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Center of mass (for two particles)

The center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero.
... more

Free-fall time (radial trajectory of an ellipse with an eccentricity of 1 and semi-major axis R/2)

The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to ... more

Worksheet 302

In the wheelbarrow of the following figure the load has a perpendicular lever arm of 7.50 cm, while the hands have a perpendicular lever arm of 1.02 m.(a) What upward force must you exert to support the wheelbarrow and its load if their combined mass is 45.0 kg? (b) What force does the wheelbarrow exert on the ground?


(a) In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot is the wheel’s axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. (b) In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel’s load) is less than the input force (from the hand nearest the load), because the input is exerted closer to the pivot than is the output.

Strategy

Here, we use the concept of mechanical advantage.

Force (Newton's second law)
Mechanical Advantage - Law of Lever
Subtraction

Discussion
An even longer handle would reduce the force needed to lift the load. The MA here is:

Division

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/

Length of an arc of a circle (central angle in radians)

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

Euler's theorem (excircles)

The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is ... more

Area between a parabola and a chord

Parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped. The area enclosed between a parabola and a chord is two-thirds ... more

Radius of a Sears–Haack Body

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Mean anomaly - function of mean longitude

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... more

Half Sphere Mass

A sphere is defined mathematically as the set of points that are all the same distance r from a given point in three-dimensional space. This distance r is ... more

True anomaly

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1- The orbit of ... more

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