A part of a machine consists of two arms OA and AP so that the angle between OA and AP is always half of that between OA and the -y-axis. The following demonstrates the movement of these two arms.
A part of a machine consists of two arms OA and AP so that the angle between OA and AP is always half of that between OA and the -y-axis. The following demonstrates the movement of these two arms.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
![A part of a machine consists of two arms OA and AP so that the angle between OA and AP is always half of that between O.A and the --axis. The following demonstrates the movement of these two arms.
a.
At a = Q rad, location =
C.
Path of P
x(a):
Y(a) =
PO
→
Hint: (x(a), (y(a)) = OP = OA+AP. Try to set up OA and AP using angles in standard position.
Length =
a
Arm O.A is 3.7 cm long and arm AP is 5.4 cm long.
Find the location of P (in cm) when a = 0 rad, rad, /2 rad and /3 rad. Round your answers to at least 2 decimal places and enter them as points (x, y).
cm
a/2
O
A
At a rad, location =
At a = π/2 rad, location =
At a = π/3 rad, location =
b. Find the parametric equations (a) and y(a) (in cm) that give the path of P for all & € [0₂]. The parameter a should represent the angle given in the diagram. Check your answer with the results from part (a). Use exact values
or round the values to at least 5 significant figures.
a = 0.7
Drag the slider to move the points. Try to reload the page if the diagram is not displayed correctly.
X
Find the length of the part of the parametric curve (i.e. the path of P) from a = 0 rad to the point where the parametric curve crosses the +-axis. Round your answer to at least 3 sig figs. You will need to use a computer for this
part.
4
C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F913f25bd-b2eb-4e87-8f80-5ec552fc3aee%2F9a9749e5-51a7-4363-83b3-136d34825f00%2Fxhpiroe_processed.png&w=3840&q=75)
Transcribed Image Text:A part of a machine consists of two arms OA and AP so that the angle between OA and AP is always half of that between O.A and the --axis. The following demonstrates the movement of these two arms.
a.
At a = Q rad, location =
C.
Path of P
x(a):
Y(a) =
PO
→
Hint: (x(a), (y(a)) = OP = OA+AP. Try to set up OA and AP using angles in standard position.
Length =
a
Arm O.A is 3.7 cm long and arm AP is 5.4 cm long.
Find the location of P (in cm) when a = 0 rad, rad, /2 rad and /3 rad. Round your answers to at least 2 decimal places and enter them as points (x, y).
cm
a/2
O
A
At a rad, location =
At a = π/2 rad, location =
At a = π/3 rad, location =
b. Find the parametric equations (a) and y(a) (in cm) that give the path of P for all & € [0₂]. The parameter a should represent the angle given in the diagram. Check your answer with the results from part (a). Use exact values
or round the values to at least 5 significant figures.
a = 0.7
Drag the slider to move the points. Try to reload the page if the diagram is not displayed correctly.
X
Find the length of the part of the parametric curve (i.e. the path of P) from a = 0 rad to the point where the parametric curve crosses the +-axis. Round your answer to at least 3 sig figs. You will need to use a computer for this
part.
4
C
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