Homework 7.1b solutions
1
The diagrams show situations in which multiple forces act on a particle1 or point-mass marked
with a blob. For each situation, calculate the magnitude and direction (relative to the horizontal) of
the resultant force.
(a)
2.0 N
3.1 N
magnitude: _____ N
direction: _____  anticlockwise2 to horizontal
magnitude: _____ N
direction: _____  anticlockwise to horizontal
(b)
16.0 N
6.0 N
(c)
2.0 N
3.0 N
1.0 N
magnitude: _____ N
2
1
direction: _____  anticlockwise to horizontal
(a)
Calculate the magnitude and direction of the resultant force on a particle which is acted on by a
force of 4.0N and a force of 10N given that the forces are:
In the same direction
(b)
In opposite directions
A particle is “an object which is small in comparison with other sizes or lengths... this means that the mass can be considered to be
concentrated at a single point... [and] we can ignore the rotational effect of any forces acting on it...” (Hooker, etal, Mechanics 1
for Edexcel AS and A level Modular Mathematics, 2008)
2
anticlockwise (U.K.) = counter-clockwise (U.S.)
2 (c)
Perpendicular to one another. (At right-angles)
3
A crane is used to lift one end of a steel beam off the ground as shown in the diagram below. When
the cable attached to the end of the beam is inclined 20 to the vertical, the force of the cable on the
beam is measured to be 6.5 kN.
Calculate the horizontal and vertical components of this force.
4
A yacht (sailing boat) is moving due north as a result of a horizontal force of 350 N in a direction of
bearing 040 due to a prevailing wind. The diagram below shows this:
(a)
Calculate the component of the force of the wind which is:
In the same direction as the yacht is moving (i.e. due north)
(b)
Perpendicular to the direction of motion (i.e. due east)
Hints and solutions: http://mathsurgery.wikispaces.com/Phys+AS+unit+2+section+7.1+-+vectors+and+scalars