MTR's performance. Friction results from gravity as the wheels contact the ground to cause a reactive force to stay upright. The car's weight, when in motion, causes rolling friction resulting in resistance to acceleration due to heat generation from the frictional transfer (Engineering ToolBox 2008). Minimising wheel and axle rotational friction is critical to maximising the vehicle's performance. The car will accelerate once the wheels have enough rotational force to overpower rolling friction causing traction. During motion, rolling friction causes deceleration as the mousetrap's kinetic energy is unable to surpass the frictional force. The mousetrap elastic potential energy transfers into kinetic energy through the rotation of the axle. Figure 4: Kinematic equation showing acceleration equal to final velocity - initial velocity over time. The change in velocity from its initial to its final overtime is acceleration (in m/s^2). The initial velocity (speed in a direction in m/s) is assumed to be zero, as the car begins at rest, therefore determining the final velocity as average velocity, by the indirect correlation between the vectors, will determine the kinematic acceleration of the car with no forces. Figure 5: Showing final velocity, which is indirectly related to the average velocity, can be substituted in the acceleration equation. Low mass and high net force will result in high acceleration.
Extended ● Average velocity substituted for final velocity. Distance and time recorded to find average velocity to calculate acceleration using the equation: ● Average acceleration plotted against weight to demonstrate relationship between mass and acceleration. Refined ● Three trials per mass used to calculate average velocity and acceleration. ● Five different masses recorded to create scatter plot to demonstrate relationships between mass and acceleration.
Risk Assessment
Risk Level Control Lacerations Medium Keep scissors and saw blades covered and use facing away from the user. Contusions Low Keep mousetrap unactivated until trials. Punctures Medium Aim tools away from user when using. Burns Medium Use PPE when operating
hot glue gun.
Results
Qualitative: The car with the additional 50g had the fastest and farthest distance over time compared to the car with no additional weight. As the weight increased after 50g, the car began to slow down over time. Quantitative: Table 1: Raw Data of Distance, Time, and Average Velocity Trials Trial 1 Trial 2 Trial 3 Avera ge Weig ht of Car (g) Dista nce (m) +/- 0.5cm Time (s) +/- 0.05s Avera ge Veloci ty (m/s in a directi on) Dista nce (m) +/- 0.5cm Time (s) +/- 0.05s Avera ge Veloci ty (m/s in a directi on) Dista nce (m) +/- 0.5cm Time (s) +/- 0.05s Avera ge Veloci ty (m/s in a directi on) Avera ge Veloci ty (m/s in a directi on)
6
Outliers Table 2: Average Acceleration, Force and Uncertainties Acceleration (m/s^2 in direction)
—————————- = Average 3 0.18 = Average Absolute Uncertainty (Max-Min) ————— = Absolute Uncertainty 2 0.19-0. ————— = Absolute Uncertainty 2 0.01 = Absolute Uncertainty Percentage Uncertainty Absolute Uncertainty —————————- x 100 = % Uncertainty Average
—————————- x 100 = % Uncertainty
5.56 = Percentage Uncertainty
Analysis
Figure 6: Average Acceleration Vs Weight of Car Graph
This investigation analyses the relationship between mass and acceleration of a MTR. The graph demonstrates a linear relationship between a car's decreasing weight and increasing acceleration further supported by the trendline. The trendline shows a strong correlation, supported by the r^2 value, representing accuracy between two variables by the variation between data and trendline values, the closer to one the more accurate. The error bars represent the uncertainty of the averages due to errors. Y=mx+c, where c is the value of the changing force applied to the car as it accelerates. It is assumed the car has a constant driving force with and without additional weight due to acceleration decreasing as mass increases. The y-intercept shows a value above zero, proving the driving force of the mousetrap wasn’t constant, lowering the causation and accuracy of the experiment. The random error occurred during trial 2 of 277.16g, falsifying the measurement to be further than average. Another error is force isn’t constant due to an invalid method. Newton’s second law states that force is equal to mass times acceleration, meaning that acceleration is indirectly proportional to force divided by mass when rearranged. And is demonstrated throughout the experiment and graph This correlates with the graph as you must lower the mass and increase the force to maximise acceleration. Newton's third law states that every force has an equal and opposite reactive force meaning that adding weight to the car, causes more drag requiring more force to overcome friction. The frictional force is increased, but the driving force remains constant to push the car with
in results. that tracks acceleration and deceleration and apply it to the MTR. Further investigating Newton's laws, replacing the mousetrap with a different consistent driving force, an electric force, reducing the previous inaccuracies. Also investigating a moving vehicle down a slope to measure the acceleration of gravity and how it acts as a force on masses. These extensions would further prove Newton's second law and support the linear relationship between acceleration and mass.
Conclusion
This investigation determines the relationship between the mass and net force of a MTR when propelled by a constant, driving force and horizontal surface. The results demonstrated a linear relationship between increasing acceleration as mass decreases. Random errors including chassis integrity, string tension and axle drift, are factors that influenced the uncertainty of the experiment. To further extend this investigation, use a constant driving force mechanism like an electric engine or force like gravity.
Bibliography
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Hall, N 2022, Newton’s Laws of Motion , Glenn Research Center | NASA, viewed 26 April
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Physics for Kids: Acceleration 2019, Ducksters.com, viewed 24 April 2023,
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The Physics Classroom 2021, Newton’s Second Law , Physicsclassroom.com, The Physics
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