C1.1 Analyse and improve a technology using Newton’s laws

Ontario Grade 11 Physics

Forces

SPH3U C1.1: Analyse a design, explain its motion, and propose an improvement

Technology is designed to help people do tasks, move objects, or stay safe. Newton’s laws help explain how a technology behaves and how its design might be improved. For example, a delivery cart needs enough forward force to accelerate its load. A bicycle helmet must help protect a rider during a collision. In both cases, analysis starts by choosing a system and identifying the forces on it. A force is a push or pull. Force, velocity, and acceleration are vectors: each has a magnitude and a direction. Mass, time, and speed are scalars: they have magnitude but no direction. This lesson uses proposed design scenarios, not claimed experimental results. Any numbers in the examples are stated design values, not measurements from a completed test.

What you will learn

Identify the object or group of objects being analysed as the system.
Use Newton’s laws to explain how forces affect the motion of a technology.
Use force diagrams and calculations to identify a design limitation.
Propose an improvement and explain how it changes the forces or motion.

1. Start with the system and the motion

A system is the object, or group of objects, being studied. State it before applying a law. If you study a loaded cart, the system might be the cart and its load together. Forces from outside that system, such as a person pushing it or the floor supporting it, can change its motion.

A reference frame is the viewpoint used to describe position and motion. For ordinary technology examples, use the ground as the reference frame unless the situation says otherwise. Choose a positive direction, such as forward or upward. A force or acceleration in that direction is positive; one in the opposite direction is negative.

Before this lesson, you may have used the idea that a change in motion means an object is accelerating. Acceleration describes how velocity changes over time. In this lesson, use the course-level relationship between net force, mass, and acceleration. Net force means the vector sum of all external forces on a system.

\vec{F}_{\text{net}}=\sum \vec{F}

Name the system and reference frame before analysing motion.
State which direction is positive.
Do not confuse a force’s magnitude with its direction.

2. Apply Newton’s laws to a design

Newton’s first law describes balanced forces. If the net force on an object is zero, it remains at rest or continues moving at constant velocity. Constant velocity means the same speed in the same direction. A technology does not need a net forward force just to keep moving at constant velocity; it needs a forward force if it must overcome backward forces or accelerate.

Newton’s second law connects net force to acceleration. For a fixed mass, a larger net force gives a larger acceleration. For a fixed net force, a larger mass gives a smaller acceleration. In SI units, force is measured in newtons (

\mathrm{N}

), mass in kilograms (

\mathrm{kg}

), and acceleration in metres per second squared (

\mathrm{m/s^2}

). One newton is equivalent to one kilogram metre per second squared.

Newton’s third law says that when one object exerts a force on a second object, the second exerts an equal-sized force in the opposite direction on the first. The two forces act on different objects. They do not cancel each other on a single-object force diagram.

A free-body diagram shows the forces acting on one chosen system. Draw each force as an arrow from the system. Label its direction and, when known, its magnitude. For a cart on a level floor, the floor’s upward support force and Earth’s downward gravitational force may balance vertically. A push forward and friction backward affect the horizontal net force. A diagram helps reveal which force a design needs to increase or reduce.

\vec{F}_{\text{net}}=m\vec{a}

Use the net force, not one force by itself, in Newton’s second law.
Forces that balance have a zero net force in that direction.
Third-law force pairs act on different objects.

3. Analyse a technology and improve it

To analyse a technology, first describe what it is intended to do. Then identify the system, its motion, and the important forces. Ask whether the forces are balanced. If they are not, determine the direction of the net force and acceleration. Compare the result with the design goal, such as accelerating a load or reducing unwanted motion.

An improvement should connect a design change to a force or motion change. For example, a cart designed to accelerate more quickly could use a stronger push or carry less mass, if those changes are practical. A cart that slides too easily on a slope might need a surface or braking feature that increases the opposing force. The proposal should also consider the design goal: increasing friction can help with grip but can make a cart harder to push.

