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Vector Applications. Created by: Jeffrey Bivin Edited by: Aaron Rogers [email protected]. Last Updated: February 14, 2011. - PowerPoint PPT Presentation
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Jeff Bivin -- LZHSJeff Bivin -- LZHS
Vector Applications
Created by: Jeffrey BivinEdited by: Aaron Rogers
Last Updated: February 14, 2011
Jeff Bivin -- LZHS
Find the component form of the vector that represents the velocity of an airplane descending at a speed of 150 mph at an angle of 30o below the westward horizontal.
150 mph30o
210o0 0150 cos 210 , sin 210v
3 1150 ,2 2
v
75 3, 75v
Jeff Bivin -- LZHS
35o
An airplane is traveling at a speed of 600 mph with a bearing of N35oW at a fixed altitude and no wind. As the plane crosses the Mississippi river, it encounters a wind blowing with a velocity of 60 mph in the direction of N40oE. What is the resultant speed and direction of the plane?
600 mph
125o
0 0600 cos125 , sin125p
40o50o
60 mph
600 mph
0 0600cos125 , 600sin125p
0 060 cos50 , sin 50w 0 060cos50 , 60sin 50w
0 0 0 0600cos125 60cos50 , 600sin125 60sin 50v p w
305.579, 537.454v
plane wind result
result
60 mph
Jeff Bivin -- LZHS
35o600 mph
125o
40o
60 mph 50o
600 mphplane wind result
305.579, 537.454v
2 2305.579 537.454v
618.252v mph
537.454tan305.579
60.379 180o o
119.621o
29.621oBearing N W
result
Jeff Bivin -- LZHS
Joey is playing tug of war with his two best friends. He is pulling with a force of 60N at 210o. Simon exerts a force of 30N at 45o. Austin exerts a force as well. To achieve equilibrium and thus, not lose the game, what is the force Austin must exert and at what angle?
60 N
210o 0 01: 60 cos 210 , sin 210Joey v
45o0 0
2: 30 cos45 , sin 45Simon v 30 N
3??? : cos , sinAustin v f
1 2 3: 0, 0For equilibrium v v v
Jeff Bivin -- LZHS
60 N
210o 0 01: 60 cos 210 , sin 210Joey v
45o 0 02: 30 cos45 , sin 45Simon v 30 N
3??? : cos , sinAustin v f
1 2 3: 0, 0For equilibrium v v v
: 60cos 210 30cos 45 cos 0o ox component f
: 60sin 210 30sin 45 sin 0o oy component f
30.748 cos 0f cos 30.748f
8.787 sin 0f sin 8.787f
Jeff Bivin -- LZHS
60 N
210o
0 01: 60 cos 210 , sin 210Joey v
45o
0 02: 30 cos 45 , sin 45Simon v
30 N3: cos , sinAustin v f
sin 8.787f cos 30.748f
2 23 cos sin v f f
1 8.787: tan30.748
direction
15.95
2 230.748 8.787
31.98 N
Jeff Bivin -- LZHS
A 10,000 pound object is suspended on a wire tied to two poles. The angle between the horizontal and the wire to the shorter pole is 22o. The angle between the horizontal and the wire to the taller pole is 49o. Find the tension in the cable to each pole.
0 01 1: cos 49 , sin 49tall w f
0 02 2: cos158 , sin158short w f
3: 10000 cos 270 , sin 270o oweight w
1 2 3: 0, 0For equilibrium w w w
10000 lbs
22o 49o
f1f2
158o
Jeff Bivin -- LZHS
0 01 1: cos 49 , sin 49tall w f
0 02 2: cos158 , sin158short w f
3: 10000 cos 270 , sin 270o oweight w
1 2 3: 0, 0For equilibrium w w w
10000 lbs
22o 49o
f1f2
1 2: cos 49 cos158 10000cos 270 0o o ox component f f
1 2: sin 49 sin158 10000sin 270 0o o oy component f f
1 2cos 49 cos158 0 o of f
1 2sin 49 sin158 10000 o of f
0
10000
Jeff Bivin -- LZHS
0 01 1: cos 49 , sin 49tall w f
0 02 2: cos158 , sin158short w f
3: 10000 cos 270 , sin 270o oweight w
10000 lbs
22o 49o
f1f2
1 2cos 49 cos158 0 o of f
1 2sin 49 sin158 10000 o of f
Put in a Matrix and use A-1Bor can use RREF
1 9806.09 .f lbs
2 6938.62 .f lbs
Jeff Bivin -- LZHS
Jeff Bivin -- LZHS
A 500 lb cart sits on a ramp inclined at 23o. What is the force is required to keep the cart from rolling down the ramp?
