Force, Work, and Energy for the MCAT: Everything You Need to Know

Learn essential MCAT topics covering work, energy, and force, complete targeted practice problems, and review answers to strengthen your exam performance.

Master the physics fundamentals behind force, work, and energy, including practice problems modeled after real MCAT questions.

Table of Contents

Part 1: Introduction to Forces, Energy, and Work

Part 2: Forces

a) Types of forces

b) Newton's three laws

c) Conservative versus nonconservative forces

Part 3: Energy

a) Types of energy

b) Conservation of energy

Part 4: Work

a) Work done by constant force

b) Work-kinetic energy theorem

c) Power

d) Mechanical advantage

e) Torque

Part 5: High-Yield Terms and Equations

Part 6: Passage-Based Questions and Answers

Part 7: Standalone Questions and Answers

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Part 1: Introduction to forces, energy, and work

Forces, energy, and work are some of the first subjects taught in most introductory physics classes. While these are only medium-yield MCAT subjects, understanding them can help with much more than force and energy-specific questions. They're super important for most other physics topics, and they might even help you develop an intuition for some concepts in biology or chemistry.

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Part 2: Forces

"Force" is a word you've probably heard before in a number of ways, but its definition in physics is more precise: A force is a push or pull that makes something accelerate if it is unopposed.

That's it! Later we'll talk about different reasons why something might be pushed or pulled, but at the end of the day, this definition will stay the same. Simply imagining forces as pushes and pulls will get you a long way.

Forces are also vectors, which mean that they have both magnitude and direction. Every force must have both. To think about vectors, imagine an arrow similar to the ones shown below.

Figure 1    Forces are vectors

An arrow has to have some length, and it has to point in some direction; otherwise, it's not an arrow. Like all vectors, forces can also be combined. Forces in the same direction will make a bigger force, and forces in opposite directions will cancel out.

The last thing you should know about forces is also important: the unit of measurement for forces is Newtons.

Now that we've gone over the basics, let's look at some different types of forces.

a) Types of forces

Imagine you throw a football and kick a soccer ball shortly afterwards. The magnitude of each force will depend on different properties, specifically the strength of your arm muscles versus your leg muscles. In the same way, the universe has different kinds of "muscles" that come up a lot in physics problems. Let's talk about two of the most common ones.

Gravitational Force: This is the force that pulls masses toward each other. You remember it from all those times you jumped in the air and didn't fly off into space! There is a general equation for the gravitational force between any two objects in the universe, but when you're on earth, the equation simplifies to the following:

F_g = m × g
where F_g = the force on the object due to gravity,  m = the mass of the object,  and g = 9.8$\frac{\mathrm{m}}{\mathrm{s²}}9.8\; m/s$, the acceleration due to gravity.

The force of gravity on an object is also called that object's weight. People often think weight and mass are the same, but they actually aren't. Here's a definition for each:

• Mass: the amount of matter in something, measured in kilograms.

• Weight: the strength of the gravitational force on something, measured in Newtons.

To get from mass to weight for an object on earth, multiply by 9.8. So, if a backpack has a mass of 10 kg, it weighs 98 N.

Friction: This is the force that tries to slow down an object sliding across a surface. To find the magnitude of friction, you use the following equation:

f = F_N × μ
where f = the force of friction, F_N = the normal force, and μ = the coefficient of friction.

(A normal force is the force that a surface pushes on the object with. It is called "normal" because in physics "normal" is a synonym for "perpendicular," and surfaces always push objects in a perpendicular direction. On a horizontal surface, the normal force is equal to the object's weight.)

There are two more important things to remember about friction:

• Friction is a non-conservative force. We'll talk about this more later, but it essentially means that friction sucks energy out of the system.

• The coefficient of friction depends on the materials involved and whether or not the object is moving. The coefficient of static friction is used when the object is at rest. It gives the maximum force that friction can resist with before the object begins to move. Once the object is moving, the coefficient of kinetic friction takes over. It gives a weaker constant force that resists movement.

