Don’t Confuse The Force-Velocity Curve With Newton’s Second Law

I recently received a barrage of messages from someone questioning statements I made in my article on the force-velocity curve. He claims I do not understand basic physical principles because he confuses the force-velocity curve with Newton’s second law of motion, which are completely different things. He then builds on his confusion of this in an attempt to make a case for fast repetition speeds. While I think most readers understand the difference I’m going to explain it any way, since some people are obviously confused by it, and explain why both of these are reasons to move slowly during exercise, not fast.

The force-velocity curve depicts the variation in the force of muscular contraction at different concentric (lifting, positive) and eccentric (lowering, negative) contraction velocities. It shows the higher the velocity of concentric contraction the lower the force a muscle can produce. This is because the faster the actin and myosin filaments in your muscles slide past each other the fewer cross-bridges they are able to form (read the original force-velocity curve article for a more detailed explanation of this). Because of differences in how the cross-bridges function during eccentric contraction there is little variation in eccentric force production at different velocities.

The Force-Velocity Curve

Newton’s second law of motion states the acceleration of an object, the rate of change in its velocity, depends on its mass and the forces acting upon it. For a given mass, the more force you apply the greater the acceleration. This means your muscles must contract with more force when lifting a barbell or machine weight stack to accelerate it more quickly.

The force-velocity curve shows how much force a muscle can produce at different contraction velocities. The faster your muscles contract concentrically the less force they are capable of producing.

Newton’s second law describes how much force your muscles must produce to accelerate a given load at some rate. The faster you want to accelerate the more force you have to produce.

These are the reasons you can not lift a heavy weight as fast as you can lift a lighter weight. The heavier the weight being lifted the more force required to accelerate it, and with a given weight you have to apply more force to accelerate it faster, but the faster your muscles contract concentrically the less force they can produce. So, the faster you want to lift during an exercise the less weight you can use (lowering is another thing altogether, there is no limit to how heavy a weight you can drop, however in most exercises you are limited to using a weight you can also lift).

Some proponents of fast repetition speeds claim the greater force required to accelerate more quickly when lifting a weight is beneficial because of the increased muscle tension, however this ignores that the tension is only higher relative to the weight used, and only during the initial acceleration. During the initial acceleration you impart kinetic energy to the mass being moved, energy which reduces the force you must apply to keep the weight moving proportionally for a brief period after (when throwing something it is this kinetic energy that keeps it moving after you’ve let go). If when lifting a weight you apply fifty more percent force than the force of gravity on it during the initial acceleration you will have to apply fifty percent less force after this due to kinetic energy. The average force still ends up being the same as the force of gravity on the weight, it just varies more, higher and lower, with greater acceleration. If you lift more slowly you will be capable of producing more force and using a heavier weight, allowing for a greater average tension, but while keeping the force within known, safe levels.

Also, while you must use a challenging level of resistance to effectively stimulate improvements in muscular strength and size and other factors of functional ability, it is not necessary for you to produce as much force as you are capable of during every repetition of an exercise, and for the sake of safety you wouldn’t want to. Research shows a high intensity of effort, specifically training to the point of momentary muscular failure, is more important than the load used.

Newton's second law of motion

Another problem with relying on rapid acceleration to increase resistance force and tension during exercise is that it is not precise. Unless you are using equipment with force-measuring capability you don’t know how much the force actually varies from the force of gravity on the weight, and the greater your acceleration when lifting the more the force will vary over the range of motion. At slower repetition speeds which make it possible to change direction with much lower acceleration the force required for acceleration and the reduction in force caused by kinetic energy may only vary from the force of gravity on the weight by a few percent, so the force encountered is more consistent over the full range of motion of the exercise (not including variation from changing musculoskeletal leverage, stored energy, and other factors).

Some proponents of fast repetition speeds claim moving faster during exercise allows you to use a heavier weight despite the reduction in muscle force production at faster concentric contraction velocities because the reps are shorter, but this is only true when performing the same number of reps since the faster reps would result in a shorter time under load. Obviously, you can lift a heavier weight for thirty seconds than you can for sixty. If, however, the sets are matched for time instead of repetitions, you will be able to lift a heavier weight at a slower speed, because your muscles are stronger at slower concentric contraction velocities. You can use a lot more weight when performing three twenty-second repetitions than twenty three-second repetitions. Since time under tension and relative effort are more important for stimulating muscular strength and size increases than the amount of mechanical work performed, moving more slowly makes more sense.

