Transcript Document

The first exam will be on Tuesday, September 25, room 109 in
Heldenfels building.
Section 807 and half of the Section 808 (students with last
name starting with A to H) will have exam from 7 to 8 pm.
Students from Section 808 with last name starting with J to Z,
and all students from Section 809, will have exam from 8:15
pm to 9:15 pm.
Students that have the exam from 7 to 8 pm will not be allowed
to leave earlier than 8 pm.
No calculators and cell phones in the room during the test.
Don’t use your own scratch paper; there will be plenty of it in
the room.
Please DO NOT FORGET TO BRING YOUR STUDENT ID!
Ch. 6 Quiz
A block of mass M is pushed against a vertical surface. The
coefficient of friction between the surface and the block is
equal to . If angle  is known, what is the minimum
magnitude of P to hold the block still?
P

What is included?
Chapters 1-6
Kinematics, 2D motion, vectors,
Newton’s Laws
Kinematics

 dV
a
dt

 dr
V
dt
In components:
dVy
dVx
ax 
; ay 
dt
dt
dx
dy
Vx  ; V y 
dt
dt
If

a

is given, you can find V and
Vx   a x dt ; Vy   a y dt
x   Vx dt ;
y   V y dt

r
Vectors






A  Ax i  Ay j B  Bx i  By j
  
C  A B ?



C  Cx i  C y j
Cx  Ax  Bx
C y  Ay  By
Newton’s 2nd Law


F  ma
Fx  max
Fy  ma y
DO NOT use Const acceleration case
formulas when acceleration is a function
of time. You have to integrate or
differentiate! What are the Const
acceleration case formulas?
1 2
x(t )  ac t  v(0)t  x(0)
2
v(t )  act  v(0)
v (t 2 )  v (t1 )  2ac ( x(t 2 )  x(t1 ))
2
2
DO NOT write the vector sign over a
projection!
If



F  Fx i  Fy j ,
Fx , Fy are scalars!
DO NOT forget that Fp has two
components: Fpcos θ and Fpsin θ
Q
DO NOT forget that Vi has two
components: Vicos θ and Vi sin θ
y
Vi

x
Do Not Forget to
•Write down what is given and
express the answer in terms of what is
given
•Box the answer
Double play problem
A Recipe for Solving Second Law Problems
1. Sketch
Isolate the body (only external forces but not forces
that one part of the object exert on another part)
2. Write down 2nd Newton’s law


F  ma
Choose a coordinate system
Write 2nd Newton’s law in component form:





F  Fx i  Fy j  max i  ma y j
Fx  max , Fy  ma y
3. Solve for acceleration
Pulling Against Friction
A sled of mass m is on a surface with coefficients of kinetic
friction k and static friction s. You pull with a constant
force F at an angle Q. The sled does not leave the surface and
moves to the right.
1. What is a minimum force needed to bring the sled in motion?
2. What is the magnitude of the acceleration?
3. What angle maximizes the acceleration?
Friction
Two types of friction:
1. Kinetic: The friction force
that slows things down
2. Static: The force that
makes it hard to even get
things moving
Kinetic Friction
• For kinetic friction, it turns out that the
larger the Normal Force the larger the
friction. We can write
FFriction = KineticFNormal
Here  is a constant
• Warning:
– THIS IS NOT A VECTOR EQUATION!
Static Friction
• This is more complicated
• For static friction, the friction force can vary
FFriction  StaticFNormal
Example of the sled:
– If I don’t push, what is the static friction
force?
– What if I push a little?
Box on an inclined plane
A box with mass m is placed on a frictionless incline
with angle  and is allowed to slide down.
a) What is the normal force?
b) What is the acceleration of the box?

No friction
Massless, unstretchable string; frictionless pulley
The advantage of a pulley
What minimum force F is
needed to lift the piano of
mass M?