Figure 2     The coefficient of static friction is bigger than the coefficient of kinetic friction.

Instead of calculating forces working on every single particle within an object, it is sufficient to consider the force as acting on a single point. To simplify calculations, a force is considered to work on the center of mass of an object. The center of mass is a single point inside an object that represents the weighted average location of the mass distribution.

Every type of force has its own rules, but this means you'll often be given these equations if you need them in a problem. The following rules are true for all forces, and it's more likely that you'll have to remember them on your own.

b) Newton's three laws

These three laws are true for all forces; Newton's laws tell you what the forces we talked about earlier do. Here's what each says:

Newton's First Law: An object at rest will stay at rest unless a force acts on it, and an object in motion will stay in motion unless a force acts on it.

The first law is the reason you'd fly off a bike if you ride into a curb: you're moving, and the curb only applies a force to the bike, so you keep on moving, right onto the (hopefully) grass.

Newton's Second Law: The summation of forces on an object is equal to the mass of the object times its acceleration. This is often depicted as:

ΣF = m × a
where ΣF = the net force, m = the mass of the object, and a = the acceleration of the object.

The second law is very important, so let's go through each term in that equation.

ΣF: the net force, or the one leftover after you combine all the initial forces. This reminds us that we have to consider every force acting on an object before we can say for sure whether it’s accelerating. It opens the door for combining forces or for forces to cancel out. To help sort through all the different forces, we often draw free-body diagrams, which are shown below. 

Figure 3    Net force free body diagram. Since forces are vectors, forces in the same plane (the x-axis or the y-axis) should be added together. By convention, to the right and up are considered positive.

m: the mass. Mass is inversely proportional to acceleration. Under the same force, a more massive object will accelerate less. For example, if you push an elephant and a puppy with the same force, which one will accelerate slower? Probably the elephant!

a: the acceleration. Acceleration is a change in velocity over a change in time. It is directly proportional to force. For the same mass, a bigger force means a bigger acceleration. When force is constant, so is acceleration, which lets you use all the constant acceleration equations (they're on a list at the end of this guide). Acceleration is also a vector. Since mass has no direction of its own to worry about, acceleration will always point in the same direction as the net force.

Newton's Third Law: For every action, there is an equal and opposite action. Think about every force having a giver and a receiver, let's say a hand and a punching bag. This law says that for everything your hand does to the punching bag, the punching bag does back to your hand. So, if you punch the bag really hard, your hand is going to hurt because the bag hit your hand just as hard.

c) Conservative versus non-conservative forces

Conservative forces store energy in a way that does not affect the total energy of the system. They always have an associated potential energy (we'll talk about this soon!). Non-conservative forces dissipate energy or take energy out of the system. Another way to think about this is that the work (coming up soon, too!) done by a conservative force is the same no matter what path the object takes, while the work done by a non-conservative force does depend on the path taken. An example of a conservative force is gravity, and an example of a non-conservative force is friction.

Figure 4    For the conservative force F, each travelling each path will result in the same amount of work.

To continue, we need to talk about energy.

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Part 3: Energy

"Energy" is another word you've probably heard in a non-scientific context. For now, we can say that:

Energy is the quantity that describes how much activity is going on in an object, or how much activity an object might have in the future. The units for energy are Joules.

a) Types of energy

Kinetic energy is the energy contained by moving objects.

Most often we consider translational kinetic energy, which describes the energy when objects have a velocity. The equation is:

E_k = $\frac{1}{2}$mv²
where E_k = kinetic energy,  m = mass,  and v = velocity.

You might also come across rotational kinetic energy, which has a similar equation and describes objects that are spinning.

Potential energy is the energy of an object that has the potential to be in motion.

Potential energies are related to conservative forces, so there are a few different types. The first is gravitational potential energy. The equation is:

U_g = m × g × h
where U_g = potential energy due to gravity,  m = mass,  g = 9.8$\frac{\mathrm{m}}{\mathrm{s²}}$ as acceleration due to gravity,  and h = height.

