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Weight Training: Anaerobic Exercise Mechanics & Impact on Muscle Growth

Part A – Work & Energy transformations occurring during an exercise  

            During exercising, energy is supplied to the muscles as chemical energy.  This energy is then converted to mechanical work (potential and kinetic energies) during the physical process of weight training.  The ultimate objective of this particular lab is to determine the kinetic and potential energies of the weight (e.g. dumbbell) by using the equations E_k = ½mv² and E_p= mgh.  

            For isotonic exercises, more mechanical work done means that more tearing of the muscles is occurring.  By tearing the muscles, the muscle fibres will be mended, and made thicker than before.  

Materials

• Meter stick
• Timer
• Free Weights (dumbbells, between 20 and 30 lbs)
• Human subject

Procedure

1. The subject should begin doing a bench press exercise, in which he will pause at three stages of the exercise.  These stages will include initial and final stages, as well as an “in-between” stage  (refer to Figure 2.1)

Figure 2.1- Initial and final stages of a bench press (using a barbell)  

2.      Measure the displacement of the weight from the reference point, where E_p= 0, which is the lowest point during the exercise

3.      Measure the time to complete half a repetition (“rep”)  

Observations  

Table 1.1- Distance versus Time for half a repetition using 38.5lbs total

 Table 1.2- Distance versus Time for half a repetition using 43.5lbs total

 Table 1.3- Distance versus Time for half a repetition using 48.5lbs

 Analysis  

Firstly, because our masses are in lbs, we must convert them to kilograms.

1kg = 2.2lbs, thus

• 38.5lbs/2.2 = 17.5kg
• 43.5lbs/2.2 = 19.8kg
• 48.5lbs/2.2 = 22.0kg

To calculate the velocity of each of the trials, we use the formula v = d/t

• for 38.5lbs: v = 0.4650m/1.06s = 0.439m/s
• for 43.5lbs: v = 0.4650m/1.17s = 0.397m/s
• for 48.5lbs: v = 0.4650m/2.16s = 0.215m/s

We will first calculate the amount of work done for half of a repetition using various masses.  The formula W = F•d

• for 38.5lbs: W = (17.5kg * 9.81m/s²) * 0.4650m = 79.8J
• for 43.5lbs: W = (19.8kg * 9.81m/s²) * 0.4650m = 90.3J
• for 48.5lbs: W = (22.0kg * 9.81m/s²) * 0.4650m = 100J

This is assuming the barbell is traveling at constant velocity.  

To calculate the kinetic energy, the formula E_k = ½mv²

• for 38.5lbs: E_k = ½(17.5kg)(0.439…m/s)² = 1.69J
• for 43.5lbs: E_k = ½(19.8kg)(0.397…m/s)² = 1.91J
• for 48.5lbs: E_k = ½(22.0kg)(0.215…m/s)² = 2.12J

To calculate the potential energy at the top of the extension of the exercise, the formula E_p = mgh

• for 38.5lbs: E_p = (17.5kg)(9.81m/s²)(0.4650m) = 79.8J
• for 43.5lbs: E_p = (19.8kg)(9.81m/s²)(0.4650m) = 90.3J
• for 48.5lbs: E_p = (22.0kg)(9.81m/s²)(0.4650m) = 100J

Discussion

            For most isotonic exercises, the more work done by the individual in the process of bodybuilding, the better the workout is.  This is due to the fact that generally muscles undergo more micro-tears when doing more work, which in turn signals for an increased production of actin and myosin filaments.  However, in order to achieve maximum results during workouts, one must find the balance between the number of repetitions they do and the amount of weight they lift.  If an individual attempts to weight train with weights that are too heavy, they won’t get a very good workout.  This is because while they are doing more work per repetition, they are not capable of doing very many repetitions, and therefore don’t do very much work.  On the other hand, a person working out with an overly light weight will be able to do a lot of repetitions, but the amount of work done per repetition will be miniscule.  Furthermore, the human body experiences maximum muscle growth when skeletal muscles are put under a lot of stress and experience tears (accomplished by lifting heavy weights).  Therefore, lifting light weights in your workout routine is not recommended for bodybuilding.           

Conclusion  

            The quantity of work done during an exercise routine is a better measure of the energy expended rather than how much the routine affects muscle growth.  However, within a reasonable intensity range, exercise routines in which a greater amount of work is done is usually better for bodybuilding purposes.

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Part B – Investigating torque in weight training  

            Torque is essentially the rotational effect on a body due to an applied force.  As an exercise involving the arm(s) is being performed, there is for a tendency for the arm to rotate.  Thus, there is torque in the arm as it is being exercised.  To calculate the amount of torque used, we use the formula τ = r_┴ x F, where r_┴ = r · sin θ.  We can measure r_┴ and F, as illustrated in the following diagram.  

