Question

The efficiency of a muscle during weight lifting is equal to the work done in lifting the weight divided by the total energy output of the muscle (work done plus internal energy dissipated in the muscle). Determine the efficiency of a muscle that lifts a \(161-\mathrm{N}\) weight through a vertical displacement of \(0.577 \mathrm{m}\) and dissipates \(139 \mathrm{J}\) in the process.

Short answer

Answer: The efficiency of the muscle during weight lifting is 40%.

Step-by-step solution

Find the work done by the muscle in lifting the weight

To determine the work done by the muscle in lifting the weight, we can use the formula: Work = Force × Displacement × cos(angle) Here, the force is the weight lifted (given as 161 N) and the displacement is the vertical distance the weight is lifted (given as 0.577 m). Since the force is acting in the same direction as the displacement, the angle between them is 0 degrees. The cosine of 0 degrees is 1. Work = 161 N × 0.577 m × 1 = 92.817 J The work done by the muscle in lifting the weight is 92.817 Joules.

Determine the total energy output of the muscle

Now, we need to find the total energy output of the muscle. This can be calculated by adding the work done in lifting the weight and the energy dissipated in the muscle during the process. The energy dissipated is given as 139 J. Total energy output = Work done in lifting the weight + Energy dissipated in the muscle Total energy output = 92.817 J + 139 J = 231.817 J The total energy output of the muscle is 231.817 Joules.

Calculate the efficiency of the muscle

With both the work done in lifting the weight and the total energy output of the muscle, we can calculate the efficiency using the formula: Efficiency = (Work done in lifting the weight) / (Total energy output of the muscle) Efficiency = (92.817 J) / (231.817 J) = 0.400 (approx) To express this as a percentage, multiply the value by 100. Efficiency = 0.400 × 100 = 40% The efficiency of the muscle during weight lifting is 40%.