Figure 5    The total energy is the sum of an object's kinetic and potential energies.

Other common potential energies include elastic potential energy, which describes a compressed or stretched spring, and electric potential energy, which describes a charged object that is inside an electric field. Equations for both of these are included at the end of this guide.

Thermal energy is the energy that describes the movement of microscopic particles in an object.

Thermal energy increases with an object's temperature. A question relating specifically to thermal energy falls under thermodynamic principles, but in this context, it's enough to know that thermal energy and heat might be a place some ways energy escapes our system.

For more information about thermodynamic principles, be sure to refer to our guide on thermodynamics.

b) Conservation of energy

Another incredibly important concept in physics is the conservation of energy, which states that energy cannot be created nor destroyed. In other words,

E₁ = E₂
where E₁ = the initial energy  and E₂ = the final energy, assuming that no work is done to a system.

Instead, energy is just transferred. For example, a ball at the top of the hill loses its potential energy, but that energy is transformed into kinetic energy. So, when the ball is at the bottom, it is moving faster than it was at the top.

Figure 6    The forms of energy change, but the total energy is conserved.

This is true for the universe as a whole, but when we look at a smaller system, we have to account for the energy that leaves the system we're paying attention to. So, the more applicable equation is:

E₂ = E₁ - W_NC
where W_NC = work performed by non-conservative forces.

We'll talk more about work in the next section, but you might see from that equation that it is some sort of transfer of energy, and when it is done by a non-conservative force like friction, the energy is transferred out of the system entirely. For example, work done by non-conservative energy is the reason a skateboarder can't ride a halfpipe forever. Eventually, the friction in their wheels takes all of their energy away.

Hint: Problems may tell you to "ignore friction" or that "air resistance is negligible." You can take these as hints that W_NC = 0 and that energy is conserved.

To understand this a little better, we can finally discuss the concept of work.

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Part 4: Work

Work is a transfer of energy via a force. Just like energy, it's measured in Joules.

a) Work done by constant force

When work is done by a constant force, it is defined by the following equation:

W = F × d × cos(θ)
where W = work performed by a force,  F = the constant force applied,  d = the distance the force is applied across,  and θ = the angle between the directions of the force and the distance.

There are a few things to note about this equation.

First, if the distance is zero, the work is zero. The force has to successfully move the object to do work. If you push a boulder but it doesn't move, you're not transferring any energy into it.

Second, to do work, the force has to be pointing at least partially in the same direction as the distance. If distance and force are parallel, theta is 0 degrees, the cosine of theta is 1, and work is done. If they are perpendicular, theta is 90 degrees, the cosine of theta is 0, and no work is done. This is why it takes a lot more energy to push a sled up a hill than along its base. Similarly, distance and force are pointing in opposite directions, the work will be negative and will transfer energy out of the system. This is why friction dissipates energy!

Figure 7    Work at different values of theta

b) Work-kinetic energy theorem

The work on a particular object is equal to the change in that object's kinetic energy. This is called the work-kinetic energy theorem, which is an equation you already saw above.

E₂ = E₁ - W_NC

c) Power

Power is the amount of energy transferred per unit time, and the units for power are Watts. This means that power is the amount of work divided by a change in time:

P = $\frac{\mathrm{\Delta W}}{\mathrm{t}}$
where P = power, ΔW = the change in work,  and t = time.

d) Mechanical advantage

Mechanical advantage tells you how beneficial it is to use a certain machine. Each simple machine has its own way of calculating mechanical advantage, but we'll focus on the lever.

For a lever, the mechanical advantage is the ratio of the force you put into the machine to the force it gives you back.

e) Torque

In this guide, we've primarily focused on translational motion. Translational motion occurs as an object moves uniformly in one direction. For instance, a force applied to a box on a ramp results in the work and translational motion of the box.

