'

Search results

Found 104 matches
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

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

Magic cube (simple)

In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a number of integers arranged in a n x n x n pattern such that the ... more

Sine of the sum of two angles (Bhāskara formula)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Cosine of the sum of two angles (Bhāskara formula)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Amagat's law

Amagat’s law or the Law of Partial Volumes of 1880 describes the behaviour and properties of mixtures of ideal (as well as some cases of non-ideal) ... more

Sine of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Tangent of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Cosine of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Sum of natural numbers raised to the fourth power

The formula is a special case of general Faulhaber’s formula and gives the sum of natural consecutive numbers raised to the fourth power,(starting ... more

Sum of natural numbers raised to the fifth power

he formula is a special case of general Faulhaber’s formula and gives the sum of natural consecutive numbers raised to the fifth power,(starting with 1), ... more

Sum of the infinite terms

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

Secant of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Cosecant of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Magic hypercube

In mathematics, a magic hypercube is the k-dimensional generalization of magic squares, magic cubes and magic tesseracts; that is, a number of integers ... more

Tangent of the sum of two angles (Bhāskara formula)

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Specific Orbital Energy

In the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual ... more

Sum of consecutive (triangular) cubes (Nicomachus's theorem)

In number theory, the sum of the first n cubes is the square of the nth triangular number. The sequence of squared triangular numbers is

0, 1, 9, ... more

Sum of consecutive (pyramidal) squares

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square ... more

Resistances connected in series

In a series configuration, the current through all of the resistors is the same, but the voltage across each resistor will be in proportion to its ... more

Magic square

In recreational mathematics, a magic square is an arrangement of distinct numbers, usually integers, in a square grid, where the numbers in each row, and ... more

Mechanical equilibrium - 3=3 Torque example

As applied to a rigid body,a standard definition of mechanical equilibrium is:
A rigid body is in mechanical equilibrium when the sum of all forces on ... more

Inductors connected in series

Components of an electrical circuit or electronic circuit can be connected in many different ways. The two simplest of these are called series and parallel ... more

In any convex quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals plus four times the square of ... more

Net present value

In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present ... more

British flag theorem (Rectangles)

Rectangle is any quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its ... more

Semiperimeter of a triangle

The semi sum of the length of a triangle’s sides

... more

Inductors in Series

Components of an electrical circuit or electronic circuit can be connected in many different ways. The two simplest of these are called series and parallel ... more

Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is “worth” at a ... more

Inductors in Parallel

Components of an electrical circuit or electronic circuit can be connected in many different ways. The two simplest of these are called series and parallel ... more

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

...can't find what you're looking for?

Create a new formula

Search criteria:

Similar to formula
Category