# Homework Help: Static loads on human body

1. Sep 17, 2011

### mahkum

This question requires you to model the human body so that you can analyse the static loads, (comparing the pilates position and the abdominal sit-up position, figure above)
Using the body mass ‘M’ of 94 kg and a body height ‘h’ of 1.73 metres, establish which exercise requires the most effort from the abdominal muscles to hold the position shown and by what factor.
The table shows the details of body parts so that comparison between the two positions can be performed.

Table:
Body Parts Mass in terms of M,
the person’s mass Length, I, in terms of h, the person’s height Position of cetnre of mass along from upper end of the body part
Thighs 0.2M 0.24h 0.43/
Shanks + feet 0.13M 0.29h 0.47/
Head + neck 0.08M 0.182h 0.36/
Trunk + arms 0.59M 0.332h 0.50/

For the purpose of this question, the mass and position of the hands and arms can be considered to be part of the trunk. Place your origin at the join between the bottom of the trunk and the top of the thighs, i.e. where the abdominal muscles act. Assume that the angle the legs in the pilates position makes with the floor is 60o , whereas the angle the head and neck make with the floor is 45o.
For the sit-up exercise, the trunk is at 30o to the floor and the legs are bent so that the knee joint makes a 90o bend.
To gain full marks:
a) Give valid assumptions on how you model the body components
b) Sketch clear, fully labelled free-body diagrams of the two positions, showing the known and unknown external acting forces and moments
c) Provide accurate equilibrium equations by resolving the loads and moments
d) Calculate the unknown external loads and moments
e) Calculate the moment provided by the abdominal muscles to achieve the position

2. Relevant equations

3. The attempt at a solution