part 1: fan carts\nobjective: determine how the mass of an object affects its acceleration when subject to a…
part 1: fan carts\nobjective: determine how the mass of an object affects its acceleration when subject to a constant force.\nusing the lab software, we will be able to see a graph of the carts velocity over time. how would you calculate the acceleration of the cart as it is pushed by the fan, using the velocity over time?\nmake a prediction: increasing the mass of the cart should (increase / decrease / not change) its acceleration.\nknowing the acceleration and mass of the cart, what equation can we use to calculate the force acting on it?\ndata and analysis\n| cart mass (kg) | change in velocity (m/s) | time (s) | calculated acceleration (m/s²) | calculated force (n) |\n| ---- | ---- | ---- | ---- | ---- |\n| trial 1: 0.54 kg | 0.90m/s | 2.60s | 0.369m/s² | |\n| trial 2: 1.06kg | 0.610m/s | 3.98s | 0.1532m/s² | |\n| trial 3: 1.52kg | 0.400m/s | 2.50 | 0.1604m/s² | |\nuse your data or calculations to answer the central question: how does increasing the mass of an object affect its acceleration?\ndraw a free - body diagram for the cart, showing the weight, normal force, and fan force (ff).\nusing your data, show your calculations for the average force from the fan.
Answer
Explanation:
Step1: Calculate acceleration from velocity - time
Acceleration $a=\frac{\Delta v}{\Delta t}$. For example, in Trial 1, $a_1=\frac{0.90}{2.60}= 0.346\ m/s^{2}$ (rounding - off differences with given value may occur due to rounding in the provided data).
Step2: Make a prediction
According to Newton's second - law $F = ma$, when $F$ is constant, $a=\frac{F}{m}$. So increasing the mass $m$ should decrease the acceleration $a$.
Step3: Identify the force - mass - acceleration equation
The equation is $F = ma$, where $F$ is the force, $m$ is the mass and $a$ is the acceleration.
Step4: Analyze the effect of mass on acceleration
From the data, as the mass increases from Trial 1 ($m_1 = 0.54\ kg$) to Trial 3 ($m_3=1.58\ kg$), the acceleration decreases from $0.346\ m/s^{2}$ (calculated) to $0.1624\ m/s^{2}$. So increasing the mass of an object decreases its acceleration when the force is constant.
Step5: Draw free - body diagram
The weight $W = mg$ acts downwards, the normal force $N$ acts upwards (perpendicular to the surface, balancing the weight if on a horizontal surface), and the fan force $F_f$ acts in the direction of motion of the cart.
Step6: Calculate average force
For Trial 1, $F_1=m_1a_1 = 0.54\times0.346 = 0.187\ N$. For Trial 2, $F_2=m_2a_2=1.06\times0.1532 = 0.162\ N$. For Trial 3, $F_3=m_3a_3=1.58\times0.1624 = 0.257\ N$. The average force $\bar{F}=\frac{F_1 + F_2+F_3}{3}=\frac{0.187 + 0.162+0.257}{3}=\frac{0.606}{3}=0.202\ N$.
Answer:
- Acceleration is calculated as $a=\frac{\Delta v}{\Delta t}$.
- Increasing the mass of the cart should decrease its acceleration.
- The equation is $F = ma$.
- Increasing the mass of an object decreases its acceleration when the force is constant.
- Free - body diagram: Weight $W = mg$ downwards, normal force $N$ upwards, fan force $F_f$ in the direction of motion.
- Average force calculation shown above, average force $\bar{F}=0.202\ N$.