The Physics of Human Strength

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Welcome to the Physics of Strength

What make a person strong? According to Frederick Hatfield, Ph.D. and former world record holder in the Squat, there are 38 factors affecting strength. I have put them here for you to read quickly, but the original article can be found on

1. Muscle Fiber Arrangement
2. Musculoskeletal Leverage
3. Tissue Leverage
4. Freedom of Movement Between Fibers
5. Tissue Viscoelasticity
6. Intramuscular/intracellular friction
7. Ratio of Fiber Types
8. Range of Motion
9. Freedom From Injury
10. Connective Tissue Structure
11. Stretch Reflex
12. The Feedback Loop
13. Endocrine System Functions (hormones)
14. Extent of hyperplasia (cell splitting) or fiber fusion
15. Extent of myofibrillarization
16. Motor Unit Recruitment
17. Energy transfer systems' efficiency
18. Extensiveness of capillarization
19. Mitochondrial growth and proliferation
20. Stroke volume of the left ventricle
21. Ejection fraction of the left ventricle
22. Pulmonary (ventilatory) capacity
23. Efficiency of gas exchange in the lungs
24. Heart rate
25. Max VO2 uptake
26. Freedom from disease
27. Arousal Level ("psych")
28. Ability to concentrate
29. Incentive
30. Social learning
31. Coordination
32. "Spiritual" factors
33. The "placebo" effect
34. Equipment
35. Environment
36. Effect of gravity
37. Opposing and assisting forces

This pretty much covers everything. As you can see, it takes a culmination of physical, natural, mental, spiritual, and psychological factors to be strong. It also takes time. The laws of physics play a huge role in what it means to be strong. On this site we will focus especially on the last two, the effect of gravity and forces. The physical concepts that will be used in this site include Newton's laws (of course), gravity, work, power, velocity and acceleration, static equilibrium, and conservation of mechanical energy. All concepts and useful equations will be explained as they are used.

What is the Squat?

The parallel squat (shown to the left) is the most important lift in all of sports and the most efficient exercise in building strength. It incorporates back and leg strength, stability, and coordination. Almost every athlete can benefit from doing squats.

How do you do Squats?

Squats are done with a weighted bar on your shoulders, in the natural groove between the muscles, with your feet a little farther than shoulder-width apart.

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MLA Citation:
"The Physics of Human Strength." 22 May 2018
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Keeping your back rigid at a slight arch and your head up, bend at the knees until your thighs are parallel to the ground. Pause momentarily at this position and ascend to your initial position. Squats should be done with a weight belt on and a spotter handy. The most important things to remember when doing a squat are to never let your head down or your back bend, and be sure to reach parallel, so the squat is more effective.
A man squats heavy in competition (

The Physics of the Squat

What makes squatting the most effective lift? The answer is the downward pull of gravity on the lifter. The squatter is essentially pushing directly against gravity. Gravity is a an attractive force that acts on every thing that has mass in the universe. Isaac Newton, famous physicist and mathematician, discovered the laws that govern this force. His law of universal gravitation states that:

Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

From this law, the the acceleration due to this force of gravity near the surface of the earth is approximately 9.8 meters per second squared. This means that if two object are dropped from the same height, they will hit the ground at the same time, regardless of how much they weigh(of course, one must neglect air resistance). This is how weight is defined. An objects weight is defined as the acceleration of gravity g multiplied by its mass m (mg). For example, a person having a mass of 50 kilograms(kg) would have a weight of 490 kg meters per second squared, or 490 Newtons(N). The acceleration of gravity constant was found using Newton's famous three laws of motion:

1. In the absence of external forces, an object at rest remains at rest and an object in motion remains in motion with a constant velocity.

2. The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.(The equation (F=ma, or Force=mass * acceleration).

3. If two objects interact,the force exerted by the first object on the second object is equal in magnitude and opposite in direction to the force by the second object on the first.

The Squat incorporates all of these laws. For example, take the man squatting in the picture below. Let's say that he has a mass of 100 kg and the weight has a mass of about 350 kg. What force must he exert on the bar to stop himself at parallel, the position shown in the picture?