However, applied forces can also result in rotational motion. Rotational motion occurs when a force is applied to an object that is fixed to a pivot point. For instance, a force applied to a wrench results in the turning of a bolt. This turning is rotational motion.

Figure 8    Translational motion results from work, while rotational motion results from a torque.

A torque, also known as a moment, results from the application of force at a distance from a fixed pivot point. Torque can be calculated using the following equation:

τ = rFsin(θ)
where τ = resulting torque, r = distance from the applied force to the pivot point (also known as a lever or moment arm),  F = magnitude of the applied force,  and θ = angle at which the force vector is applied to the perpendicular lever arm.

Note that when a force is applied straight-on, torque is equal to rFsin(θ) = rFsin(90°) = r × F

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Part 5: High-yield terms and equations

Force: a push or pull that makes something accelerate if unopposed and is measured in Newtons

Vector: a quantity that has both magnitude and direction

Gravitational force: the force between any two masses

Weight: a word that describes how hard gravity pulls down on something and equals the gravitational force on the object

Mass: the amount of matter in something and is measured in kilograms.

Friction: the force that opposes sliding motion

Normal force: the force that a surface applies to an object on top of it and is always perpendicular to the surface

Coefficient of static friction: when multiplied by the normal force, gives the maximum resistance friction will give before an object begins to move

Coefficient of kinetic friction: when multiplied by the normal force, gives the constant friction force that opposes the movement

Newton's first law: objects in motion will stay in motion, and objects at rest will stay at rest, unless forces act on them

Newton's second law: acceleration of an object is proportional to the net force on it and inversely proportional to its mass

Newton's third law: for every action, there is an equal and opposite reaction

Net force: the final sum of all the initial forces

Displacement: the change in an object's position

Velocity: the change in an object's position over a change in time

Acceleration: the change in an object's velocity over a change in time

Conservative force: a force that doesn't dissipate energy, and work done by it is path-independent

Non-conservative force: a force that does dissipate energy, and work done by it is path-dependent

Energy: the amount of activity in something now or is predisposed to have in the future

Translational kinetic energy: the energy in an object that is moving, or has a velocity

Rotational kinetic energy: the energy in an object that is rotating

Potential energy: the energy of an object that has the potential to be in motion.

Gravitational potential energy: the potential energy of an object due to gravity

Elastic potential energy: the potential energy of a stretched or compressed spring

Electric potential energy: the potential energy of a charge in an electric field

Thermal energy: the energy from an object's temperature, such as microscopic kinetic energy

Conservation of energy: energy isn't created or destroyed, and in a closed system, you only gain or lose energy from the work put into the system

Work: a transfer of energy caused by a force

Work-kinetic energy theorem: the work put into an object equals its change in kinetic energy

Power: the amount of energy transferred per unit time, or work divided by time

Mechanical advantage: how beneficial it is to use a certain simple machine

Equations

Newtons's second law: ΣF = m × a

Gravitational force on earth: F_g = m × g, where g represents 9.8$\frac{\mathrm{m}}{\mathrm{s²}}$ (this value is specific to earth)

Force of friction: F = F_N × μ

Translational kinetic energy: E_k = $\frac{1}{2}$mv²

Gravitational potential energy: U_g = m × g × h

Conservation of energy: E₂ = E₁ - W_NC

Work done by constant force: W = F × d × cos(θ)

Work-kinetic energy theorem: E₂ = E₁ - W_NC

Power: P = $\frac{\mathrm{\Delta W}}{\mathrm{t}}$

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Part 6: Passage-based questions and answers

Researchers determine that the variability in responses to a novel protein therapy can be attributed to a random process in which a protein is chemically conjugated to organelles. In a study, researchers want to gain insight into the dynamics of protein binding to each of these organelles. In order to do this, the researchers set up three cellular systems with the following properties: an organelle, which is fixed in place, is bound to a protein, which is otherwise free to move around a cell. The researchers have discovered that the bonds between the protein and organelle can be reasonably approximated by a spring, which resembles the following equations:

F_s = -k × x

U_s = $\frac{1}{2}$ × k × x²

F_s is the force of the spring, U_s is the potential energy stored in the spring, k is the spring constant, which is different for each bond, and x is the distance the spring is stretched.

