# 9.6 Forces and torques in muscles and joints

 Page 1 / 6
• Explain the forces exerted by muscles.
• State how a bad posture causes back strain.
• Discuss the benefits of skeletal muscles attached close to joints.
• Discuss various complexities in the real system of muscles, bones, and joints.

Muscles, bones, and joints are some of the most interesting applications of statics. There are some surprises. Muscles, for example, exert far greater forces than we might think. [link] shows a forearm holding a book and a schematic diagram of an analogous lever system. The schematic is a good approximation for the forearm, which looks more complicated than it is, and we can get some insight into the way typical muscle systems function by analyzing it.

Muscles can only contract, so they occur in pairs. In the arm, the biceps muscle is a flexor—that is, it closes the limb. The triceps muscle is an extensor that opens the limb. This configuration is typical of skeletal muscles, bones, and joints in humans and other vertebrates. Most skeletal muscles exert much larger forces within the body than the limbs apply to the outside world. The reason is clear once we realize that most muscles are attached to bones via tendons close to joints, causing these systems to have mechanical advantages much less than one. Viewing them as simple machines, the input force is much greater than the output force, as seen in [link] .

## Muscles exert bigger forces than you might think

Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in [link] , and compare this force with the weight of the forearm plus its load. You may take the data in the figure to be accurate to three significant figures.

Strategy

There are four forces acting on the forearm and its load (the system of interest). The magnitude of the force of the biceps is ${F}_{\text{B}}$ ; that of the elbow joint is ${F}_{\text{E}}$ ; that of the weights of the forearm is ${w}_{\text{a}}$ , and its load is ${w}_{\text{b}}$ . Two of these are unknown ( ${F}_{\text{B}}$ and ${F}_{\text{E}}$ ), so that the first condition for equilibrium cannot by itself yield ${F}_{\text{B}}$ . But if we use the second condition and choose the pivot to be at the elbow, then the torque due to ${F}_{\text{E}}$ is zero, and the only unknown becomes ${F}_{\text{B}}$ .

Solution

The torques created by the weights are clockwise relative to the pivot, while the torque created by the biceps is counterclockwise; thus, the second condition for equilibrium $\left(\text{net}\phantom{\rule{0.25em}{0ex}}\tau =\text{0}\right)$ becomes

${r}_{2}{w}_{\text{a}}+{r}_{3}{w}_{\text{b}}={r}_{1}{F}_{\text{B}}.$

Note that $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =1$ for all forces, since $\theta =\text{90º}$ for all forces. This equation can easily be solved for ${F}_{\text{B}}$ in terms of known quantities, yielding

${F}_{\text{B}}=\frac{{r}_{2}{w}_{\text{a}}+{r}_{3}{w}_{\text{b}}}{{r}_{1}}.$

Entering the known values gives

${F}_{\text{B}}=\frac{\left(0\text{.}\text{160}\phantom{\rule{0.25em}{0ex}}\text{m}\right)\left(2\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)+\left(0\text{.}\text{380}\phantom{\rule{0.25em}{0ex}}\text{m}\right)\left(4\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)}{0\text{.}\text{0400}\phantom{\rule{0.25em}{0ex}}\text{m}}$

which yields

${F}_{\text{B}}=\text{470 N}.$

Now, the combined weight of the arm and its load is $\left(\text{6.50 kg}\right)\left(\text{9.80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)=\text{63.7 N}$ , so that the ratio of the force exerted by the biceps to the total weight is

$\frac{{F}_{\text{B}}}{{w}_{\text{a}}+{w}_{\text{b}}}=\frac{\text{470}}{\text{63}\text{.}7}=7\text{.}\text{38}.$

Discussion

This means that the biceps muscle is exerting a force 7.38 times the weight supported.

#### Questions & Answers

hello friends what is hadronic heating systems
Hydronics is the use of a liquid heat-transfer medium in heating and cooling systems.
Balogun
what is mass
is the amount of an object
Sendawula
mass is the measure of the inertia of a body
Ishmeal
advantages of CRO over ordinary voltmeter
what is the difference between displacement and distance?!
what is equilibrium
If a system is said to be under equilibrium whenever there is no force act upon it... And it remain in its initial stage..
soniya
what is velocity
Ahmed
time rate of displacement of a body is called velocity
velocity is the gradient of acceleration time graph
Etana
actually equilibrium is when a body is in total balance where in no external force is acting on it. Or the forces on the left hand side equal those on the left hand side and downward forces equal upward forces & anticlockwise moment equal clockwise moment about the same point.
Etana
I mean left hand side and right hand side
Etana
What is conductivity
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
Cffrrcvccgg
how to find magnitude and direction
how to caclculate for speed
Arjune
derivation of ohms law
derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
is there really flow of electrons exist?
babar
Yes It exists
Cffrrcvccgg
explain plz how electrons flow
babar
if electron flows from where first come and end the first one
babar
an electron will flow accross a conductor because or when it posseses kinectic energy
Cffrrcvccgg
electron can not flow jist trasmit electrical energy
ghulam
free electrons of conductor
ankita
electric means the flow heat current.
electric means the flow of heat current in a circuit.
Serah
What is electric
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
electric means the flow of electric current through conductor
the continuos flow of electrons in a circuit is called electric
ANUBHA
electric means charge
ghulam
electric means current
flow of current.
Sendawula
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
D=1km=1000m t=5mins×60secs=300sec s=d/t=3.333m/s
Daniel
I think Daniel Glorious is ryt
Amalia
why we cannot use DC instead of AC in a transformer
becuse the d .c cannot travel for long distance trnsmission
ghulam
what is physics
branch of science which deals with matter energy and their relationship between them
ghulam
Life science
the
what is heat and temperature