Let's call the mass of the man m and the mass of the weight M. The total downward force acting is:

F = mg + Mg = (100 kg)(9.8 m/s^2) + (350 kg)(9.8 m/s^2) = 4410 N

Since F = ma and the man, at this instant he is at parallel is not accelerating, therefore a =0 and the net force acting in the system must equal 0. This means that the man must exert a force equal and opposite to the force applied. This force is called a normal force(n). The downward force exerted on the man is 4410 N, so when he is sitting at parallel, he must be exerting a force of 4410 N as well. This problem is an example of static equilibrium, or when an object has no acceleration, making the net force equal to zero. The man must exert a force greater than 4410 N to lift the weight from parallel.

What force must the man exert to accelerate the weights up at 1 m/s^2? Once again, we use Newton's second law, F = ma. The equation for the forces acting on the object is:

F = ma = n - (M + m)g = n - 4410= (450kg)(1 m/s^2)

n = force of man = 450 N + 4410 N = 4860 N

The man must exert a force of 4860 N on the bar to accelerate the weights at 1 m/s^2.

The man adds 50 kg to the bar. If he is capable of exerting a force of 5050 N on the bar, will he be able to lift the weights to their initial position(assuming he can exert that force for a long time)? If so, what is the acceleration of the bar?

The total downward force of the weights would be (100 kg + 350 kg + 50 kg)(9.8 m/s^2) = 4900 N

Therefore the man will be able to lift the weight, and his acceleration will be:

a = F/m = (5050 - 4900)/(500 kg) = .3 m/s^2

What is the Bench Press?

The Bench Press (right) is a simple but effective exercise that builds strength in the chest, shoulders, and arms. It is probably the most popular and well known exercise in weightlifting. It is also very effective because it works more than one muscle group.

How do you the Bench Press?

The Bench Press is performed lying on your back on a flat bench. Position your hands on the bar a little wider than shoulder width apart. Lift the weight from the rack and position it above your chest. Lower the weight to your chest, right above your ribs and let it touch lightly. Immediately push the weight back to its starting position. The most important things to remember when benching are to always have a good spotter and never bounce the weight off your chest. Also remember to keep your wrists straight and rigid.
The bench press (

The Physics of the Bench Press

Much like the Squat, the factor that makes the Bench Press so effective is the push directly against the downward pull of gravity. The same laws of Physics applied to the Squat on the previous page can be applied here as well. But there are other concepts that can be applied to both lifts.

One such concept is the concept of work. This is not work in the sense that most people know. Work can be defined as:

Work W done on an object by an agent exerting a constant force on the object is the product of the component of the force in the direction of the displacement and the magnitude of the displacement.

In equation form : Fd cos(x) where F=the applied force, d=displacement, and x=the angle the force acts at.

For example, take the man benching in the picture below. He applies a force of 2500 N on the weight and displaces the weight .5 meters. How much work did he do on the weights?

The force applied is 2500 N and the displacement is .5 m. Since the force is in the direction of the displacement, the angle is 0 degrees and COs(0) =1 so

FD=2500 N * .5m = 1250N*m

The Newton-meter is used so much that it has been given the name Joule(J), so the Work done by the man is 1250 J.

Another physical concept that can be applied to the bench press is power. Power in the physical sense can be defined as work over time or:

Power P =Work(W)/Time interval(T)

It takes the man in the picture 2 seconds to raise the bar from his chest to his initial position(.5 meters). From the last question, we know that the work done by the lifter is 1250 J. If the time interval is 2 seconds, then:

P = 1250J/2s = 625 J/s

Joules per second are also known as watts (W), so the total power of the lifter is 625 W.

The Deadlift is a very simple exercise but works several muscle groups and is very effective in building strength. It is similar to the Squat except that the weight is lifted from the floor.

Start out with the weights on the floor and the feet anywhere from shoulder width apart to twice shoulder width apart (whichever you find more effective). With the back flat and rigid and the head pointed upward, bend at the knees and lift the weights up to standing position. Be careful not to bend your back too much, it could easily cause an injury. The deadlift is a dangerous lift and should only be done if you have no history of back problems.