0cos67500
f
0500 cos67 f
500 lbs
23o
500 lbs
67o
195.366 .lbs fGravityNormal
Vector
f
Jeff Bivin -- LZHS
A 1500 lb cart sits on a ramp inclined at 18o. What is the force is required to keep the cart from rolling down the ramp?
0cos721500
f
01500 cos72 f
1500 lbs
18o
1500 lbs
72o
463.525 .lbs f
f
Jeff Bivin -- LZHS
A mover exerts a force of 55 pounds in a horizontal direction on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate.
55 lbs
55 20work lbs ft
1100work ft lbs
20 ft.𝑤𝑜𝑟𝑘= 𝒇𝒐𝒓𝒄𝒆 · 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
Jeff Bivin -- LZHS
A mover exerts a force of 55 pounds at an angle of 45o below the horizontal on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate.
45o
55 lbs
55 cos 45 , sin 45 20 cos0 , sin 0o o o owork
777.817work ft lbs
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖 𝑠𝑡𝑎𝑛𝑐𝑒
55 cos 45 , sin 45 20 1, 0o owork
55cos 45 20 55sin 45 0o owork
55cos 45 , 55sin 45 20, 0o owork
20 ft.
Jeff Bivin -- LZHS
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
A sled is to be pulled by a rope at a 37o angle above the horizontal with a force of 63 lbs.. Find the amount of work done to move the sled 15 feet.
37o63 lbs
0 0 0 063 cos37 , sin37 15 cos0 , sin 0work
754.711work ft lbs
15 ft.
0 063 cos37 , sin 37 15 1, 0work
0 063cos37 15 63sin 37 0work
0 063cos37 , 63sin 37 15, 0work
Jeff Bivin -- LZHS
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
A mover exerts a horizontal force of 35 pounds on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13o above the horizontal. Find the work done on the crate.
13o
35 lbs
35 cos0 , sin 0 40 cos13 , sin13o o o owork
1364.118work ft lbs
40 ft.
35,0 40cos13 , 40sin13o owork
35 40cos13 0 40sin13o owork
35 1, 0 40 cos13 , sin13o owork
Jeff Bivin -- LZHS
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
A mover exerts a force of 35 pounds parallel to the ramp on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13o above the horizontal. Find the work done on the crate.
13o35 lbs
35 40work lbs ft
1400work ft lbs Note: The force is in the same direction of
the movement. Therefore, all the
force is moving the crate.
Jeff Bivin -- LZHS
A mover exerts a force of 35 pounds on a crate at an angle of 20o below the horizontal as it is pushed up a ramp that is 50 feet long and inclined at an angle of 23o above the horizontal. Find the work done on the crate.
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒23o
35 lbs
35 cos 20 , sin 20 50 cos 23 , sin 23o o o owork
1279.869work ft lbs
50 ft.
35cos 20 , 35sin 20 50cos 23 , 50sin 23o o o owork
35cos 20 50cos23 35sin 20 50sin 23o o o owork
20o
Jeff Bivin -- LZHS
Jeff Bivin -- LZHS
The following slides are the same examples previously examined that calculate the work needed to move an object. However, an alternative method is demonstrated.
Jeff Bivin -- LZHS
A mover exerts a force of 55 pounds at an angle of 45o below the horizontal on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate.
45o
f
55 lbs45o
055 cos 45 20work lbs ft
777.817work ft lbs
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
55cos 45 fo
55 cos 45o f
Jeff Bivin -- LZHS
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
A sled is to be pulled by a rope at a 37o angle above the horizontal with a force of 63 lbs.. Find the amount of work done to move the sled 15 feet.
37o63 lbs
063 cos37 15work lbs ft
754.711work ft lbs
f
63cos37 fo
63 cos37o f
Jeff Bivin -- LZHS
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
A mover exerts a horizontal force of 35 pounds on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13o above the horizontal. Find the work done on the crate.
13of
35 lbs13o
035 cos13 40work lbs ft
1364.118work ft lbs 35cos13 fo
35 cos13o f
Jeff Bivin -- LZHS
𝑤𝑜𝑟𝑘= 𝑓𝑜𝑟𝑐𝑒 · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
A mover exerts a force of 35 pounds parallel to the ramp on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13o above the horizontal. Find the work done on the crate.
13o35 lbs
35 40work lbs ft
1400work ft lbs Note: The force is in the same direction of
the movement. Therefore, all the
force is moving the crate.