Transcript Normal Force

The first exam will be held on Tuesday, September 23, in room
109 Heldenfels from 7 to 9:30 p.m.
Section 807 and half of section 808 (students with last names
beginning from letters A through K) should come at 6:55 p.m. for
an exam that starts at 7:00 and ends at 8:00 p.m. The rest of
section 808 and section 809 should come at 8:10 for an exam
that starts at 8:15 and ends at 9:15 p.m. Those who take the first
exam cannot leave before 8 p.m.
No textbook, calculators, or notes are permitted on the exam.
The exam will include Chapters I through VI.
A Recipe for Solving Problems
1. Sketch
Identify all forces acting on each body, or “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 convenient 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. Apply 3rd Law
4. Solve for acceleration or whatever is asked
Units of Force
1 Newton  1N  1kg  m / s
2
British system:
units of mass: 1 slug  14.59 kg
units of force: 1 pound  1lb  1 slug  ft / s 2  4.448N
One pound is 0.4536 kg
One pound is the weight of 0.4536 kg on the
Earth
Weight, the force of gravity, and the
normal force
No friction
P
m1
m1
m2
Free body diagram
N2
N1
F12
P
F21
m2
m1
m2 g
m1g
F12=F21
P
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
Refrigerator
• If you push a refrigerator when
there is no friction what happens?
• In the real world what happens?
Especially when it’s fully loaded
and on a sticky kitchen floor?
– When does static friction kick in?
– When does kinetic friction kick in?
Friction
There is some maximum value the friction force can
achieve, and once we apply a force greater than this
maximum there is a net force on the object, so it
accelerates.
The maximum of the force of friction varied linearly
with the amount that the block pushes on the table.


F friction   N
 < 1- coefficient of friction,

isNthe normal force
The friction force only exists when there is another
force trying to move an object
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 refrigerator:
– If I don’t push, what is the static friction
force?
– What if I push a little?
Is it better to push or pull a
sled?
You can pull or push a sled with the same force
magnitude, FP, and angle Q, as shown in the figures.
Assuming the sled doesn’t leave the ground and has
a constant coefficient of friction, , which is better?
FP
FP
Pulling Against Friction
A box of mass m is on a surface with coefficient
of kinetic friction . You pull with constant
force FP at angle Q. The box does not leave
the surface and moves to the right.
1. What is the magnitude of the acceleration?
2. What angle maximizes the acceleration?
Q
Box on an inclined plane
A box with mass m is placed on a frictionless incline
with angle q and is allowed to slide down.
a) What is the normal force?
b) What is the acceleration of the box?
H
q
c) What is the box velocity at the bottom of the plane?
A small block, mass 2kg, rests on top of a
larger block, mass 20 kg. The coefficient of
friction between the blocks is 0.25. If the larger
block is on a frictionless table, what is the
largest horizontal force that can be applied to it
without the small block slipping?
F
N1
N2
N1
N1
F
N1
m1 g
m2 g
A block of mass 20 kg is pushed against a vertical
surface as shown. The coefficient of friction
between the surface and the block is 0.2. If
θ=300, what is the minimum magnitude of P to
hold the block still?
P
θ