Problem 9 - Campbell Biology

Question

demonstrate how energy is stored in tendons during hopping, an instructor asked student volunteers to hop at a frequency that felt "natural"" and then, after resting, to hop at exactly half that frequency. Hopping was done at a standard height and volunteers" mass, \(\mathrm{O}_{2}\) consumption, and \(\mathrm{CO}_{2}\) production were measured. Here is a representative set of results calculated for one student. $$\begin{tabular}{|c|c|} \hline Frequency (hops/sec) & Energy used (joules/sec) \\ \hline 1.85 & 735 \\ \hline 0.92 & 716 \\ \hline \end{tabular}$$ The student consumed 159 joules/sec when standing. For each hop frequency, subtract this standing value from the energy used during hopping. Then divide by the hop frequency to calculate the energy cost per hop. How does the energy cost per hop differ at the two frequencies, and how might this be related to energy storage in tendons?

Step-by-Step Solution

Answer

The energy cost per hop is lower at the natural frequency, suggesting efficient energy storage in tendons.

Step 1: Calculate Net Energy Used

Subtract the energy used while standing (159 joules/sec) from the energy used during hopping at each frequency.

Step 2: Calculate Energy Cost per Hop

Divide the net energy used (calculated in Step 1) by the hop frequency for each frequency.

Step 3: Analyze the Results

Compare the energy cost per hop at the two different frequencies and provide an analysis on how this might relate to energy storage in tendons.

Key Concepts

Biomechanics

Biomechanics involves studying the mechanical aspects of living organisms. In the context of hopping and energy storage in tendons, it explores how forces act on the body and how the body generates and absorbs these forces. When you hop, tendons in your legs act like springs. They store elastic energy when you land and then release it when you take off again. This reduces the amount of work your muscles have to do, making movement more efficient. Understanding biomechanics helps us appreciate how small changes in movement, like hopping frequency, can have significant impacts on energy usage.

Metabolic Cost of Locomotion

The metabolic cost of locomotion refers to the amount of energy the body uses to move. It's directly related to how efficiently our muscles and tendons work together. Let's break down the exercise results:

• At 1.85 hops/sec, the student used 576 joules/sec for hopping after subtracting standing energy (735 - 159 joules/sec).
• At 0.92 hops/sec, the student used 557 joules/sec for hopping.

Now, we calculate the energy cost per hop:
1.85 hops/sec: Energy cost per hop = 576 joules/sec / 1.85 hops/sec ≈ 311 joules per hop.
0.92 hops/sec: Energy cost per hop = 557 joules/sec / 0.92 hops/sec ≈ 605 joules per hop.
When hopping at a natural frequency, the energy cost per hop is lower compared to hopping at half the frequency. This reveals how our body optimizes energy usage through tendons' elastic properties.

Physiology of Movement

Physiology of movement examines how the body's systems work together to produce movement. Tendons play a crucial role in this by storing and releasing energy. When you hop, your muscles contract and stretch the tendons. Upon landing, tendons absorb some of the impact energy and then spring back when you push off again. This mechanism not only aids in reducing the workload on muscles but also ensures smoother and more controlled movements. Essentially, tendons help in converting mechanical energy efficiently which otherwise would be lost as heat.

Energy Efficiency

Energy efficiency in movement is about doing more with less energy. The exercise showed that at a natural hopping frequency, the energy cost per hop was lower. This is because tendons are more effectively used at natural movement frequencies, allowing better energy storage and release. So, at the natural frequency (1.85 hops/sec), tendons recoil more efficiently, storing and returning energy optimally. In contrast, at half the frequency, tendons and muscles don't work as harmoniously, leading to higher energy usage per hop. This insight can help in designing better training regimes and understanding locomotion in various species.