Question

part 1: fan carts
objective: determine how the mass of an object affects its acceleration when subject to a constant force.
using 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?
make a prediction: increasing the mass of the cart should (increase / decrease / not change) its acceleration.
knowing the acceleration and mass of the cart, what equation can we use to calculate the force acting on it?
data and analysis

cart mass (kg)	change in velocity (m/s)	time (s)	calculated acceleration (m/s²)	calculated force (n)
trial 2: 1.06kg	0.610m/s	3.98s	0.1532m/s²
trial 3: 1.52kg	0.400m/s	2.50	0.1604m/s²

use your data or calculations to answer the central question: how does increasing the mass of an object affect its acceleration?
draw a free - body diagram for the cart, showing the weight, normal force, and fan force (ff).
using your data, show your calculations for the average force from the fan.

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:

1. Acceleration is calculated as $a=\frac{\Delta v}{\Delta t}$.
2. Increasing the mass of the cart should decrease its acceleration.
3. The equation is $F = ma$.
4. Increasing the mass of an object decreases its acceleration when the force is constant.
5. Free - body diagram: Weight $W = mg$ downwards, normal force $N$ upwards, fan force $F_f$ in the direction of motion.
6. Average force calculation shown above, average force $\bar{F}=0.202\ N$.