![Page 1: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/1.jpg)
VectorsVectors
To describe two dimensional forces and motion
![Page 2: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/2.jpg)
GRAPHICAL GRAPHICAL TECHNIQUETECHNIQUE
• You need graph paper, protractor, and a ruler
• Define the scale for your graph
• Draw all lines to scale (including angle and length)
• Move vectors to line up head to tail
![Page 3: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/3.jpg)
ANALYTICAL TECHNIQUEANALYTICAL TECHNIQUE
• Use of trigonometric functions
• break everything into triangles
• always have two components
• make columns of each component (X,Y)
• be sure to keep any sign for direction
sin = opposite hypotenuse
cos adjacent hypotenuse
tan opposite adjacent
![Page 4: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/4.jpg)
VECTORS
![Page 5: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/5.jpg)
Vector Practice Problem
A plane is flying with North at 200 kph. A wind of 40 kph is blowing due East. What is the resultant velocity of the plane?
Find the magnitude of resultant first.
c2 = a2 + b2
c2 = (200)2 + (40)2
c = 204 kph
Now, find the angle for direction.
Tan = wind/plane
Tan = 40/200
= 11.3o
Answer: 204 kph at 11.3o east of north
![Page 6: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/6.jpg)
• Static– Force to prevent an object from moving– Coefficient of static friction: s
• Kinetic– Force to oppose motion once an object is moving– Coefficient of kinetic friction: k
f = FNf: friction: coefficient
FN: normal force
ss > > kk
![Page 7: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/7.jpg)
W = m g
f = FN
F = ma
F=ma
![Page 8: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/8.jpg)
CH 5 HOMEWORK
80. Ex=3.54, Ey=3.54; Fx=-3.54, Fy=-3.54; Ax=-3, Ay=0
81. Picture83. 40 m, 45o east of
south
86. 79 N, 54o NE
88. 6.5 m/s, 32o from vertical
90. 0.25597. 435 N, right98. 150 N, 110 N104. 490 N, 150 N,
49 N kinetic, 200N
![Page 9: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/9.jpg)
FRICTION LAB
Materials:
– spring scale
– 1 kg mass
– 6 V battery
– sand paper
– notebook paper
– wood block
![Page 10: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/10.jpg)
OBJECTIVE
• Each group must find the coefficient of friction for each surface (sand paper, notebook paper, table) for each object (6 V battery and wood block)
• Is friction really dependent upon the surface and object used?
![Page 11: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/11.jpg)
PROCEDURES
• Using each object in turn, find its weight using the spring scale
• Drag each object across each surface and determine the force (in Newtons) to do so
• Record the data in the table
• Determine the coefficient of friction from the friction equation
• Do your numbers make sense?
![Page 12: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/12.jpg)
FRICTION LAB CHARTOBJECT W Fsand Fpaper Ftable sand paper table WOOD BLOCK
BATTERY
![Page 13: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/13.jpg)
VectorsVectorsandand
ForcesForces
• Materials– Textbook– Ruler– Protractor– Wood block– Spring scale– Penny
• Objective– To review vectors and
forces from chapters 4 & 5
![Page 14: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/14.jpg)
Vectors and ForcesVectors and Forces
Procedure #1
• Determine the mass of the wood block.m = _____ g = _____ kg
• Convert mass from g to kg.
• Calculate its weight (use equation).W = _____ N
• Draw and label the force vectors on the wood block when hanging from the spring scale
![Page 15: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/15.jpg)
Vectors and ForcesVectors and Forces
Procedure #2• Lay your textbook flat on the desk.• Place the wood block on top.• Draw and label the force vectors on it.• Attach the spring scale to it. Determine
the force needed to just start it moving.• Draw and label the force vectors on it.• Determine the coefficient of static friction
between the book and wood. Show me equation and work.
![Page 16: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/16.jpg)
Vectors and ForcesVectors and Forces
Procedure #3
• Remove the wood block and place a penny on top of the book.
• Raise the lid of the book. Record the angle when the penny begins to slide off.
• Draw and label the force vectors on the penny just before it slides.
![Page 17: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/17.jpg)
Vectors and ForcesVectors and Forces
Procedure #4• Remove the penny and place the wood
block back on book.• Attach the spring scale again.• Pull the wood block along the book at a
constant velocity (a=0m/s2). Record the amount of force needed to do this.
• Determine the coefficient of kinetic friction. Show me equation and work.
• How does it compare to the static coefficient? Explain your results.
![Page 18: Vectors To describe two dimensional forces and motion](https://reader036.vdocument.in/reader036/viewer/2022082422/5697bf721a28abf838c7ec3e/html5/thumbnails/18.jpg)
Test equations – Ch.4&5
vf = vi + a t
x = vi t + 1/2 a t2
vf2 - vi
2 = 2 a x
x = (vf + vi) t/2
vf = vi - g t
y = vi t - 1/2 g t2
vf2 - vi
2 = - 2 g y
g = 9.8m/s2
sin = opposite hypotenusecos adjacent hypotenusetan opposite adjacent
f = FN
W = mgF = ma