Another claim made by some proponents of fast repetition speeds is that even with a lighter weight, performing more repetitions in the same time frame results in a higher density of work, however this ignores that there is no direct relationship between the mechanical work performed and the more important metabolic work. Although fatigue is faster with a higher rate of mechanical work when the same weight is used, since you can lift a heavier weight when performing fewer, slower repetitions in the same amount of time the average tension and the metabolic work performed would be higher.

Those who know Ken Hutchins definition of intensity as the degree of inroad divided by time might conclude that lifting a heavier weight more slowly would result in a lower inroad/time than lifting a lighter weight more quickly if momentary muscular failure is achieved within the same amount of time, however, this assumes your starting strength is the same in both cases. Considering the force-velocity curve this is not the case. You can use a heavier weight for the same amount of time with slower reps in large part because your starting strength is higher at a slower concentric contraction velocity.

Slower reps are also safer, since even though moving more slowly allows you to lift more weight over the same amount of time the variation in force encountered is very low, unlike fast reps which can result in large, potentially harmful increases in force at the start of positive and end of negative movement. Slower reps also result in lower repetitive motion stress, reducing joint wear over time.

I think Nautilus inventor Arthur Jones summarized this best when he wrote,

…fast or sudden movement during exercise does not produce fast muscles, or stronger muscles, or bigger muscles, it produces only one thing, a thing you should be trying to avoid, it produces injuries. The next time somebody tells you to move fast during exercise, smile and walk away because you are talking to a fool; if in doubt about the best speed of movement during exercise, try doing it slower rather than faster; faster is never better, is usually worse, and is frequently dangerous.

References:

1. James Fisher, James Steele, Stewart Bruce-Low, Dave Smith. Evidence-Based Resistance Training Recommendations. Med Sport 15 (3): 147-162, 2011 DOI: 10.2478/v10036-011-0025-x

2. N.A. Burd, C.J. Mitchell, T.A. Churward-Venne, and S.M. Phillips. Bigger weights may not beget bigger muscles: evidence from acute muscle protein synthetic responses after resistance exercise. Appl. Physiol. Nutr. Metab. 37(3): 551-554, 2012.

3. Jürgen Giessing, , James Fisher, James Steele, Frank Rothe, Kristin Raubold, Björn Eichmann. The effects of low volume resistance training with and without advanced techniques in trained participants. Pre-print (this reference will be updated after this study goes into print)

4. 4. Hutchins, Ken. SuperSlow: The Ultimate Exercise Protocol, 2nd Edition. 1992

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  • nik Nov 13, 2014 @ 17:59

    Great article….I love the last quote.

    • Drew Baye Nov 13, 2014 @ 19:29

      Hey Nik,

      It’s one of my favorite Arthur Jones quotes. One of these days I’ll write a post with my ten favorites with commentary on each one. It’ll be hard to narrow it down to that, but if I don’t pick a number it could turn into a very, very long post.

  • Donnie Hunt Nov 13, 2014 @ 20:25

    I love these kinda articles Drew. Even though some of the physics are over my head. I have a sort of series of events view of how I approach an exercise

    Mental focus, visualize and mentally zero in on the muscles/part of the body that I will be contracting. This gives way to creating tension in the muscles to be worked. Consistent, controlled, significant tension eventually gives way to fatigue/inroad. Fatigue/inroad to a certain point depending on the tool used, brings me to my exercise ending point.

    Admittedly I don’t always “go there” with fatigue/inroad. Sometimes I have respites during an exercise. Are there any instances where respite during an exercise would be desirable
    in your experience and views Drew?

    • Drew Baye Nov 13, 2014 @ 22:53

      Hey Donnie,

      Yes, rest-pause training incorporates respite during the set, and studies show a brief rest between repetitions does not negatively effect improvements in strength and may even be beneficial. However, because you can handle much more weight with rest-pause than when performing continuous repetitions I’ve found it to be harder on the joints.

  • Craig Nov 14, 2014 @ 10:33

    The other consideration is that if you are moving the weight fast, then there will be more significant periods of acceleration and de-acceleration, so that the force will vary a lot more. That is especially true if a lift is done explosively, such that the weight is effectively being thrown.

    In the performance of the snatch, for example, peak accelerations on the order of 10 m^2/sec have been measured, which means the lifter has to exert force equal to double the weight of the bar. But that high force pull only lasts 100-200 milliseconds. That is so far from the conditions at which people typically strength train it is hard to really compare the two actions. I’m not even sure that the force-velocity curves that you show in your article are applicable when considering a short duration explosive effort that produces high acceleration, but relatively low displacement (i.e., during the period when high force is produced). It would be interesting to know how such curves were developed. I assume they most likely come from tests done under conditions of a steady velocity of contraction???

