The chin-up is one exercise that can be used to strengthen the biceps muscle. This muscle can exert a force of approximately 800 N as it contracts a distance of 7.5 cm in a 78 kg male. How much work can the biceps muscles (one in each arm) perform in a single contraction?
1 J
Compare this amount of work with the energy required to lift a 78 kg person 40 cm in performing a chin-up. How much is required?
2 J
Based on this analysis, could the biceps muscle be the only muscle involved in performing a chin-up?
To find the work done by the biceps muscles, we can use the formula W = F x d, where W is the work done, F is the force exerted, and d is the distance over which the force is exerted.
W = 800 N × 0.075 m = 60 J
Since there are two biceps muscles (one in each arm), the total work done by both muscles during a single contraction is:
Total work = 60 J + 60 J = 120 J
Now, let's compare this to the energy required to lift a 78 kg person by 40 cm.
The force required to lift a 78 kg person is equal to their weight, which is the mass times the acceleration due to gravity (9.81 m/s²):
Force = mass × gravity = 78 kg × 9.81 m/s² = 765.18 N
The work required to lift the person by 40 cm (0.4 m) is:
Work = Force × distance = 765.18 N × 0.4 m = 306.072 J
Comparing the work done by the biceps muscles (120 J) to the work required to lift a person (306.072 J) in performing a chin-up, we can see that the work done by the biceps muscles is less than the work required to lift the person.
Therefore, based on this analysis, the biceps muscle cannot be the only muscle involved in performing a chin-up. Other muscles, such as the back and shoulder muscles, also contribute to the necessary force and work needed for this exercise.
To calculate the work done by the biceps muscles in a single contraction, we can use the formula:
Work = Force x Distance
Given that the force exerted by the biceps muscles is approximately 800 N and the distance contracted is 7.5 cm (which is equivalent to 0.075 m), we can substitute these values into the equation:
Work = 800 N x 0.075 m
Work = 60 J
Therefore, the biceps muscles can perform approximately 60 Joules of work in a single contraction.
To compare this amount of work with the energy required to lift a 78 kg person 40 cm in a chin-up, we need to calculate the work done against gravity. The formula for work against gravity is:
Work = Force x Distance
Considering that the force acting against gravity is the person's weight, which is given by the formula:
Force = mass x acceleration due to gravity
Force = 78 kg x 9.8 m/s^2
Force = 764.4 N
Given that the distance is 40 cm (which is equivalent to 0.4 m), we can substitute these values into the equation:
Work = 764.4 N x 0.4 m
Work = 305.76 J
Therefore, the energy required to lift a 78 kg person 40 cm in a chin-up is approximately 305.76 Joules.
Based on this analysis, it is clear that the biceps muscles alone cannot provide enough work or energy to perform a chin-up. Other muscles, such as the muscles in the back, shoulders, and core, also play significant roles in the movement.
To calculate the work performed by the biceps muscles in a single contraction, we can use the formula:
Work = Force × Distance
In this case, the force exerted by the biceps muscles is approximately 800 N, and the distance over which they contract is 7.5 cm (or 0.075 meters).
Work = 800 N × 0.075 m = 60 J
Therefore, the biceps muscles can perform 60 Joules of work in a single contraction.
Now, to compare this with the energy required to lift a 78 kg person 40 cm during a chin-up, we can calculate the work using the same formula:
Work = Force × Distance
Here, the force required to lift the person is equal to their weight, which is 78 kg × 9.8 m/s^2 (acceleration due to gravity) ≈ 764.4 N. The distance lifted is 40 cm (or 0.4 meters).
Work = 764.4 N × 0.4 m = 305.76 J
Therefore, it requires approximately 306 Joules of energy to perform a chin-up with a 78 kg person.
Based on this analysis, it is clear that the work performed by the biceps muscles alone is not enough to lift a 78 kg person during a chin-up, as their work output is 60 J in a single contraction, whereas 306 J of energy is required to lift the person. This suggests that other muscles in the body, such as the back muscles, shoulder muscles, and core muscles, also contribute to the effort of performing a chin-up.