Linear Forces Speed Review

Concept overview

1. Newton’s force laws
2. Drawing FBDs properly
3. Resolving vectors
4. Finding the net force
5. Solving problems

Newton’s Laws

We can use Newton’s three laws to help explain everyday phenomena, such as:

• What force, if any, is needed to make a tennis ball bounce off the sidewalk?
• If you walk along a log floating on a lake, why does the log move in the opposite direction
• Why do you seem to be thrown forward in a car that rapidly decelerates?

Law 1: Inertia

An object in motion will stay in motion. An object at rest will stay at rest.

Alternate explanation: all objects want to resist changes in their motion. The more inertia (mass) an object has, the more it can resist change. Think of how hard it is to bring a plane to a complete stop.

Law 2: [katex] F_{net} = ma [/katex]

Any horizontal or vertical NET force acting on a mass will cause an acceleration.

Vertical net force is the sum of ALL forces vertically. The horizontal net force is the sum of ALL forces horizontally.

Law 3: Equal and Opposite Forces

Push down on your desk. Does it move? It doesn’t, because it’s pushing back up at you with the same force. When two objects interact with each other, they both apply the same force to each other.

For every action, there is an equal and opposite reaction.

Alternate explanation: think of a truck hitting a motorcycle. They will experience the same force, but since the motorcycle has less mass it will experience greater acceleration.

FBD

If you want to solve questions correctly, your best bet is to start by drawing an FBD (force body diagrams). Here are the rules for drawing common forces.

1. Weight ALWAYS points straight down. Draw the vector from the center of the object.
2. The normal force is ALWAYS 90° to the surface. Draw the vector from the bottom of the object.
3. Friction always points opposite to the direction of motion (except in circular motion, in which it points inwards)
4. Vectors can be at angles, but don’t draw the vector components unless asked to.
5. Vectors of equal magnitude should be of equal length.

Common FBDs

Know how to draw the following FBDs:

• Mass in free fall, neglecting air resistance
• Mass falling at terminal velocity
• Box sliding horizontally with friction
• Box sliding down a ramp with friction
• Elevator going up and slowing down
• Two different masses on opposite sides of a pulley

Mass vs. Weight

Mass is a scalar quantity (measured in kg). It remains constant everywhere in the universe.

Weight is a vector quantity (measured in Newtons). It is the force on a mass due to gravity. Weight changes with gravity.

[katex] \text{Weight} = F_{\text{net}} = mg [/katex]

Setting Directions

If you’ve finished Unit 1 Kinematics, you’ll be familiar with setting direction.

Gravity can be positive or negative. The direction of positive and negative motion is arbitrarily chosen. That means you can choose if up means +/- or if left means +/-.

But you need to be consistent. Indicate the directions on your FBD. If you set down to be positive, then gravity will be positive since it points down.

Resolving Vectors

We only use horizontal and vertical forces when solving force problems. Therefore, if you are using a vector that is at an angle, you need to break (resolve) it into x and y components.

Use this trig shortcut: Given the vector [katex] \vec{A} [/katex], look at the component of the triangle you are trying to find.

• If that component is opposite to the angle → use [katex] \vec{A} \sin \theta [/katex]
• If that component is adjacent to the angle → use [katex] \vec{A} \cos \theta [/katex]

If you’re still confused on vector components, read this short guide.

You can also watch the video below.

Net Forces vs. Equilibrium

The net force is the SUM of ALL forces in either the X or Y direction.

An object in equilibrium experiences zero net force in all directions. In other words, any force acting in a particular direction is canceled out with an equal but opposite force along the same axis.

Since [katex] F_{net} = 0 = ma [/katex] → this implies the net acceleration of the object is 0.

This either means the object is not moving OR moving at constant velocity. For example, a book laying on the table has 0 net force, because the weight vector and normal vector cancel out.

→ 0 Net Force = 0 acceleration = constant velocity

Common Equations

Kinetic Friction Force: [katex] f_k = \mu_kN [/katex]

Static Friction Force: [katex] f_s = \mu_sN [/katex]

• [katex]N[/katex] = normal force
• [katex]\mu_k[/katex] = coefficient of kinetic friction (for when the object is moving)
• [katex]\mu_s [/katex]= coefficient of static friction (for when the object is not moving
• [katex]\mu_s > \mu_k [/katex]
• PRO TIP: on a ramp –> [katex] \mu_s = \tan\theta [/katex]

Hooke’s Law (Spring Force): [katex] F_s = kx [/katex]

• [katex]k[/katex] = spring constant
• [katex]x[/katex] = compression or stretch of the spring

Centripetal force: [katex] F_c = ma_c = \frac{mv^2}{r} [/katex]

• [katex]v[/katex] = tangential velocity
• [katex]r[/katex] = radius of the circle

Gravitational Force between two masses: [katex] F_g = \frac{Gm_1m_2}{r^2} [/katex]

• [katex]G[/katex] = gravitational constant ≈ 6.67 × 10^-11
• [katex]m_1[/katex] = mass of object 1
• [katex]m_2[/katex] = mass of object 2
• [katex]r[/katex] = distance between [katex]m_1[/katex] and [katex]m_2[/katex]

Solving Problems Quickly

Students struggle the most on this. Using the steps (framework) below you can solve ALL force problems, it just comes down to practice. This framework was covered in depth in the Unit 2.4 course article.

1. Turn the word problem into a FBD.
2. Use the FBD to find either the horizontal or vertical net force.
3. Lastly set the net force equal to ma, to solve for the unknown variable.

There are many of types of problems involving forces. But I’ve simplified it to this list of 60 linear force questions [available for course members], based on the actual AP Physics 1 exam. These will likely show up on your test.

Common Types of Linear Force Questions

Listed below is a list of common linear force problems (in the next article we’ll add circular force problems). You should know how to solve all of these, using the 3 step method above.

As a bonus, I’ve linked short guides on how to specifically tackle each type of problem.

• Box being pushed across a floor (with friction)
• Box being pull by cord at an angle above the horizontal
• Box sliding down at incline (with friction)
• Simple Pulley systems (Atwood’s machine)
• Pulley system on table or inclines with one mass hanging off
• Systems with multiple masses, like two blocks being pushed together
• Elevators accelerating up/down
• Apparent weight in elevators, roller coasters, etc
• Gravitational force problems (force between two planets)

Extra Help

If any of this sounds confusing, you’re not alone! I’ve helped 100s of Physics students to achieve a 5 and boost class grades. You’ll start seeing results in just 3 lessons or less, guaranteed.

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10 Practice Questions for Mastery

Quick Answers

1. 2 m/s²
2. 1650 N
3. 3 kg
4. tan(10) or .176
5. C.
6. 2.1 m/s² and 6.25 N
7. E.
8. a = (Fcosθ – ƒ)/m
9. E.
10. 167 N

Practice Exam

If you’re feeling confident try completing this practice exam. Make sure to time yourself and check your answers in the end.

Here’s another Multiple Choice Test, that has questions similar to the AP Exam.

Next Speed Review

In the next speed review we’ll cover forces that cause a circular motion. We often call this centripetal forces.