The Physics of the Deadlift

Like the Bench Press and Squat, the reason the Deadlift is so effective to because of gravity. And also like the squat and deadlift, the lifter does work when lifting the weights.

Now we will talk about the all important physical concept of Conservation of Energy. Energy can be defined the capacity an object has for performing work. The law of conservation of energy states:

Energy can neither be created or destroyed. Energy may be transformed from one from to another, but the total energy of an isolated system is always constant.

There are many different kinds of energy, such as thermal energy(heat), nuclear energy, etc. The two kinds we will be concerned with are the gravitational potential energy and kinetic energy. Gravitational potential energy U can be defined as the product of the magnitude of the of gravitational force mg acting on an object and the height y of the object or in equation form:

U = mgy

Kinetic energy K is the energy of motion. It can be defined by the equation:

K = (1/2)MV^2

The total mechanical energy E of a system is defined as the sum of all the potential and kinetic energies, so:

E = K + U = (1/2)MV^2 + mgy

If energy is conserved in a system, the total initial energy must equal the total final energy, so:

Ki + Ui = Kf + Uf

Let's put this law to work in the deadlift. Say the lifter in the picture is going to lift a mass of 350 kg to a height of a little over 2 meters. If energy is conserved in the system, and the lifter starts from rest, what is the velocity of the bar right before the weight reaches the top?

To do this problem, we have to assume that the velocity of the bar is constant. If the bar starts from rest, initial potential energy is 0 because y = 0. Initial kinetic energy is also 0 because the weight starts from rest. So the equation to find the final velocity is:

0 = (1/2)MV^2 + mgy

v^2 = 2gy

v = 6.26 m/s

The velocity of the bar right before it gets to the top is 6.26 meters per second. This however, is only accurate because we assumed that energy was conserved in the system. In real life we would have to account for energy lost to heat and chemical energy from the lifter.


Paul Anderson (1932-1994)

Height: 5'9''

Weight: 330-360 pounds

Accomplishments: Paul Anderson broke and re-broke every strength record of his time. His strength is unmatched, even today. He was an Olympic gold medalist, strongman, and philanthropist. While most of records are unofficial, many good sources report of his incredible feats of strength.

He was born on October 17, 1932, in Toccoa, Georgia. He began lifting weights in high school in his backyard. He started out with only two dumbbells and some Strength and Health. He was immediately hooked. He looked through junkyards to find heavier and heavier weights to lift. By the time he went to college at Furman University for a year, his lifts were close to the American records of the time. It was at college the idea of becoming a "strongman" occurred to Paul. He left college after a year and went to live with his parents. He met Bob Peeples, a great lifter of the time, and was trained in the squat and Olympic lifts(clean and jerk). From there his career took off. His best lifts of his career include an amazing 1206 pound squat(still unmatched), a 627 pound bench press, a 380 pound one arm press, a 600 pound push press(pressing the weight overhead),and an incredible 575 pound jerk press(pulling the weight up and pressing it out). He made the Guinness Book of World Records for lifting 6,270 pounds in the backlift. This weight is listed as the most weight ever lifted by a human being. He won the gold medal at the 1957 Melbourne Olympics. In all, he broke 18 American records, 8 world records, and retired unbeaten and unchallenged.

Videos of some of Pauls amazing feats of strength:

Watch Paul one-arm press 300 pounds twice Click here.

Watch Paul lift two 55-gallon drums of concrete Click here.

Watch Paul clean and press 435 pounds Click here.

Paul was a devoted Christian and father and always had a heart for children. After he retired he devoted his life to helping troubled children. He also became a prolific public speaker and made many motivational speeches. Paul got married in 1959 and has one daughter.

In 1961, the Andersons established the Paul Anderson Youth Home, a place where young men and women ages 16 through 21 who would regularly be in jail can come for Christian rehabilitation. Paul used all his funds earned from public speaking to fund the home and benefited over 2000 young men and women. The house continues to take in troubled young people, even after Paul's death in 1994.

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