    Also, there are some physiologists who believe that such explosive movements do alter or bypass the normal muscle fiber recruitment pattern. I don’t know that you can rule out a neurological training effect from explosive movement training that might enable better power production specific to those movements. Of course, the big controversy is whether or not that neurological training effect, if it exists at all, is transferable to other activities.

    • Drew Baye Nov 14, 2014 @ 13:56

      Hey Craig,

      Yes, at fast repetition speeds there is much greater variation in the resistance encountered relative to the load due to acceleration and kinetic energy. I covered this in the seventh paragraph.

      The force-velocity curve still applies at “explosive” repetition speeds. There may be some differences in motor unit recruitment but the contraction force would still be limited by the reduction in cross-bridging at faster concentric contraction velocities.

      Whether there is any transfer is irrelevant, since it has been proven strength training with slow repetition speeds increases strength in other activities at all speeds, and when there are different but similarly effective ways of accomplishing the same training goals it makes sense to choose the one with the lowest risk of injury.

  • Anthony Nov 14, 2014 @ 11:17

    Hi Drew,

    I was wondering if you could post a video on how to perform the perfect rep by your standards. Also, how do you accurately keep track of the reps and time for the sake of accurate progression documentation. I have always found it difficult to keep track of time and reps when applying these slow reps, sometimes I tend to go fast on certain part of the reps, especially the difficult portion of the reps.

    Thanks for the article and awesome blog,

    Anthony

    • Drew Baye Jul 24, 2019 @ 13:31

      I have posted several videos instructing and demonstrating exercise performance in my private Facebook group for HIT List members. To learn more or join go to https://www.baye.com/hit-list/

      I uses a metronome app to maintain a consistent repetition cadence and since I perform only a few, very slow repetitions of each exercise it is easy to keep track of the repetition count.

  • Jamieson Bardy Nov 14, 2014 @ 12:54

    Another great article Drew!

    • Drew Baye Nov 14, 2014 @ 13:05

      Thanks Jamieson,

      I’m glad you like it.

  • Don Matesz Nov 14, 2014 @ 13:53

    Very clear explanation. I hope the fast-movement fools can understand it. I too enjoy that last quote from Jones.

    • Drew Baye Nov 14, 2014 @ 21:39

      Thanks Don,

      I hope they understand it. Maybe it will convince them to slow their reps down a little and prevent injuries and unnecessary joint wear.

  • James Nov 14, 2014 @ 20:26

    Interesting for sure.
    But i still cant wrap my head around why no coach or athlete at the top levels are using the more slow HIT style of training if its the safest and best method like you and other are claiming?
    It also seems like everyone gets greater results by improving their speed, acceleration and jumping when they use the workouts with 30-70% of RM for 3-5 reps with doing the movement as fast as possible. Like deadlift or squat for example.
    All these athletes and coaches are hired by the best of the best. I cant understand why their not using the best strength training method for their athletes then? They must have heard about Arthur Jones and Slow HIT training and i guess they also must have tried it?

    • Drew Baye Nov 14, 2014 @ 21:36

      Hey James,

      I suspect most do this for the same reason people in many other fields still use inferior, inefficient, and outmoded methods long after better ones have been discovered or developed; familiarity, tradition, and resistance to change.

      Fast movement during exercise will not improve your speed in other activities or your ability to jump any more than slow movements. Regardless of the speed of movement used during exercise as long as you are getting stronger you will become faster, more powerful, and more explosive in other activities. However, as Arthur Jones pointed out, fast reps increase your risk of injury.

    • Don Matesz Nov 16, 2014 @ 12:27

      To move any given load faster, you must apply greater force.

      Compare a Kenworth Semi-Tractor and a small sports car, say a Ferrrari. The will go faster from 0 to 60 because it is lighter and has a greater horsepower (strength) to weight ratio. But if you want to move a ton of freight from 0-60 as fast as possible you will use the Kenworth Semi-Tractor.

      Assuming consistent efficient force-application technique, if someone gets faster at moving any given resistance (including your own bodyweight i.e in sprinting or jumping) its because they got stronger relative to the resistance, i.e. you can’t get faster without getting stronger.

