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In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also ... more
A perimeter is a path that surrounds a two-dimensional shape.The perimeter of a circle or ellipse is called its circumference. A circle can be defined as ... more
Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then ... more
In geometry, a deltoid, also known as a tricuspoid or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point ... more
In geometry, a deltoid, also known as a tricuspoid or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point ... more
An ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and ... more
Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more
Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more
A perimeter is a path that surrounds a two-dimensional shape. The word comes from the Greek peri (around) and meter (measure). The term may be used either ... more
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more
Strategy
The force is equal to the weight supported:
and the cross-sectional area of the upper leg bone(femur) is:
To find the change in length we use the Young’s modulus formula. The Young’s modulus reference value for a bone under compression is known to be 9×109 N/m2. Now,all quantities except ΔL are known. Thus:
Discussion
This small change in length seems reasonable, consistent with our experience that bones are rigid. In fact, even the rather large forces encountered during strenuous physical activity do not compress or bend bones by large amounts. Although bone is rigid compared with fat or muscle, several of the substances listed in Table 5.3(see reference below) have larger values of Young’s modulus Y . In other words, they are more rigid.
Reference:
This worksheet is a modified version of Example 5.4 page 188 found in :
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/
The quantity h = (a-b)2/(a+b)2 is often used in elliptical circumference calculations e.g in Ramanujan formula for the Circumference of an Ellipse.
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The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The circumcenter of a triangle ... more
The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The circumcenter of a triangle ... more
The law of sines, sine law, sine formula, or sine rule relates the sine of an angle to the opposite side of an arbitrary triangle and the diameter of the ... more
Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass.
A
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Slant height is the height of any slant triangle of the regular pyramid, or the distance from the apex, down the side, to a point on the base ... more
In solid mechanics, torsion is the twisting of an object due to an applied torque. The torsion constant is a geometrical property of a bar’s ... more
Description
A cone is an n-dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or ... more
In optics, particularly as it relates to film and photography, depth of field (DOF) is the distance between the nearest and ... more
In optics, particularly as it relates to film and photography, depth of field (DOF) is the distance between the nearest and ... more
The Sagnac effect (also called Sagnac interference), named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is ... more
In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.
It was first ... more
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. ... more
Calculates the volume of a sphere. A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a ... more
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Calculate the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 45.0 cm long and 2.00 cm in radius.