Middle School Science Quiz: Net Force And Motion

A student tests the same cart with several net forces and records acceleration.

Which calculation would stay constant for every trial if the cart's mass does not change?

A cart has a constant mass of 2 kg. During a test, the measured acceleration is 6 m/s$^2$. What net force $F_{net}$ must be acting on the cart?

A 2 kg cart is pushed so the net force is 5 N, then 10 N, then 15 N. The measured accelerations are 2.5 m/s$^2$, 5.0 m/s$^2$, and 7.5 m/s$^2$.

Based on this pattern, what acceleration should the cart have if the net force is increased to 20 N (same cart)?

A student pushes the same 2 kg cart on a smooth track with different net forces and measures the cart's acceleration. The results are shown below.

Force $F_{net}$ (N) | Acceleration $a$ (m/s$^2$) 0 | 0 5 | 2.5 10 | 5.0 15 | 7.5

What relationship between net force and acceleration is shown by the data?

A class wants to collect data to show how net force affects motion for the same cart. They have a spring scale (to measure pulling force) and a motion sensor (to measure acceleration).

Which plan would best test the relationship between $F_{\text{net}}$ and acceleration while keeping the investigation fair?

A student gives the same ball different pushes on a smooth floor. During each push, the contact time is about the same, $\Delta t=0.5\,\text{s}$. The student measures the ball's change in speed.

Data:

• $F_{\text{net}}=4\,\text{N}$ → $\Delta v=1\,\text{m/s}$
• $F_{\text{net}}=8\,\text{N}$ → $\Delta v=2\,\text{m/s}$
• $F_{\text{net}}=12\,\text{N}$ → $\Delta v=3\,\text{m/s}$

Which statement best describes the pattern between $F_{\text{net}}$ and the motion change?

A cart starts from rest and is pushed with different net forces for the same time interval, $\Delta t = 2\,\text{s}$. The cart's mass stays the same in every trial.

Measured accelerations:

• $F_{\text{net}}=5\,\text{N}$ → $a=2.5\,\text{m/s}^2$
• $F_{\text{net}}=10\,\text{N}$ → $a=5.0\,\text{m/s}^2$

Using $\Delta v = a\Delta t$, what is the cart's change in speed when $F_{\text{net}}=10\,\text{N}$ is applied for $2\,\text{s}$?

A $2\,\text{kg}$ cart is pushed along a level track. The net force is changed while the cart's acceleration is measured.

Table: $F_{\text{net}}$ (N) vs. $a$ (m/s$^2$)

• 5 N → 2.5 m/s$^2$
• 10 N → 5.0 m/s$^2$
• 15 N → 7.5 m/s$^2$

Based on the pattern in the data, what acceleration would you predict for $F_{\text{net}}=20\,\text{N}$ on the same cart?

A student tests the same cart each time and measures the following pairs of values:

$F_{\text{net}}$ (N): 5, 10, 15 $a$ (m/s$^2$): 2.5, 5.0, 7.5

Which statement is best supported by the constant ratio $F_{\text{net}}/a$ in the data?

A student tests a cart and finds these measurements:

• When $F_{\text{net}}=10\,\text{N}$, the cart's acceleration is $a=5\,\text{m/s}^2$.

What does this single data point imply about the cart's mass (assuming Newton's Second Law applies and the net force value is accurate)?

A student applies a constant net force to the same cart for 2 seconds each time and measures the change in speed $\Delta v$.

$F_{net}$ (N) | $\Delta v$ after 2 s (m/s) 0 | 0 5 | 5 10 | 10 15 | 15

What does the data show about how net force affects the cart's motion (for the same time interval)?

A student graphs acceleration $a$ (m/s$^2$) versus net force $F_{net}$ (N) for the same cart. The graph is a straight line that goes through the origin.

What does a straight line through the origin on an $a$ vs. $F_{net}$ graph show?

In a tug-of-war, two teams pull on a rope attached to a sled on ice. The net force on the sled is the difference between the pulls. A student measures the sled's acceleration for different net forces.

$F_{net}$ (N) | $a$ (m/s$^2$) 2 | 0.5 4 | 1.0 6 | 1.5

If the net force is increased from 2 N to 6 N, how does the acceleration change?

A student applies different net forces to the same cart and records the acceleration:

$F_{\text{net}}$ (N): 5, 10, 15

a ($\text{m/s}^2$): 2, 4, 6

What happens to the acceleration when the net force increases from $5\,\text{N}$ to $15\,\text{N}$?

A $2\,\text{kg}$ cart on a track is pushed with a constant net force for $3\,\text{s}$. The cart starts from rest.

Trial A: $F_{\text{net}} = 5\,\text{N}$ Trial B: $F_{\text{net}} = 15\,\text{N}$

Which statement best compares the change in speed ($\Delta v$) in Trial B to Trial A?

A $2\,\text{kg}$ cart starts from rest. For each trial, a constant net force is applied for $2\,\text{s}$. Use $\Delta v = a\Delta t$ and $a = F_{\text{net}}/m$.

What is the cart's change in speed after $2\,\text{s}$ when $F_{\text{net}} = 10\,\text{N}$?

A student wants to design an investigation to show how net force affects acceleration for a cart. Which plan would best test the relationship between $F_{net}$ and $a$?

A cart's mass stays constant. A student finds that a net force of 6 N produces an acceleration of 3 m/s$^2$. If the student increases the net force to 18 N, what acceleration should the student predict based on the pattern $F_{net} \propto a$?

A student applies different net forces to the same cart (mass stays constant) and records acceleration. Based on the data, what happens to the acceleration when the net force increases from 4 N to 12 N?

In a tug-of-war, the net force on the rope is the difference between the teams' pulls. A teacher measures the rope's acceleration for different net forces.

Data:

• $F_{\text{net}}=2\,\text{N}$ → $a=0.4\,\text{m/s}^2$
• $F_{\text{net}}=4\,\text{N}$ → $a=0.8\,\text{m/s}^2$
• $F_{\text{net}}=6\,\text{N}$ → $a=1.2\,\text{m/s}^2$

What does the data show happens to acceleration when the net force doubles from 2 N to 4 N?