1

2

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.

[top]

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.

[top]

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.  

Figure 5.1-initial and final positions of a bench press exercise using a barbell  

Materials

1.      Stopwatch

2.      Human subjects

3.      Dumbbells (5lbs)

4. Ruler
5. Elastic

Procedure

1.      Have the subject lift the free weights until the arms are fully extended

2.      The subject should let the two dumbbells drop but stop them before they hit the sternum, as shown in the final position of Figure 5.1

3.      Have the subject lift the free weights until the arms are fully extended

4.      Measure the distance between the load and the parallel of the sternum

5.      The subject should then bring the weights down with a relatively constant velocity

6. Measure the length of the elastic at equilibrium position
7. Attach a 5 pound weight onto the elastic
8. Displace the mass upwards from equilibrium position by an indicated amount (5cm, 10cm, 15cm, 20cm, 25 cm)
9. Release the mass
10. As soon the mass goes past the equilibrium position, start the timer
11. Stop the timer when the mass stops
12. Record results.

Observations

 Table 5.1-distance between the load (10.0lbs) and the parallel of the sternum for various trials

 Table 5.2-diplacement of the mass from the equilibrium position of the elastic versus the time it takes for the elastic to stop the mass

 Analysis  

Table 5.3-Velocity of mass just before an opposing force is applied on it versus the average magnitude of the opposing force  

 Sample Calculation:

             Velocity of mass just before an opposing force is applied on it:

            V_f ² = V_i ² + 2ad

            V_f ² = 0 + 2(9.81 m/s²)(15.00 cm/100)

            V_f =1.72 m/s

             Average magnitude of opposing force:

            F_net∆t=m∆V

            F_net(0.5800s)=(10.0 lb/2.2)(1.72 m/s)

            F_net=7.82 N

            F_av=7.82 N + (9.81 m/s²)(10.0 lb/2.2)=52.4 N

 Discussion

Tendons are actually quite elastic, much like the elastic bodies used in this lab.

From the results of this lab, we can conclude that as the distance the mass was allowed to undergo free fall increased, the average force required to stop the mass also increased.  We can postulate that increasing the mass used in this lab will also have a similar effect on the average force required to stop the mass.  According to Hooke’s Law (F=kx), as the maximum force required to stop the mass increases, the amount of “stretch” the elastic undergoes also increases.  Therefore, by increasing the distance the mass is allowed to fall and/or by increasing the mass itself, we can say that the elastic will undergo a greater degree of stretch.  The tendons in the human body, much like the elastics used in this experiment, have a certain elastic limit.  Once it’s stretched beyond this limit, it will become permanently deformed and may even break.  This causes various problems, because tendons have various roles in the muscular system of the body, including saving energy during workouts and improving muscular control.  Because tendons are what connect skeletal muscles to the skeleton, caution should be exercised to not damage the tendons in your body during workouts, or you will find yourself not being able to do everyday tasks very well.

             Another drawback to using bad technique like dropping the weight on oneself during the bench press exercise is that the tendons are what absorb most of the shock from stopping the barbell before it kills the individual, so the pectoral and shoulder muscles don’t get a very good workout.  Maximum muscle stress is achieved by keeping the barbell at constant velocity during the extension and flexion phases of the exercise, in which case the impulse of the barbell should equal 0.

 Conclusion

 Proper technique should be followed in bodybuilding to prevent tendon injuries.  Bodybuilding is about improving one’s physical condition, not worsening it.

[top]

Part E - Influence of speed and intensity of workout on blood pressure and heart rate

 A faster and more intense workout will yield a higher blood pressure and heart rate in the human subject.

             The heart is described as “hollow muscular organ”; its function is to pump blood to the whole body during a person’s life.  The circulatory system of which the heart is part of sends oxygen and nutrients to the body and removes waste and carbon dioxide.  One of the demands on the heart is that it must be able to shift whenever the activity of the person changes.  Thus when activity increases and a person were to exercise, they would need more oxygen.  The increase in oxygen demand leads to the heart being forced to pump more blood and therefore the heart rate of that particular individual to increase.  “Heart rate” simply signifies the number of beats the heart undergoes per minute.  Under normal circumstances, the heart rate of and adult would be seventy beats per minute while that of a child would be one-hundred beats per minute and a baby’s would be one-hundred and twenty beats per minute.  Resting heart rates will increase due to exercise training.  For example, professional athletes have slower resting heart rates due to physical training which keeps the heart stronger so that it may pump a higher volume of blood while beating less often.  Other sources such as stress, temperature, hormones, drugs, alcohol and food can also affect heart rate.