      In addition to what Drew said about tradition and resistance to change, I think there is a resistance to HIT because it consumes less time and is less complicated than other methods. Many coaches and trainers get paid per unit time. If I get paid by the hour to accomplish a task, I have an apparent incentive to make the task fill the hour.

      Also, the more complicated I make training seem, the more I create the illusion that my special insight into various training methods, periodization, and so on is crucial to success.

      • Drew Baye Nov 17, 2014 @ 8:33

        Hey Don,

        Exactly. The stronger a muscle is, the more force it can produce, the faster it can accelerate a given load. If your one rep max for an exercise is one hundred pounds, you will not be able to lift it very quickly. If after a few months of training you have increased your one rep max to one hundred and fifty pounds, you will be able to lift one hundred pounds much more quickly, since it now requires only two-thirds of your available strength.

  • Michael Nov 15, 2014 @ 4:06

    In reference to the “someone” that’s obviously defending their use of fast reps, didn’t Arthur Jones once say something like: an ignorant person is one who doesn’t have the facts, while a stupid person is one who has been given the facts, but continues the same argument….”and stupidity goes to the bone.”

  • Ed Nov 15, 2014 @ 12:42

    Drew,

    I think this is good information and agree with everything you said when using mass-based resistance. Do you agree that once rep speed is slow enough – that the effects of momenturm and acceleration become de-minimus? For me that is at a rep speed of around 3-3 or 4-4. Turn arounds are most important because that is where your are changing direction and will see most of the effects.

    But, what about resistance that does not rely on mass and gravity? For example if you train with a Keiser air machine, bowflex revolution, or even latex tubing – you can try to accelerate the movement arm, but even if you get it to move faster there is virtually no momentum or ballistics taking place. So for those of you who are foolish enough to want to perform fast, explosive reps, non-intertial resistance is probably a better way to do that.

    Ed

    • Drew Baye Nov 17, 2014 @ 22:31

      Hey Ed,

      Yes, once you start using cadences slower than about three to four seconds over typical exercise range of motion there is little difference in the variation in force due to acceleration. I wrote about this in detail in Repetition Speed Recommendations However, you would be able to produce more force moving more slowly, and use a heavier weight.

      You should move slowly even when using machines with pneumatic or elastic resistance, because although deloading due to kinetic energy is less of an issue, you still have to produce considerably more force to accelerate rapidly, and the deal with the reactionary force. The harder you push or pull something, the harder it pushes or pulls you back, and if you attempt to move explosively against any kind of resistance the initial force during acceleration can be high enough to injure you.

      There is no good way to perform an exercise fast. Or, as American Kenpo Grandmaster Ed Parker once wrote, “There is no right way to do a wrong thing.”

  • Lukas Nov 15, 2014 @ 16:25

    I know a gym where there are no weight stacks on the machines, the resistance is given by a cylinder filled with pressurized air. You vary the resistance by varying the air pressure in the cylinder. Do these same physical principles apply to such a set-up?

    • Drew Baye Nov 17, 2014 @ 12:47

      Hey Lukas,

      Yes, you would still have to apply more force to accelerate more quickly against the same level of air pressure. You should still move slowly when using machines which have pneumatic cylinders instead of weight stacks.

  • Don Matesz Nov 16, 2014 @ 17:49

    Drew, have you seen this: http://www.championshipproductions.com/cgi-bin/champ/p/Basketball/High-Intensity-Strength-Training-Series_BD-03910.html

    Michael Bradley, Florida State University Men’s Basketball Strength and Conditioning Coach, is using super slow technique and HIT for his athletes.

    • Drew Baye Nov 17, 2014 @ 8:35

      Hey Don,

      I know Michael and have met with him a few times when he was in the area visiting Jim Flanagan, and he’s highly knowledgeable and Florida State is lucky to have him. I have not seen this video before, but it’s a great example of how athletes should train. The only thing I would disagree with now is the part on pre-exhaustion, since research shows it makes no difference what order you perform the simple and compound exercises in or whether you rush between them.

      • Don Matesz Nov 17, 2014 @ 12:54

        So contrary to claims made above, there are coaches using HIT and Super Slow. Coach Dick Conner also comes to mind; he uses SS and HIT to train powerlifters and athletes.

        • Drew Baye Nov 17, 2014 @ 22:35

          Hey Don,

          Yes, and Dick Connor’s lifters have done very well with his training. People also forget that even the US Olympic Lifting team trainer Bob Hoffman used a protocol which he called muscle contraction with measured movement (MCMM) which incorporated a ten second lifting movement, a ten second lowering movement, and a ten second rest between reps. Slow repetition speeds are not new, and there are athletes and strength coaches using them.

