fisica1-youn-e-freedman-exercicios-resolvidos

4.1: a) For the magnitude of the sum to be the sum of the magnitudes, the forces must
be parallel, and the angle between them is zero. b) The forces form the sides of a right
isosceles triangle, and the angle between them is 90 ° . Alternatively, the law of cosines
may be used as
2
2
( 2F
) − 2F
cosθ
,
2 2
F + F =
from which cosθ = 0 , and the forces are perpendicular. c) For the sum to have 0
magnitude, the forces must be antiparallel, and the angle between them is 180 ° .
4.2: In the new coordinates, the 120-N force acts at an angle of 53 ° from the − x -axis,
or 233 ° from the + x -axis, and the 50-N force acts at an angle of 323 ° from the + x -
axis.
a) The components of the net force are
R = ( 120 N)cos 233° + (50 N)cos 323°
= −32 N
R
x
y
= ( 250 N) + (120 N)sin 233° + (50 N)sin 323°
= 124 N.
2 2
124
b) R = R x
+ Ry
= 128 N,
arctan( − 32
) = 104°
. The results have the same magnitude,
and the angle has been changed by the amount ( 37° ) that the coordinates have been
rotated.
4.3: The horizontal component of the force is ( 10 N)cos 45° = 7.1 N to the right and the
vertical component is ( 10 N)sin 45° = 7.1 N down.
4.4: a) F x
= F cos θ , where θ is the angle that the rope makes with the ramp ( θ = 30°
in
F N
this problem), so F F r
=
x
=
60.0
69.3 N.
=
cos θ cos 30°
=
b) F = F sin θ = F tanθ
= 34.6 N.
y
x