             Blood pressure is essentially the force of one’s blood on the arteries’ walls.  It is measured by the systole, the “highpoint” where the heart releases blood by contracting, and the diastole - the “low point” in which the heart relaxes and thus is filled with blood.  When blood pressure is measured, it is generally measured in mm of mercury (mmHg) in a sphygmomanometer.  The maximum blood pressure is systole and the minimum is the diastole for a “cardiac cycle”.  Normal blood pressure should be should be 80/45 in babies while individuals at thirty years of age should have a blood pressure of 128/80.  If ones blood pressure were too high, some of the blood vessels could explode, yet if the blood pressure was too low, the brain would “starve” or not be able to get what it needs.  Thus, the body controls blood pressure in various ways to meet its needs.  For example, it can tighten or loosen the blood vessels also the heart can change the amount of blood it pumps.  Blood pressure will be affected by the flexibility of arteries, the diameter or width of the artery, the thickness or viscosity of blood and the volume of blood.  The volume of blood can change if a lot of blood is lost causing the blood pressure to go down.  As well, the heart rate can affect blood pressure. As one exercises, their heart rate increases thus resulting in an increase of blood pressure.  As the heart rate decreases, the blood pressure decreases.

 Materials

• Blood pressure monitor
• Three humans
• Stop watch
• Ruler
• Barbell
• 6 stool and a cushion or a bench press

 Procedure  

1. Set up stools and cushions refer  so that the stools are in a line and some cushions and towels care padding it , use a light and small cushion for the head and a few towels for the rest if wanted
2. Have the human subject sit relaxing and not really doing much for at least roughly 10 minutes
3. Measure the subject’s blood pressure and heart rate
4. Have the subject start on the bench press
5. Measure the distance travelled by the barbell from the bottom to the top and the time it takes for the barbell to travel this distance
6. After the exercise, measure the subject’s blood pressure and heart rate
7. Repeat the steps for the wanted trials

Observations  

Table 6.1 – Heart rate and blood pressure before and after an intense workout (8 reps) using 58.5lbs  

 Table 6.2 – Heart rate and blood pressure before and after a fast workout (20 reps) using 23.5lbs  

  Analysis  

Table 6.3 – Velocity of the mass during the workout versus the change in heart rate and blood pressure after an intense bench press workout (8 reps using 58.5 lb)  

 Table 6.3 – Velocity of the mass during the workout versus the change in pulse and blood pressure after an fast bench press workout (20 reps using 23.5 lb)  

 Discussion  

            In part B of the lab section, we investigated how the quantity of work done during bodybuilding exercise routines affects the effectiveness of these routines.  However, the amount of work done during a workout is just one of the factors that influence how effective the workout is.  This is shown very clearly by the results of this lab.  Two individuals executed an intense workout, followed by a rest period, then a fast workout.  The amount of work done in both exercises is about the same.  However, both individuals clearly experienced differences in how much their heart rates and blood pressure changed during the two workouts.  The fast workout seems to yield a greater change in heart rate and blood pressure.  Why did this occur?  Our hypothesis is that during the intense bench press exercise, the demand for ATP was so high that the body must resort to anaerobic respiration to supply the necessary muscles with energy.  Anaerobic respiration involves glucose getting turned into pyruvate, then being converted to lactic acid, and finally it’s converted back to glucose in the liver and the process continues.  Anaerobic respiration produces ATP, but does not create CO₂ as a waste product.  The body does not need to get rid of an increased quantity of CO₂, so breathing rate, heart rate, and blood pressure all remain the same.  However, anaerobic respiration and aerobic respiration must occur and the same time to supply the skeletal muscles with enough ATP.  Since aerobic respiration does produce CO₂ as a waste product, breathing rate, heart rate, and blood pressure will go up dramatically.  The fast bench press workout relied on mainly aerobic respiration while the intense bench press workout relied on both aerobic and anaerobic respiration, therefore the individuals who did the fast workout experienced a greater change in blood pressure and heart rate.  The same individuals doing the intense workout experienced a lesser change in blood pressure and heart rate  

Conclusion  

While it seems that the change in heart rate and blood pressure of the two individuals executing the bench press exercise is influenced by the velocity at which they are moving the barbell, more scientific testing is needed to confirm this.  The results of this lab indicated that fast bench press workouts results in a greater in heart rate and blood pressure than the intense bench press workouts.  Therefore, for general health purposes, fast workouts are better because it gets heart rate up more.  Increased heart rate during exercise trains the heart to pump more blood per contraction, which increases the fitness level of the individual.  For bodybuilding purposes, the intense workout is better because muscle filaments are being re-synthesized stronger and bulkier than before.  Research indicates that while aerobic exercise results in a higher endurance of the muscle, the size of the muscle itself does not change.

[top]

[main page]