  • Steven Turner Nov 16, 2014 @ 18:39

    Hi Drew,

    If I took James 30%-70% load

    I could only imagine a huge difference in speed and acceleration between 30% and 70% and 3-5 reps. You would think that a lift at 70% would have to be significantly slower than 30%. A question I would like to ask is do my muscles get faster with 30% load or 70% load if it is 30% than I am wasting a lot time and energy if I use 70% load.

    If it is plyometric jumps – I am 100kg do I add 30kg or 70kg to my body weight for my musles to be fastest they can.

    If you were to invest your money with a stockbroker and he said that he could get you a return on your investment 30-70% I think that you would question him about your money investment.

    Is it 30% or 70% massive differences in percentages?

    • Drew Baye Nov 17, 2014 @ 11:28

      Hey Steven,

      James meant this is a typical range of loads used by people doing fast reps, not a guideline for doing them.

  • Bradley Nov 17, 2014 @ 7:48

    ‘Those who know Ken Hutchins definition of intensity as the degree of inroad divided by time might conclude that lifting a heavier weight more slowly would result in a lower inroad/time than lifting a lighter weight more quickly if momentary muscular failure is achieved within the same amount of time, however, this assumes your starting strength is the same in both cases. Considering the force-velocity curve this is not the case. You can use a heavier weight for the same amount of time with slower reps in large part because your starting strength is higher at a slower concentric contraction velocity.’

    I also would like to add that during a superslow set which may last around 90 seconds, the fist 60 seconds are mainly a warm up, and the last 30 seconds is where the real stuff starts happening. So when people say that the inroad/time is less with superslow, its actually not, since most people doing fast repetitions are performing multiple sets to warm up the muscles before hand to prevent injury.

    Another thing Drew,

    ‘at fast repetition speeds there is much greater variation in the resistance encountered relative to the load due to acceleration and kinetic energy’

    I have to admit that I think this variation is actually necessary for some people training on equpiment with poor resistance curves. I believe its called ‘camming on the fly’ But I would also say that it doesnt necessarily require rediculously fast repetition speeds, more like 4/4 as opposed to 10/10.

    • Drew Baye Nov 17, 2014 @ 10:21

      Hey Bradley,

      The variation in force caused by a faster rate of acceleration is neither necessary nor beneficial for people training on equipment or when performing free weight exercises with incongruent resistance curves and increases the risk of injury. When performing exercises with sticking points people often accelerate rapidly to get through them, because they are focusing on getting reps, rather than efficient muscular loading. Rather than trying to cheat to get through sticking points, if you fail at a sticking point continue to contract isometrically for a while to make up for whatever inroading you might have accomplished if you could have completed another rep or two. Don’t risk a pulled or torn muscle for the sake of getting a few more reps.

      • Ben Tucker Nov 21, 2014 @ 19:59

        I’ve concerns about this, too, even with free weights.
        Being weakest at the bottom of a press, we all get stuck. My question is, should you shorten your range of motion to stay in the set?
        Because it feels like I’ve more to give after getting stuck on the bottom.

        Basically, to me, it just feels more like the laws of leverage giving way as opposed to true failure. It seems like true failure would be better achieved when you’re squeezing closer to the top of the rom. Same could be said for pulling motions.

        Am I misguided here?

        • Drew Baye Nov 28, 2014 @ 1:35

          Ben,

          As long as you are achieving momentary muscular failure within a reasonable time under load it doesn’t matter where in the range of motion it occurs. If you’re really stuck it is because you don’t have more to give, you are already working maximally at that point. During timed static contractions you are stuck at one position for the entire exercise, but it is very effective for improving muscular strength and size.

  • Bradley Nov 17, 2014 @ 7:58

    Obviously moving fast initially must allow for more force prodcution with a given weight, otherwise we would be seeing massivley muscular long distance runners and very skinny sprinters. But its that point at the end of the set when everything slows down thats the most important, regardless of whether youve done it fast or slow to begin with.

    • Drew Baye Nov 17, 2014 @ 8:44

      Bradley,

      Yes, and there is no need or advantage to moving faster earlier in the set, since what is important isn’t the average resistance force your muscles are working against, but the relative intensity of effort of the exercise.

  • Bradley Nov 17, 2014 @ 8:03

    Is average force production really greater at the end of a slow rep set compared to a fast rep set? I wouldve though that they’d pan out the same, with greater fluctuations in force with the faster repetitions?