A calculation can show whether a proposed change is likely to help under stated conditions. It cannot, by itself, prove that a real product performs as predicted. A proposed test could compare the same cart and load before and after a design change, using the same starting conditions and a stated measurement plan. Results would be measured evidence only after the test is actually carried out. A simulation can help explore a model, but its output is simulated evidence, not a physical measurement.

a=\frac{F_{\text{net}}}{m}

Explain the link between a design change and the resulting force or motion.
State assumptions and distinguish a prediction from measured evidence.
Consider whether an improvement creates a trade-off.

Worked example

Improve a powered delivery cart

A cart and its load have a combined mass of

40.0\ \mathrm{kg}

. A proposed motor exerts a forward force of

120\ \mathrm{N}

. Resistive forces total

40.0\ \mathrm{N}

backward. Find the cart’s acceleration and suggest a design improvement if the goal is an acceleration of at least

2.5\ \mathrm{m/s^2}

.

Set the system and direction
Treat the cart and load together as the system, viewed from the ground. Choose forward as positive. The unknown is the cart’s acceleration.
Find the net force
The forward motor force is positive and the backward resistance is negative. Subtracting gives the net force in the chosen direction.
$F_{\text{net}}=(120\ \mathrm{N})-(40.0\ \mathrm{N})=80.0\ \mathrm{N}$
Calculate acceleration
Apply Newton’s second law using the total system mass. Keep the units in the substitution.
$a=\frac{80.0\ \mathrm{N}}{40.0\ \mathrm{kg}}=2.00\ \mathrm{m/s^2}$
Compare with the goal
The predicted acceleration is below the target. One possible improvement is a motor that provides more forward force, provided the other conditions remain the same.

Answer: The predicted acceleration is

2.00\ \mathrm{m/s^2}

forward. It does not meet the

2.5\ \mathrm{m/s^2}

goal.

Check: The units reduce to

\mathrm{N/kg}=\mathrm{m/s^2}

. The positive sign means forward acceleration. A net forward force should produce forward acceleration, so the direction is reasonable. The calculation is a prediction based on the stated forces, not a measured cart result.

Worked example

Choose a force for a lifting platform

A platform and its load form a

250\ \mathrm{kg}

system. It must accelerate upward at

0.80\ \mathrm{m/s^2}

. Use

9.8\ \mathrm{m/s^2}

for the magnitude of gravitational acceleration. Find the required upward cable force.

Set the system and direction
The system is the platform and its load. Use the ground as the reference frame and choose upward as positive. The unknown is the cable force.
Identify the forces
The cable pulls upward, while gravity pulls downward. With upward positive, the net force equals the cable force minus the weight. The weight has magnitude mass multiplied by gravitational acceleration.
$F_{\text{net}}=F_{\text{cable}}-mg$
Rearrange and substitute
Newton’s second law gives the required net force for the stated upward acceleration. Add the weight to that net force to find the cable force.
$F_{\text{cable}}=m(a+g)=(250\ \mathrm{kg})(0.80+9.8)\ \mathrm{m/s^2}=2.7\times10^3\ \mathrm{N}$

Answer: The cable must exert approximately

2.7\times10^3\ \mathrm{N}

upward for the stated acceleration.

Check: The units are kilograms times metres per second squared, which equals newtons. The cable force is greater than the platform’s weight because the platform accelerates upward. The result is rounded to two significant figures, matching the least precise given value.

Worked example

Assess a braking improvement

A test design is predicted to have a total backward braking force of

360\ \mathrm{N}

on a

90.0\ \mathrm{kg}

cart and rider moving forward. Find the acceleration while braking. Then compare it with a proposed design that raises the backward force to

450\ \mathrm{N}

without changing the mass.

Set the system and direction
Treat the cart and rider as one system. Use the ground as the reference frame and choose forward as positive. The braking forces point backward, so they are negative.
Calculate the original acceleration
The net force is backward. Divide it by the system mass to find the acceleration, including its direction through the negative sign.
$a=\frac{-360\ \mathrm{N}}{90.0\ \mathrm{kg}}=-4.00\ \mathrm{m/s^2}$
Calculate the proposed design
Use the same system mass and sign convention. The proposed larger backward force produces a larger-magnitude backward acceleration.
$a=\frac{-450\ \mathrm{N}}{90.0\ \mathrm{kg}}=-5.00\ \mathrm{m/s^2}$

Answer: The original predicted acceleration is

4.00\ \mathrm{m/s^2}

backward. The proposed design predicts

5.00\ \mathrm{m/s^2}

backward.

