Transcript Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Sections

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Sections 807, 808, 809
Lecture 5
Overview of Today’s Class
•Hw Quiz
•Vectors
A ball is thrown vertically upward with a velocity of
magnitude v1 from a window at height H. In addition to
gravity acting on the ball there is another force so that the
acceleration in the up direction is –g+t where  is a constant
and t is the time. What is the ball’s position when the
acceleration is zero?
Falling with air resistance
dv
a
 g  kv
dt
A rocket, initially at rest, is fired at t=0 vertically down
from a building of height H. The rocket’s acceleration,
including the effects of gravity, is downwards with
increasing magnitude given by a(t)=t, where  is a
known constant. When does it hit the ground and how
fast is it going when it hits?
You want to measure
the height of a
building. You stand
2m away from a 3m
pole and see that it’s
“in line” with the top
of the building. You
measure 16 m from
the pole to the
building.
What is the height of
the building?
16 m
Adding Vectors by Components
1. Draw a diagram
2. Choose x and y axes. Choose them in a way that make
your work easier. (E.g. choose one axis along the
direction of one of the vectors so that the vector will
have only one component).
3. Resolve each vector in x and y components
4. Calculate each component using sine and cosine. Be
careful with signs: any component that points along the
negative x or y axis gets a negative sign.
5. Add the x components together to get the x component
of the resultant. Similar for y:
Vx=V1x+V2x+…
Vy=V1y+V2y+…
6. If you want to know the magnitude and direction of
the resultant vector,
V  V V
2
x
2
y
tan  
Vy
Vx
CRAYFISH, SWAN, AND PIKE
(Translation of I. Krylov's fable)
Let crayfish, swan and pike
Draw heavy loaded cart,
Each being just a part
Of harness they dislike.
They try a lot, and everyone
Starts pulling it with zeal;
The problem is that each of them
With his path wants to deal!
The swan makes upward for a cloud,
The crayfish falls behind;
The pike dives sharply in the deep,
And cart moves not from site.
The moral of the verse is that
Accordance should prevail
Amid the people who have plans
To work but not in vain.
Russian fable: Swan, Crawfish, and Pike
Fs
Lake

Despite
their
huge effort the
box does not
move!

River
Fp
Fc
Find Fs and Fc if Fp, θ, and  are
given
Given two vectors,






A  4i  3 j and B  5i  2 j
a) find the magnitude of each vector
b) Write an expression for the vector difference
 
A  B using unit vectors
Quiz



Given two vectors, a  4i  6 j

 
and b  7i  3 j :
  
a) Find the components of the vector r  a  b
b) Find the magnitude of
makes with the x axis.

r
and the tangent of the

angle r
 

a) Express the vectors F1, F2, and F in terms of their components.
3
y

F2
2
3

F3
x
1

F1

F4 ,
b) Find the components of the fourth force,
that should be
added for the object to be in static equilibrium.
A cannon at the origin points up at an angle θ with
the x axis. A shell is fired which leaves the barrel
with a velocity of magnitude Vm.
a) When does the shell reach its maximum height?
b)What is the maximum height?
c) What is the range (horizontal distance)?
d)What is the velocity of the shell when it hits the
ground?
Have a great day!
Hw: All Chapters 3
problems and exercises
and
4