DATA You are a mechanical engineer working for a manufacturing company. Two forces, F → 1 and F → 2 , act on a component part of a piece of equipment. Your boss asked you to find the magnitude of the larger of these two forces. You can vary the angle between F → and F → from 0° to 90° while the magnitude of each force stays constant. And. you can measure the magnitude of the resultant force they produce (their vector sum), but you cannot directly measure the magnitude of each separate force. You measure the magnitude of the resultant force for four angles θ between the directions of the two forces as follows: (a) What is the magnitude of the larger of the two forces? (b) When the equipment is used on the production line, the angle between the two forces is 30.0°. What is the magnitude of the resultant force in this case?
DATA You are a mechanical engineer working for a manufacturing company. Two forces, F → 1 and F → 2 , act on a component part of a piece of equipment. Your boss asked you to find the magnitude of the larger of these two forces. You can vary the angle between F → and F → from 0° to 90° while the magnitude of each force stays constant. And. you can measure the magnitude of the resultant force they produce (their vector sum), but you cannot directly measure the magnitude of each separate force. You measure the magnitude of the resultant force for four angles θ between the directions of the two forces as follows: (a) What is the magnitude of the larger of the two forces? (b) When the equipment is used on the production line, the angle between the two forces is 30.0°. What is the magnitude of the resultant force in this case?
DATA You are a mechanical engineer working for a manufacturing company. Two forces,
F
→
1
and
F
→
2
, act on a component part of a piece of equipment. Your boss asked you to find the magnitude of the larger of these two forces. You can vary the angle between
F
→
and
F
→
from 0° to 90° while the magnitude of each force stays constant. And. you can measure the magnitude of the resultant force they produce (their vector sum), but you cannot directly measure the magnitude of each separate force. You measure the magnitude of the resultant force for four angles θ between the directions of the two forces as follows:
(a) What is the magnitude of the larger of the two forces?
(b) When the equipment is used on the production line, the angle between the two forces is 30.0°. What is the magnitude of the resultant force in this case?
Two vectors are given by a = 1.5î−4.0ĵ and b = −11.9î + 8.1ĵ. What is the magnitude of b?
i already found out magnitude of b is 1.44
but how to calculate the angle between vector b and the positive x-axis?
Two vectors are given by A = 4 î + 7 j and B = -6 î + 2 j.
(a) Find A x B.
(b) Find the angle between A and B
Part 1 of 4 - Conceptualize
A is in the first quadrant and B is in the second quadrant of the xy plane. The cross product A x B points along the positive z axis. We estimate the magnitude of this cross product to be less than the
product of the magnitudes of the vectors.
Part 2 of 4 - Categorize
We express the cross product A x B in determinant form and evaluate the determinant. Then we use the magnitude of the cross product AB sin 0 to find 0.
The cross product of the two vectors A and B can be expressed in determinant form.
î
x B
4
(a) Evaluating the determinant gives the following. Remember to keep track of the signs!
o) + 3(0 –
A x B
=
Determine the angles made by the vector V = -60i + 44j with the positive x- and y-axes. Write the unit vector n in the direction of V.
Answers:
0x =
ey=
n=
i+
i
i
i
i
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