Chapter 2.7-2.8 Position Vectors and Force Vector Directed along a line

Newton's Law of Gravitational Attraction is shown below:

�=��1�2�2

where m₁ and m₂ are the masses of two distinct particles. The force F is defined as the weight, W, of a particle when m₁ is the mass of the particle and m₂ is:

the mass of the Earth

Identify the scalar terms in the equation:

F=F(r/r)

F, r

unit vector magnitude?

magnitude and its dimensions the equation is dimensionally homogenous.

F=F(r/r)

F=F(u)

A unit vector has a magnitude of 

1

What are the units of a unit vector?

unitless

Position vectors have units of______

Length

Always subtract the tail from the head

r=head-tail

Force vector formula

F=FU=F(r/r)

Unit vectors are direction vectors that have magnitude of ____ (unit-less) and, therefore, only give information about direction

1

If a force is directed along a line, then we can represent the force vector in Cartesian coordinates by
using a unit vector and the force’s magnitude. Steps:

1) Find the position vector, r, along two points on that line.
2) Find the unit vector describing the line’s direction, u=r/|r|.
3) Multiply the unit vector by the magnitude of the force, F=|F|U.

Given: The FB and FC force along the
cables AB and AC, respectively.
Find: The magnitude of the resultant
force.

FR=1.18 kN

a: 66.1

b: 92.9

c: 156

Express each of the forces in Cartesian vector form and determine the magnitude and coordinate
direction angles of the resultant force.

Fr: 73.5lb

a: 100

b; 159

c: 71.9