52) Displacement di is in the yz plane 63.0° from the positive direction of the y axis, has a positive z component, and has a magnitude of 4.50 m. Displacement dz is in the xz plane 30.0° from the positive direction of the x axis, has a positive z com- ponent, and has magnitude 1.40 m. What are (a) d d2, (b) d x d2, and (c) the angle between d and d?
52) Displacement di is in the yz plane 63.0° from the positive direction of the y axis, has a positive z component, and has a magnitude of 4.50 m. Displacement dz is in the xz plane 30.0° from the positive direction of the x axis, has a positive z com- ponent, and has magnitude 1.40 m. What are (a) d d2, (b) d x d2, and (c) the angle between d and d?
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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52) Displacement di is in the yz plane 63.0° from the positive
direction of the y axis, has a positive z component, and has a
magnitude of 4.50 m. Displacement d, is in the xz plane 30.0°
from the positive direction of the x axis, has a positive z com-
ponent, and has magnitude 1.40 m. What are (a) d d,, (b)
d, x d2, and (c) the angle between d, and d,?
3-52
XZ- YZ VeRs
a di is inthe YZ plane :
di
Oi=63°, di =4.5m
• di is a the XZ plaue.:
Dz=30°
dh= 14 m
す。
dz
Fid ther components:
Xi=0, Y,= di coso, = +2.04296m ņ +2004 m
+4.00a53 m
~ +4.01 m
%3D
Y2=0, Xz = dz cosor = +l.2/244m
Br=dz seüßz= +0.7m
N +1.21 m
2
a) di -di = xte4 44E+2,82=+2.80667 m
ņ 12.81m²
D xお
(1.43007 m²) i +(4.86131 wi?) Ĵ
+ (- 247697 m²) ĥ
N TI43 m²) ? + (4.86mt)+(-248 m²) Î
) dr-tz = di dz coso
COO =
didz
O445503
O = 63.5445° N 63.50
%3D
s necessary for static equilibrium to exist
(c) In static equilibrium, the net torque about any point is zero
(d) An object in equilibrium cannot be moving
The series is valid only if is in radians. Notice that if is small (0<<1), cach term in the series
is much less in magnitude than the previous tem. The small angle annaximationamaunts
using only the tinst term of the series
nsF-0 and Ei 0must be satisfied
If eis small, thc error generated by the small angle approximation i
and the fractional eror is roughly 06. For example, the error is le
0.01 or 6<0.2 radians. In fact the err for e-0.2 radians is 0.7 p
y and sufficient conditions for static equilibrium a
2 / 2
sEF-0 and r-0 must be satisfied
Questions and Example Problems from
Question
Which of the following describe o for the SHM of the figure below (a) -<d<2,
asE Al 0Uourcan be moving with constant speed (translational or rotational)
when the conditionsF=0 and -0 are satisfied
71
→)
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