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# Lab 3: Newton's Second Law ## Objective To experimentally validate Newton's Second Law by measuring the acceleration of a system with varying force and mass. ## Materials * Air track * Air supply * Glider * Assorted masses * String * Pulley * Photogate and timer ## Introduction...

# Lab 3: Newton's Second Law ## Objective To experimentally validate Newton's Second Law by measuring the acceleration of a system with varying force and mass. ## Materials * Air track * Air supply * Glider * Assorted masses * String * Pulley * Photogate and timer ## Introduction Newton's Second Law of Motion is mathematically stated as: $\qquad \sum \overrightarrow{F} = m\overrightarrow{a} $ Where $\sum \overrightarrow{F}$ is the net force vector acting on an object of mass $m$, and $\overrightarrow{a}$ is the acceleration vector of the object. In this experiment, we will be applying a constant force to a glider on an air track, and measure the resulting acceleration. Because the air track is nearly frictionless, we can state: $\qquad F_{net} = F_{applied}$ We will apply a constant force by attaching a string to the glider, running that string over a pulley, and hanging a known mass, $m_h$ on the end. The force applied to the glider by the string will be the tension in the string, which we can calculate as: $\qquad F_{applied} = T = m_h g$ We will measure the acceleration of the glider using photogates and a timer. ## Procedure ### Part 1: Varying Force 1. Set up the air track so that it is as level as possible. 2. Measure the mass of the glider, $m_g$ and record it in **Table 1**. 3. Place the glider on the air track. Connect a string to the glider, pass it over the pulley, and hang a mass $m_h =$ 0.005 kg on the end. 4. Position two photogates a distance $d =$ 0.5 m apart. 5. Release the glider and record the time it takes to pass through each photogate, $t_1$ and $t_2$, in **Table 1**. 6. Repeat steps 3-5 for $m_h =$ 0.010 kg, 0.015 kg, 0.020 kg, and 0.025 kg. ### Part 2: Varying Mass 1. Measure the mass of two additional masses, $m_{a1}$ and $m_{a2}$ and record them in **Table 2**. 2. Place the glider on the air track. Connect a string to the glider, pass it over the pulley, and hang a mass $m_h =$ 0.015 kg on the end. Add the two additional masses to the glider. 3. Position two photogates a distance $d =$ 0.5 m apart. 4. Release the glider and record the time it takes to pass through each photogate, $t_1$ and $t_2$, in **Table 2**. 5. Repeat steps 2-4, removing one additional mass, then removing both additional masses ## Data Analysis 1. Calculate the initial and final velocities of the glider for each trial using the equation: $\qquad v = \frac{\Delta x}{\Delta t} = \frac{L}{t} $ Where $L$ is the length of the glider. Record these values in **Tables 1 & 2**. 2. Calculate the acceleration of the glider for each trial using the equation: $\qquad a = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{\Delta t} $ Where $\Delta t$ is the time it takes for the glider to travel between the photogates. Record these values in **Tables 1 & 2**. 3. Calculate the applied force for each trial using the equation: $\qquad F_{applied} = T = m_h g$ Record these values in **Tables 1 & 2**. 4. Create a graph of $F_{applied}$ vs. $a$ using the data from **Table 1**. Add a linear trendline to the data and record the equation of the trendline. 5. Calculate the inverse of the acceleration ($\frac{1}{a}$) for each trial in **Table 2**. 6. Create a graph of $\frac{1}{a}$ vs. $m$ using the data from **Table 2**. Add a linear trendline to the data and record the equation of the trendline. ## Tables **Table 1: Varying Force** | $m_g$ (kg) | $m_h$ (kg) | $t_1$ (s) | $t_2$ (s) | $v_1$ (m/s) | $v_2$ (m/s) | $\Delta t$ (s) | $a$ (m/s²) | $F_{applied}$ (N) | | :--------: | :--------: | :-------: | :-------: | :---------: | :---------: | :----------: | :---------: | :---------------: | | | 0.005 | | | | | | | | | | 0.010 | | | | | | | | | | 0.015 | | | | | | | | | | 0.020 | | | | | | | | | | 0.025 | | | | | | | | **Table 2: Varying Mass** | $m_g$ (kg) | $m_{a1}$ (kg) | $m_{a2}$ (kg) | $m_h$ (kg) | $t_1$ (s) | $t_2$ (s) | $v_1$ (m/s) | $v_2$ (m/s) | $\Delta t$ (s) | $a$ (m/s²) | $\frac{1}{a}$ (s²/m) | | :--------: | :-----------: | :-----------: | :--------: | :-------: | :-------: | :---------: | :---------: | :----------: | :---------: | :-------------------: | | | | | 0.015 | | | | | | | | | | X | X | 0.015 | | | | | | | | | | | X | 0.015 | | | | | | | | | | | | 0.015 | | | | | | | | ## Questions 1. How does your first graph relate to Newton's Second Law? 2. How does your second graph relate to Newton's Second Law? 3. What sources of error are present in this experiment? 4. How could this experiment be improved?