    • Drew Baye Nov 17, 2014 @ 8:40

      Hey Bradley,

      If the weight used is the same, the average force production will be the same (assuming all else is equal), although there will be more variation in force with greater acceleration. However, if you are moving more slowly, you can use a heavier weight for the same time under load.

  • Bradley Nov 17, 2014 @ 12:09

    Thanks Drew. Do you have any clue as to why we can lift a heavier weight for longer if we move slower?Your comment seems to condradict itself.

    • Drew Baye Nov 17, 2014 @ 12:42

      Bradley,

      If you move slower during exercise you can lift a heavier weight for the same duration, or the lift the same weight for a longer duration, due both to the force-velocity curve and eccentric contraction being more metabolically efficient. At slower concentric contraction velocities your muscles can contract with more force, allowing you to lift a heavier weight, and although the increased cross-bridging responsible for this would increase the metabolic cost of concentric contraction, the greater metabolic efficiency of the longer eccentric contraction would balance this out.

      There is no contradiction here. I wrote “… if you are moving more slowly, you can use a heavier weight for the same time under load.”

      Years ago I conducted an experiment comparing the time it took subjects to achieve momentary muscular failure at different cadences, and found both SuperSlow (10/10) and negative emphasized repetitions (2/10) allowed for a longer time under load with the same weight than moderately fast reps (2/2). This means to achieve failure in the same time when using a slower speed, either for the entire repetition or just the negative, you would require a heavier weight.

  • Bradley Nov 17, 2014 @ 12:16

    Surely i wouldve thought the average force production is what determines the level of effort? As this is the muscle fibres job; to contract and produce force.

    .

    • Drew Baye Nov 17, 2014 @ 12:32

      Bradley,

      Read What Is Exercise Intensity?

      There are different ways to look at this, but the most important is not the average level of effort, but that you work up to a maximum effort by continuing an exercise to the point of momentary muscular failure.

  • Bradley Nov 17, 2014 @ 17:15

    Hey Drew, Thanks for your reply. I apologise for not re-reading what you wrote before commenting, I realised you did not contradict yourself at all.

    • Drew Baye Nov 17, 2014 @ 22:33

      Hey Bradley,

      No problem. It’s a complex subject.

  • Donnie Hunt Nov 18, 2014 @ 9:37

    This article has triggered a lot of interesting discussion.

    • Drew Baye Nov 18, 2014 @ 12:34

      Hey Donnie,

      I’m sure it has, but anybody who argues this is wrong is ignorant of the physiology involved. If anybody questions the inverse relationship between concentric contraction velocity and muscle force production I suggest they visit their local university and ask to speak with a physiology professor about it, or pick up any exercise physiology text. It will tell them exactly what I have written above.

      In the second edition of the textbook Skeletal Muscle Structure, Function, and Plasticity: The Physiological Basis of Rehabilitation by Richard Lieber on page 60 it says,

      “Muscles are strengthened based on the force placed across them during exercise. The force-velocity relationship of muscle indicates that high velocity movements correspond to low muscle force, and that low velocity movements correspond to high muscle force. Since strengthening requires high force-producing exercises, the velocities must, necessarily be relatively low. High velocity movements may have other beneficial effects (e.g. improve muscle activation by the nervous system), but not at the muscle tissue level. The take home message – keep velocity low for strengthening.”

      …and on page 83 it says

      “It has been experimentally determined from biochemical studies that the cross-bridge connections between actin and myosin attach at a certain rate and detach at a certain rate. These rates are referred to as rate constants. At any point, the force generated by a muscle depends on the total number of cross-bridges attached. Obviously, this number represents the net balance between the number of cross-bridges attached versus detached. Because it takes a finite amount of time for cross-bridges to attach (based on the rate constant of attachment), as filaments slide past one another faster and faster (i.e., as the muscle shortens with increasing velocity), force decreases because of the lower number of cross-bridges attached. Conversely, as the relative filament velocity decreases (i.e., as muscle velocity decreases), more cross-bridges have time to attach and to generate force, and thus force increases.”

      In the fourth edition of Exercise Physiology: Human Bioenergetics and Its Applications by George Brooks on page 390 it says,

      “As compared to lifting light loads, isotonic responses to given stimuli when lifting heavy loads results in a greater latent period, slower movement, and less movement. The effect of strength training is to make the load appear lighter. The force-velocity relationship is hyperbolic in nature. Greater loads produce slower speeds but greater tension.”