Excessive stress on the joints causes bone degradation, and can cause osteoporosis.  The more weight you lift during workouts, the more torque your arm has during various phases of the exercise, and the more stress is put on your joints.  Therefore, people with bone problems should be conscious of how much weight they lift during workout.  

Figure 3.1- where r and θ occur during a bicep curl exercise  

Materials

1.      Protractor

2.      Ruler

3.      Human subject

4.      Dumbbells (between ten and thirty pounds)  

Procedure

1.      Record the length of the fulcrum to the load (r)

2.      The subject should begin a bicep curl pausing at five stages, including the initial and final stages (as demonstrated in Part A), while recording theta (the angle from the forearm to just below the bicep muscle) for each stage.  

Observations

r is 32.50 cm  

Table 2.1- The angles formed between the fulcrum and the lever arm at various positions in a bicep curl exercise using 10.0lb free weights  

 Table  2.2- The angles formed between the fulcrum and the lever arm at various positions in a bicep curl exercise using 20.0lb free weights

Table 2.3- The angles formed between the fulcrum and the lever arm at various positions in a bicep curl exercise using 30.0lb free weights

Analysis

Table 3.4 - Torque of the dumbbell versus the force that needs to be exerted by the elbow joint at various positions in a bicep curl exercise using 10.0 lb free weights

 Table 3.5 - Torque of the dumbbell versus the force that needs to be exerted by the elbow joint at various positions in a bicep curl exercise using 20.0 lb free weights

  Table 3.6 - Torque of the dumbbell versus the force that needs to be exerted by the elbow joint at various positions in a bicep curl exercise using 30.0 lb free weights

Sample Calculations:  

            Torque of Dumbell:

            τ = r_┴ x F = rsinθ x F

            τ=(30.0lb/2.2)(9.81m/s²)(0.3250m)sin(180.0-90.0)=43.5 N·m           

            Force that needs to be exerted by the elbow joint:

            First, we have to find θ for the applied force of the bicep.

                        c²=a²+b²-2abcos(C)

We know that the bicep insertion (where the force of the bicep is applied) is approximately 5.00cm or 0.0500m from the fulcrum (the elbow).  We also know that the distance between the elbow joint and the elbow is 0.3000m.

                        c²=(0.0500m)²+(0.3000m)²-2(0.0500m)(0.3000m)cos(90.0)

                        c=0.3041381265…m

            By using the sine law:

                        a/sin(A)=c/sin(C)

                        0.0500m/sin(A)= 0.3041381265…m/sin(90.0)

                        A=9.462322208°

                        b/sin(B)=c/sin(C)

                        0.3000m/sin(B)= 0.3041381265…m/sin(90.0)

                        B=80.53767779°

            To find θ:

                        θ=180.0°-80.53767779°=99.46232221…°

Since the dumbbell-arm lever system is in rotational and translational equilibrium, we know that ∑F=0 and ∑τ=0.

Let the load be τ_l and let the applied force be τ_A.

τ₁-τ_A=0                        τ₁=τ_A

            τ₁=F_A x r_Asinθ_A

            (43.5 N·m)=F_A x (0.0500m)sin(99.46232221…°)

            F_A=882.0005666…N

                ∑F_x=0

            F_x – (882.0005666…N)cos(90.0°-9.462322208…°)=0

            F_x = 145 N

            ∑F_y=0

            F_y-(882.0005666…N)sin(90.0°-9.462322208…°)+(30lb/2.2)(9.81m/s²)=0

            F_y = 736.2267…N

            a²+b²=c²

                (145 N)²+(736.2267…N)²=c²

            c=750 N

            tanθ=(736.2267…N)/(145 N)

            θ=78.9° down from forward horizontal           

Discussion  

            Maximum torque is generated by the dumbbell at phase 3 of the exercise (where the forearm is parallel to the ground).  This makes sense because when the force gravity provided by the dumbbell is perpendicular to the forearm of the individual doing the bicep curl, the lever arm will be at its greatest length.  Therefore, since τ = r_┴ x F where F is a constant, maximizing the length of the lever arm will yield in maximum torque generation.  As the forearm shifts away from the maximum lever arm position, the torque generated by the load will decrease proportionally.  

            According to our lab results, as the angle between the upper arm and the forearm decreased, so did the stress on the elbow joint.  However, according to various sources on the internet, maximum stress on the elbow joint should occur when the forearm of the individual doing the exercise is parallel to the ground.  Internet sources also stated that the torque generated by the dumbbell in this exercise should be directly proportional to the amount of stress the elbow joint is put under.  This discrepancy is most likely caused by some kind of experimental error.  The lab results obtained in this lab show us that even by doing the bicep curl with fairly light weights, a large amount of force is exerted on the elbow joint.  Using excessive weight during workouts or working out too often can lead to bone degradation, which causes many problems later on in life (including arthritis).  Bodybuilders are advised from doing exercises that put excessive stress on joints in the body because more muscle mass at the expense of skeletal health is not worth it in the long run.  