Check: Both answers have units of

\mathrm{m/s^2}

and are negative because the acceleration is opposite the chosen forward direction. The larger braking force gives a larger-magnitude acceleration for the same mass. This comparison alone does not establish which design is safer; it only describes the predicted motion under the stated model.

Common mistakes and how to avoid them

Using the motor force alone in Newton’s second law.

Correction: Add all external forces as vectors first. Use the resulting net force in the relationship between force, mass, and acceleration.

Thinking a moving object must have a net force in its direction of motion.

Correction: An object can move at constant velocity when the net force is zero. A net force is needed to change its velocity.

Drawing a third-law pair as two forces that cancel on one system.

Correction: The paired forces act on different objects. Draw a free-body diagram for one system at a time.

Calling a predicted or simulated result an experimental measurement.

Correction: Label calculations as predictions and simulation outputs as simulated results. Claim measured evidence only when a physical test has been performed and measurements collected.

Lesson summary

Choose a system, reference frame, and positive direction before analysing forces.
Newton’s first law describes motion when net force is zero; Newton’s second law connects net force, mass, and acceleration; Newton’s third law describes paired forces on different objects.
Use a force diagram and the net force to explain how a technology behaves.
A useful improvement changes a relevant force or mass and supports the design goal. State assumptions and check units, direction, significant figures, and reasonableness.

Check your understanding

Question 1

A device has a net force of

18\ \mathrm{N}

forward and a mass of

6.0\ \mathrm{kg}

. What is its acceleration?

$3.0\ \mathrm{m/s^2}$ forward
$3.0\ \mathrm{m/s^2}$ backward
$108\ \mathrm{m/s^2}$ forward
$0\ \mathrm{m/s^2}$

Show answer and explanation

3.0\ \mathrm{m/s^2}

forward

Newton’s second law gives

a=F_{\text{net}}/m=(18\ \mathrm{N})/(6.0\ \mathrm{kg})=3.0\ \mathrm{m/s^2}

. The net force is forward, so the acceleration is forward.

Question 2

A cart moves forward at constant velocity. What can be concluded about its net force?

It is zero.
It must point forward.
It must point backward.
It must equal the cart’s mass.

Show answer and explanation

It is zero.

Constant velocity means there is no change in velocity, so acceleration is zero. Newton’s second law then gives a zero net force.

Question 3

A designer increases the braking force on a cart but keeps its mass the same. What does Newton’s second law predict?

A larger-magnitude acceleration opposite the cart’s forward motion.
A smaller-magnitude acceleration in the forward direction.
No change in acceleration.
The cart’s mass becomes larger.

Show answer and explanation

A larger-magnitude acceleration opposite the cart’s forward motion.

With the same mass, a larger net force magnitude gives a larger acceleration magnitude. A backward braking force causes acceleration opposite the forward direction.

Key terms

System: The object or group of objects chosen for analysis.
Reference frame: The viewpoint used to describe an object’s position and motion.
Net force: The vector sum of all external forces acting on a system.
Acceleration: The rate at which velocity changes, including a change in speed, direction, or both.
Free-body diagram: A diagram showing the external forces acting on one chosen system.

Continue through SPH3U

View the complete SPH3U Ontario Grade 11 Physics curriculum and lessons

About this lesson and its review

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation C1.1. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

Official curriculum reference

Report a correction or ask a question

C1.1 · Analyse and improve a technology using Newton’s laws

Ontario Grade 11 Physics

SPH3U C1.1: Analyse a design, explain its motion, and propose an improvement

What you will learn

1. Start with the system and the motion

2. Apply Newton’s laws to a design

3. Analyse a technology and improve it

Improve a powered delivery cart

Choose a force for a lifting platform

Assess a braking improvement

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SPH3U

About this lesson and its review