Q2/32/0/N/12
3 Fig. 2.1 is a head-on view of an airliner flying at constant speed in a circular horizontal
The centre of the circle is to the left of the diagram.
Fig. 2.1
(a) On Fig. 2 1. draw the resultant force acting on the airliner Explain your answer
(b) The weight of the airliner is 1.20 * 106 N and there is an aerodynamic lift force of
1.39 - 10 N acting at 30° to the left of the vertical.
By drawing a scale vector diagram, or otherwise, show that the resultant of these two
forces is in the same direction as the resultant force you drew in (a).
Answers
Explanation:
4 ed) 3.1 A point is located in a polar coordinate system by the coordinates r = 2.50 m and = 35.0o .
Find the cartesian coordinates of this point, assuming the two coordinate systems have the same origin.
Conceptual Questions
Q3.3 The magnitudes of two vectors A and B are A = 5 units and B = 2 units. Find the largest and smallest values possible for the resultant vector R = A + B.
If vectors A and B point in the same direction, the magnitude of R is 7 units.
If vectors A and B point in the opposite direction, the magnitude of R is 3 units.
Q3.5 If the component of vector A along the direction of vector B is zero, what can you conclude about these two vectors.
The two vectors are perpendicular (it can also be said they are orthogonal).
Q3.6 Can the magnitude of a vector have a negative value?
No, a magnitude is always positive or zero.
Q3.7 Which of the following are vectors and which are not:
force --> vector
temperature --> scalar
volume --> scalar
rating of a television show --> scalar
height --> vector (a well would have a negative height)
velocity --> vector
age --> scalar
Q3.8 Under what circumstances would a nonzero vector lying in the xy plane ever have components that are equal in magnitude?
If the vector lies along the 45o line in the first or third quadrants the two components will be exactly equal. If the vector lies along the 45o line in the second or fourth quadrants the two components will be equal in magnitude.
Problems from the current (5th) edition of Serway and Beichner.
3.2 Two points in the xy plane have cartesian coordinates (2.00, - 4.00) m and ( - 3.00, 3.00) m.
Determine
(a) the distance between these points and
We can find the distance between the two points from the Pythagorean Theorem,
distance = d = SQRT [ (x)2 + (y)2 ]
d = SQRT [ ( - 3.00 - 2.00 )2 + ( 3.00 - ( - 4.00) )2 ] m
d = SQRT [ ( - 5 ) 2 + ( 7.00) 2 ] m
d = SQRT [ 25.00 + 49.00 ] m
d = SQRT [ 74.00 ] m
d = 8.60 m
(b) their polar coordinates
P1 = (2.00, - 4.00) m
P1's distance from the origin, or its radius r1, is
r1 = SQRT [ (2.00)2 + ( - 4.00 )2 ] m = SQRT [ 4 + 16 ] m = SQRT [ 20 ] m
r1 = 4.47 m
tan [1 ] = opp/adj = y1 / x1 = ( - 4) / 2 = - 2
1 = - 63.4o
Answer:
horizontal by eye
arrow to left
idea of airliner accelerating/changing direction AND caused by force in that
direction o.w.t.t.e. OR centripetal force
OR force/acceleration towards centre of circle