C.1basic concepts 73
Addition of forces in 2 d space
A force is a vector (physical quantity that has magnitude and direction).
In a Cartesian coordinate system a 2dvectorFcan be written as:
F=Fxi+Fyj=Fcos(θ)i+Fsin(θ)j=F(cos(θ)i+sin(θ)j),
whereFis the magnitude of the force, andθis its angle relative to thex
axis,FxandFyare the components ofFin the directions of thexandy
axis, respectively, andiandjare unit vectors in these directions. IfFx
andFyare known, thenFandθcan be determined by:
F=
√
Fx^2 +Fy^2 and tan(θ) =
Fx
Fy
- Element-by-element calculations
The coefficient of frictionμcan be determined in an experiment by
measuring the forceFrequired to move a massmas shown in Figure 16.
WhenFis measured andmis known, the coefficient of friction can be
m
F
friction
Figure 16: Friction
calculated by:
μ=
F
mg,
whereg=9.81 m/s^2. Results from measuringFin six tests are given in
Table 8. Determine the coefficient of friction in each test, and the average
from all tests.
Table 8: Friction experiment results
test no. 1 2 3 4 5 6
mass (kg) 2 4 5 10 20 50
force (n) 12.5 23.5 30 61 117 294
