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Worksheet 306

Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in the figure below, 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.


(a) The figure shows the forearm of a person holding a book. The biceps exert a force FB to support the weight of the forearm and the book. The triceps are assumed to be relaxed. (b) Here, you can view an approximately equivalent mechanical system with the pivot at the elbow joint

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 FB, that of the elbow joint is FE, that of the weights of the forearm is wa , and its load is wb. Two of these are unknown FB, so that the first condition for equilibrium cannot by itself yield FB . But if we use the second condition and choose the pivot to be at the elbow, then the torque due to FE is zero, and the only unknown becomes FB .

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 (net τ = 0) becomes

Force (Newton's second law)
Torque
Force (Newton's second law)
Torque

Note that sin θ = 1 for all forces, since θ = 90º for all forces. This equation can easily be solved for FB in terms of known quantities,yielding. Entering the known values gives

Mechanical equilibrium - 3=3 Torque example

which yields

Torque
Addition

Now, the combined weight of the arm and its load is known, so that the ratio of the force exerted by the biceps to the total weight is

Division

Discussion

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

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Angular Frequency

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, ... more

Péclet number (for mass transfer)

The Péclet number (Pe) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is named after the French ... more

Péclet number (for heat transfer)

The Péclet number (Pe) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is named after the French ... more

Worksheet 292

What is the cost of running a 0.600-kW computer 6.00 h per day for 30.0 d if the cost of electricity is $0.120 per kW ⋅ h ?

Multiplication

where t is the total consumption time, td is the days of consumption and th the hours of consumption per day

Power-average (related to Work)

where P is Power consumption rate, E is the energy supplied by the electricity company and t is consumption time

keywords:
ballistics

Multiplication

where C is the total cost and CkW is the cost per kilowatt hour

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Linear damping oscillation

Damped harmonic motion is a real oscillation, in which an object is hanging on a spring. Because of the existence of internal friction and air resistance, ... more

Jerk

In physics, jerk, also known as jolt, surge, or lurch, is the rate of change of acceleration; that is, the derivative of acceleration with respect to time, ... more

Turbulent Schmidt Number

Schmidt number (Sc) is a dimensionless number. The turbulent Schmidt number describes the ratio between the rates of turbulent transport of momentum and ... more

Mechanical Power (Displacement)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time.
The same amount of work is done when ... more

Power-average (related to Work)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. The same amount of work is done when carrying a ... more

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