Conclusion  

The force exerted by the bicep in the bicep curl is directly proportional to the amount of stress the elbow joint is put under.  However, due to conflicting research and lab results, it’s not clear whether or not the amount of torque generated by the dumbbell is directly proportional to the amount of stress the elbow joint experiences.  Further experimentation is required before these lab results can be considered conclusive.

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Part C – Muscles acting as levers  

A lever is fundamentally a device which allows the movement of a load using a force around particular pivot point.  Levers can be divided in to three different classes.  Arms are generally third class levers, which simply signifies that there is a stationary pivot point and a load at the two extremes and an applied force in the middle.  An example of this is the concentration curl where the elbow remains stationary while the forearm lifts the dumbbell, which represents the load.  It is the bicep which generates the applied force but the force is transferred to the forearm by the bicep insertion, the tendon which connects the bicep to the forearm.  The unique characteristic of this particular class of levers is that the muscle does not need to contract much although it inverse proportionally exerts a much greater force in order to create a great deal of movement of the load.  

Because arms are generally third class levers, very little movement in the muscle causes a significant amount of movement of the load which means a greater amount of force is needed to move the load.  Thus, the arm can move a load rapidly but is ineffective at lifting heavy loads relative to secondary and first class levers.  

            Due to the fact that humans the bicep-arm system is a third class lever.  The muscle must exert a greater force than that provided by the load.  Therefore, more muscle tearing occurs than if the arm is a 2^nd or 1^st class lever, which is beneficial for bodybuilding.    

Figure 4.1-the arm acting as a third class lever  

To demonstrate that the arm is quite ineffective at lifting heavy loads, a ratio between the contraction of the muscle and the movement of the load can be determined.  

Materials

·        Human subject

·        Ruler

·        Dumbbells (15lbs)

·        Protractor  

Procedure

1.   Measure the length between the fulcrum and the load

2.   The subject should begin a concentration curl pausing at the initial and final stages while recording the angle between the initial and final stages of the arm as demonstrated in the diagram below.

Figure 4.2-initial and final positions in a bicep curl  

3. Measure the contraction of the bicep muscle at the initial and final positions

 Observations  

Table 3.1-Displacement from the fulcrum to the bicep versus the angle of movement between initial and final positions of the arm  

      ·        Di’s distance between the fulcrum and the load (dumbbell) = 32.50cm

• Ajay’s distance between the fulcrum and the load (dumbbell) = 34.20cm

  Analysis  

Because the motion of the arm is not straight, we must calculate the arc length of the displacement, using the formula arc length = r*q.  However, we must first convert degrees to radians:

(130.0^o – 40.0^o) * (π/180^o) = 1.57rad  

• arc length 1 = r*q = (32.50cm) * 1.57rad = 51.1 cm
• arc length 2 = r*q = (34.20cm) * 1.57rad = 53.7 cm

Now to calculate the ratio of how much the bicep moved versus how much the load moved:

Displacement of load/displacement of muscle=(51.1cm)/(7.00cm-1.10cm)=8.66

Displacement of load/displacement of muscle=(53.7 cm)/(7.50cm-1.50cm)=8.95

Average=(8.66cm+8.95cm)/2=8.81cm  

On average, for every centimeter the bicep contracted, the load moved 8.81 cm.  

Conclusion  

According to the formula for torque (τ = r_┴ x F) and our lab results, the bicep must exert a force 8.81 times as big as the load because the load arm is approximately 8.81 times as big as the force arm.  This is advantageous during workout because you can get the bicep to exert a comparatively large force on a load that may not weigh very much.  More muscle filaments are torn when the bicep must exert a massive force to lift the load and therefore triggers the production of bulkier actin and myosin filaments.  Bulkier actin and myosin filaments make the muscle bigger and stronger than before, which is what bodybuilding is all about.

Part D – Impulse in weight training  

During an exercise, at the halfway point of a repetition, it can often be disadvantageous to let the weight drop.  For example, during a bench press exercise if the barbell is dropped, the weight will simply accelerate down.  The barbell must be stopped with a great amount of force with the sternum, various ligaments & tendons applying an opposing force and the barbell must be stopped in a very short period of time before it falls on the subject’s neck.  Thus in this scenario, the pectorals are not getting the maximum amount of workout as possible relative to letting the weight down with a constant velocity.  Thus, when the barbell is kept at a constant velocity on the way down, the force applied is less because it is over a greater amount of time.  The equation to determine the impulse is impulse=F_net · ▲t and thus when a constant velocity is kept, F_net=0 and the impulse is equal to zero.  Hence, when the impulse is zero, the exercise is generally more effective.

             Letting the weight drop during the bench press is very harmful to the tendons in the shoulder and chest region.  For this situation, F_net∆t=m∆V, where m∆V is a constant.  The force that is exerted on the tendons in the shoulder and chest region is increased dramatically because the barbell is being stopped in a short amount of time (before the barbell can kill the person).  This causes tendon damage in these areas.