T Nation

Negative Force Exerted by a Muscle?

We (probably) all know that F = ma, meaning the net force exerted on an object equals the mass of the object times its acceleration.

Mass is a scalar quantity, but acceleration is a vector. It can be negative and positive. If the final velocity of the movement is less than the initial velocity, we have an acceleration in the negative direction (as opposed to the motion), so the net force exerted is subsequently negative.

The force exerted by a muscle, as reiterated by many coaches, if again ma, so we can apply the same force to a 500 lbs weight as a 200 lbs weight performed in different accelerations.

One thing I really wonder is this case: You perform a heavy bench press single. You lower the weight, push off the chest with relative ease, and your velocity greatly decreases near the lock out as your triceps shake, and in the end you complete the lift, but your final velocity was much less than your initial velocity.

Does this mean the muscle just exerted negative force to do work in the positive direction or is there something else happening at the neurophysiological level that prove the acceleration positive after all?

Think of it as a (very) simplified statics problem. The barbell in a bench press weighs 200lb downward. Your muscles need to exert at least 200 lb upward to hold the barbell still. As long as the barbell is moving away from your body (up), you are exerting a force over 200 lb to move it. When the barbell is coming down towards your chest, your muscles are exerting a force upward but the NET force is downward. At the top of the bench press (arms locked out), you are still exerting 200 lb of force upwards.

[quote]Lakkhamu wrote:
Does this mean the muscle just exerted negative force to do work in the positive direction or is there something else happening at the neurophysiological level that prove the acceleration positive after all?[/quote]

Also, I want to add that negative force is relative to the coordinate system you are using. In the bench press scenario, if your positive direction is towards your body, then the barbell force is positive and the force produced by your muscles is always negative.

Lol, no. Firstly this is a wildly simplistic model and not an accurate representation.

Now, using your example of a bench press rep consider the motion in 1 dimension (vertically along a line).
For simplicity assume the distance from bar on chest to lockout is 1m. Obviously the acceleration and velocity at both of these points is zero as the bar is stationary.

The acceleration at a given time t during the rep can be calculated from s = ut + 0.5at^2
where s = displacement = 1
u = initial velocity = 0
a = accelaration
t = time

Hence at^2 = 2. Since t^2 > 0, a is always >0 and so F=ma >0

Alternatively you can show that the average acceleration over the course of the rep is equal to zero, since the bar is accelerated off the chest and then must decelerate to stop at lockout.

Using equation v^2 = u^2 + 2as (same definitions as before but with v= final velocity)

We have 0 = 0 +2*a*1  ->   a = 0

No. You are ignoring the force of gravity.

F=MA but F is the net force on the object.

So more correctly:

F1 (force of muscle) - F2 (force of gravity) = MA

When the obect is decelerating, the force of gravity is larger than the force the person is exerting. Net force is in the “negative” (downward) direction.