If the protein was not bound to the organelle, it would begin a random walk, which resembles the process of diffusion in the cell. In their system, the researchers observe that the cytoplasm exerts a net force on the protein that pulls it directly away from the organelle in the opposite direction of the bond created between the protein and organelle. By observing the random walks of similar proteins in the cell, the researchers are able to deduce that the diffusive force is equal to 0.01 Newtons. Interested in properties related to the strength of each bond, they are also able to measure the displacement of each protein from the would-be equilibrium position of the spring if the diffusive force were not present. Their results are in the table below.

System	Protein Displacement
A	0.01 × 10-6m
B	0.02 × 10-6m
C	0.005 × 10-6m

Note: The information in this passage was created for the sole purpose of presenting an MCAT-style passage and should not be construed to be factually true.

Question 1: Which fundamental law of physics helps determine the final displacement of the protein under the influence of the force of the bond and the diffusive force?

A) Conservation of energy

B) Newton's second law

C) Newton's first law

D) Principle of mechanical advantage

Question 2: In which system is the bond the strongest?

A) System A

B) System B

C) System C

D) They're all the same

Question 3: What is the value of the spring constant in System A?

A) 0.5 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$

B) 1.0 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$

C) 1.5 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$

D) 2.0 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$

Question 4: How much energy is stored in the bond in system A?

A) 5 × 10^-11J

B) 5 × 10¹¹J

C) 1 × 10^-11J

D) 1 × 10¹¹J

Question 5: If the diffusive force is turned off, and the proteins spring back towards their organelles, which law of physics can be used to determine the velocity of the protein moving towards the organelle?

A) Conservation of energy

B) Principle of mechanical advantage

C) Power

D) Conservation of matter

Answer key for practice passage

1. Answer choice B is correct. The final position of the protein will be at the location where the two forces cancel out, and the net force is zero; this is Newton's second law (choice B is correct.) The conservation of energy does not help here because we don't know anything about the potential energy caused by diffusion (choice A is incorrect.) Newton's first law states that an object in motion tends to stay in motion unless acted upon by an external force, but it does not provide an equation by which we can obtain an answer (choice C is incorrect). Mechanical advantage is a measure of how helpful simple machines are, which is not relevant to this question (choice D is incorrect.)

2. Answer choice C is correct. The strongest bond will have the highest value of k in the formula F_s = -k × x. To find k, you divide the diffusive force given by the passage by the displacement of the protein. Each system has a different displacement according to Table 1, so the systems do not have the same k (choice D is incorrect). Since System C had the smallest displacement, dividing F_s by x will give the biggest number, so System C had the strongest bond (choice C is correct; choices A and B are incorrect).

3. Answer choice B is correct. To find the value of the spring constant, k, you have to divide the given force by the measured displacement: k = $\frac{F_{\mathrm{s}}}{\mathrm{x}}$. The given force is 0.01 N, and the displacement measured for System A is 0.01 × 10^-6m. Dividing will give you 1.0 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$ (choice B is correct). 0.5 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$ is the value of k for System B (choice A is incorrect), and 2.0 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$ is the value of k for System C (choice D is incorrect).

4. Answer choice A is correct. The equation for potential energy stored in a spring is U_s = $\frac{1}{2}$ × k × x². We found the value of k, 1.0 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$, in question number 3. We plug in this value, and the measured displacement into the formula. So U = $\frac{1}{2}$ × (1.0 × 10⁶$\frac{\mathrm{N}}{\mathrm{m}}$) × (0.01 × 10^-6m) × (0.01 × 10^-6m) = 0.5 × 10⁶ × (0.0001 × 10^-12) = 0.000005 × 10^-11J (Choice A is correct).

