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?
the following example is given:
vector1 =+(60.0N)i+(103.9N)j
vector2 =+(75.2N)i−(27.4N)j
vector 3=−(100.0N)i+(0.0N)j
vecor net =+(35.2N)i+(76.5N)j
Convert this net force to polar coordinates; that is, find the total vector magnitude and angle.
If three forces, 1 , 2 , and 3 , are in equilibrium, what is the relationship between the sum of the first two forces and the third force? Write your answer as an equation.
onsider the vector = −(51.7 N)i + (63.9 N)j
(a) Convert this value to polar coordinates (magnitude and angle).
(b) When converting this to polar coordinates, what answer does your calculator give
you for the angle of the vector? Explain whether this is correct or not (including the correct angle if applicable).
Find the angles that vector
D = (2.2î − 4.5ĵ + 1.3) m makes with the +x-, +y-, and +z-axes. (Enter the smallest positive angle for each in degrees.)
?x=
°?y=
°?z =
Consider the following two vectors:U = 1.3i + 2.2j + 4.1kV = -5.5i - 6.5j + 11.3k
What is the magnitude of the vector U?
What is the magnitude of the vector V?
What is the angle between U and V? Enter this as an angle between 0 and 90°.
Chapter 1 Solutions
University Physics with Modern Physics, Books a la Carte Edition (14th Edition)
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