Prelim;
Week 1
Learning objectives; at the end of the topic you will learn to
1) Convert units.
2) Identify and differentiate vectors and scalars.
3) Add and subtract vectors and apply it to a worded problems.
Important systems of units;
1km = 1000m,
1m = 39.37in = 3.281ft,
1in = 2.540cm,
1mil = 1.6094km = 5280ft,
1kg = 1000g = 2.205lb.
Conversion
Ex; a long rectangular object 0.25km long, 25cm wide and 25mm thick. What is its volume in cubic meter?
.25km = 2.5hm = 25dam = 250m
25cm = 2.5dam = .25m
25mm = 2.5cm = .25dam = .025m
Volume of a rectangle is V = L.W.H = (250m)(.25m)(.025m) = 1056m 3
Ex; change 115in to centimeter
115in x
.
= (115)(2.54cm) = 292cm
Ex; how many seconds are there in 1 hour?
hr x
x
= 60 x 60 = 3600s
Ex; express 60mil/hr in ft/s
x
x
=
(
)(
)
= 88ft/s
CHAPTER 1
FORCES ACTING ON AN OBJECT: VECTORS
2 types of quantities;
1) Vector
2) Scalar
VECTOR ADDITION; graphical method
B’
Ex; A = 10in E
A’
B = 10in N
R
A
B
Finding for the angle tan ø = =
=1
Ø = 450
Finding the magnitude of the resultant vector R.sin 45
sin 450 =
so
since H = R
R=
=
.
= 14.14in EN
for angles more or less than 900 sin law and cosine law will apply.
B
𝛽
Cosine law
R2 = A2 + B2 – 2AB cos ∝
R2 = A2 + B2 + 2AB cos ∅
Sin law
∝
=
∅
=
O 𝜃
𝛼 A
Ex; two vectors of 8units and 5units makes an angle of 600 with each other. What is there vector sum?
R2 = A2 + B2 + 2AB cos ∅
R2 = 82 + 52 + 2(8)(5)(cos 600)
R = 11.4units