5. Answer choice A is correct. At the moment the diffusive force is turned off, the spring is extended and loaded to move the protein back towards the organelle. However, at that exact moment, the protein has no kinetic energy and only potential energy. Over time, as the protein speeds up and the spring moves back towards its equilibrium position, the protein will gain kinetic energy and lose potential energy. The total energy levels will stay the same, however, due to the law of conservation of energy (choice A is correct; choices B, C, and D are incorrect).

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Part 7: Standalone questions and answers

Question 1: Ignoring air resistance, if a researcher dropped a 10kg ball and a 1 kg ball out of the same window, which would hit the ground first?

A) The 10kg ball would hit the ground first because it's heavier.

B) The 1 kg ball would hit the ground first because gravity can make it accelerate more.

C) Both would hit the ground at the same time because they have the same weight.

D) Both would hit the ground at the same time because they have the same acceleration due to gravity.

Question 2: What is the work done by gravity on an object with mass m that is originally at rest, then falls 10 meters?

A) −m × g

B) $\frac{1}{2}$m × 10²

C) 10mg

D) -10mg

Question 3: Ignoring friction, which of the following slopes will make an object sliding down it move with the fastest vertical speed at the bottom?

A) A very short and steep slope with height h.

B) A very long and subtle slope with height h.

C) A slope that starts steep but becomes less steep for a total height h.

D) They will all have the same speed at the bottom.

Question 4: Which of the following are the units of force?

A) Pascal

B) kg

C) $\frac{\mathrm{kg\; \times \; m}}{\mathrm{s}}$

D) $\frac{\mathrm{kg\; \times \; m}}{s^2}$

Question 5: Which of the following is the equation given by Newton's second law?

A) PE = mgh

B) F = ma

C) PV = nRT

D) V = IR

Answer key for standalone practice questions

1. Answer choice D is correct. The length of time each ball is in the air will be determined by its acceleration toward the ground. To find the accelerations, use Newton's second law. The net force in this case will be the force of gravity, which is F = m × g. Setting m * g equal to m × a, you'll see the masses cancel out, and you're left with a = g for both of the balls (choice D is correct). The 10kg ball is heavier, but it won't hit the ground first (choice A is incorrect). The 1kg ball will not hit the ground first either nor would it be accelerated more (choice B is incorrect). The balls do not have the same weight because they have different masses (choice C is incorrect.)

2. Answer choice C is correct. The work done on an object by a constant force is equal to the force times the distance traveled times the cosine of the angle between them. The force of gravity is F = m × g and the distance travelled is 10m, so we know the answer is either C or D (choices A and B are incorrect). We know that the force of gravity points down and the displacement is also down. Since force and displacement are parallel and in the same direction, θ = 0 and cos(0) = 1 (choice C is correct). The work is only negative if the force and displacement are pointing in opposite directions (choice D is incorrect).

3. Answer choice D is correct. To find the velocity at the bottom, we recall the Work-Kinetic Energy Theorem. We know that whichever slope allows the most positive work to be done by gravity will make the object go the fastest. However, we also know that gravity is a conservative force, so the path of the object does not matter. The only point we have to pay attention to is that at the end of each slope, the ball will have fallen a total distance h. So, each slope will give the same final speed (choice D is correct; choices A, B, and C are incorrect).

4. Answer choice D is correct. Force is given by the equation, F = mass × acceleration. The units of mass are kilograms (kg), and the units of acceleration are meters per second squared ($\frac{\mathrm{m}}{s^2}$). So, choice D is correct. Pascal's are the units for pressure (choice A is incorrect).

5. Answer choice B is correct. Newton's second law states that force is equal to mass multiplied by acceleration (choice B is correct). PE = mgh is the equation for gravitational potential energy (choice A is incorrect). PV = nRT is the ideal gas law (choice C is incorrect). V = IR is Ohm's law for circuits (choice D is incorrect).

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