Download Physics 1422 - Introduction

Physics 203 – College Physics I
Department of Physics – The Citadel
Physics 203
College Physics I
Fall 2012
S. A. Yost
Chapter 4
Newton’s Laws – Part 3
Physics 203 – College Physics I
Department of Physics – The Citadel
Weight and Normal Force
If you stand on a scale, what force
does a scale measure? (N or W)
N
It measures the normal force
between you and the scale.
This equals the weight by
Newton’s second law – provided
you are in an inertial reference
frame.
W
N+W=0
Physics 203 – College Physics I
Department of Physics – The Citadel
Weight in an Elevator
a = 2.2 m/s2
An elevator accelerates
upward at 2.2 m/s2.
What does the passenger
apparently weigh, as
measured by the scale in
the elevator, if his mass is
100 kg?
Physics 203 – College Physics I
Department of Physics – The Citadel
Weight in an Elevator
A net force on the passenger
causes the upward
acceleration:
a = 2.2 m/s2
N
F = N – W = ma.
W = mg.
N = ma + W = m(a+g)
= (100 kg)(12.0 m/s2)
= 1200 N.
W
Physics 203 – College Physics I
Department of Physics – The Citadel
Tension
Pulling on a rope applies tension. The force
always acts along the rope if it is free to bend.
Physics 203 – College Physics I
Department of Physics – The Citadel
Measuring Tension
The magnitude of the tension in the rope shown
is the magnitude of the force F pulling on it,
which is also what would be reading on the
balance..
-F
F
Physics 203 – College Physics I
Department of Physics – The Citadel
Example:
Gymnast
on
Rings
q  90
What is the tension in
each rope supporting
a 150 lb gymnast if
they make the angle
of q relative to
horizontal?
Evaluate the tension at
q = 30o.
q
q
T2
T1
q
q
y
x
Fg
Physics 203 – College Physics I
Department of Physics – The Citadel
Example:
Gymnast
on
Rings
q  90
x: T1x + T2x = 0
q
y: T1y + T2y – Fg = 0
T
2 T sin q = Fg = 150 lb
T = 75 lb / sin q.
At 30o, T = 150 lb.
T2
T1
T1 cos q – T2 cos q = 0
T1 = T2
q
q
q
y
x
Fg
Physics 203 – College Physics I
Department of Physics – The Citadel
Pulleys
Pulleys can be used to
redirect tension. Tension
always follows the string.
If the pulley does not resist
the motion of the string, it
is said to be frictionless.
If the pulley is frictionless,
and massless then the
magnitude of the tension
is the same on both sides.
Otherwise, T1
T2 .
T1
T1 = T2
T2
Physics 203 – College Physics I
Department of Physics – The Citadel
Gymnast on Pulley
The gymnast weighs
150 lb. What is the
tension on the
rope?
T1
T2
T1 + T2 = Fg = 150 lb
T1 = T2 = 75 lb
Fg
Physics 203 – College Physics I
Department of Physics – The Citadel
Atwood Machine
If the blocks have
masses m1 = 6.0 kg
and m2 = 4.0 kg,
what is the
acceleration of the
blocks?
Assume the pulley is
massless and
frictionless, and
neglect the mass of
the string.
m2
m1
What is the tension
in the string?
Physics 203 – College Physics I
Department of Physics – The Citadel
Inclined Plane
3m
A block slides down
the inclined plane
shown, starting at
the top. How long
does it take to reach
the bottom?
4m
Physics 203 – College Physics I
Department of Physics – The Citadel
Inclined Plane
Fnet = ma
N
Fnet = mg sin q = 3/5 mg
a = 3/5 g = 5.88 m/s2
Time to reach bottom…
x = ½ a t2
q
Fnet
mg q
sin q = 3/5
5 m = (2.94 m/s2) t2
t = 1.3 s.
a = g/5 = 1.96 m/s2
Physics 203 – College Physics I
Department of Physics – The Citadel
Friction
If I push on an object and it doesn’t move, it means
another force is pushing back to balance my
force: static friction.
Fp = Ff
Fp
Ff
Physics 203 – College Physics I
Department of Physics – The Citadel
Friction
At some point, if I push hard enough the object will
start to move. This limit to the amount of force
friction can supply turns out to be proportional to
the normal force.
Ff max = ms N
Fp
Fp = Ff
N
coefficient of
static friction
Ff
Physics 203 – College Physics I
Department of Physics – The Citadel
Friction
Once the object is moving, the friction is called
kinetic friction, and is again proportional to the
normal force, but with a smaller coefficient.
Ff max = mk N
mk < ms
Fp
N
coefficient of
kinetic friction
Ff
Physics 203 – College Physics I
Department of Physics – The Citadel
Friction
Is the amount of friction affected whether I put the
object on its long side or short side?
No
Is the amount of friction affected by how fast I push
the object?
Fp
F
p
No
Physics 203 – College Physics I
Department of Physics – The Citadel
Friction
Suppose the coefficients of kinetic and static
friction are mk = 0.7 and ms = 0.8, and the box
weighs 700 N. It is at rest on a table.
a) If I push with a force of 400 N, what is the force
of friction?
Ff = 400 N.
Fp < ms FN = 560 N
Fp
Ff
Physics 203 – College Physics I
Department of Physics – The Citadel
Friction
b) If I push with a force of 600 N, what is the force
of friction?
Fp > ms N = 560 N.
Ff = mk N = 490 N
c) If I then reduce my force to 400 N, what is the
force of friction?
Ff = 490 N
until it stops.
Fp
mg=700 N
Ff
mk = 0.7
ms = 0.8
Physics 203 – College Physics I
Department of Physics – The Citadel
Inclined Plane with Friction
If the board is tilted until the box just starts to slide,
at an angle q = 37o.
What is the coefficient
static friction?
N
Ff
q
mg
of
Physics 203 – College Physics I
Department of Physics – The Citadel
Inclined Plane with Friction
It is convenient to pick axes so that two of the forces align
with them.
x
Decompose the weight into
x and y components.
N
Ff
q
q
The forces balance.
x
x: Ff = mg sin q
y: N = mg cos q
ms = Ff/N = tan q = 0.75
mg
q= 37o
Physics 203 – College Physics I
Department of Physics – The Citadel
Two Blocks
Two blocks of mass 5.0 kg each are being pulled at
a constant speed by a 2.0 N force. What is the
tension T in the rope connecting them?
T
5 kg
2.0 N
5 kg
Physics 203 – College Physics I
Department of Physics – The Citadel
Two Blocks
What pulling force must be applied to accelerate the
blocks at a rate of 0.2 g, and what is the tension in
the rope?
T
5 kg
2.0 N
5 kg