Transcript Chapter 2 - Motion in One Dimension

Forces
• Contact Forces - those
resulting from physical contact
between objects
–
–
–
–
Normal Force
Friction
Tension (spring/rope)
Compression
• Action at a Distance Force Field Forces
– Gravity
– Electromagnetic
– Strong Nuclear Force
• Holds Nucleus Together
– Weak Nuclear Force
• Decay Process
•Force - The capacity to cause physical change in the motion of an object.
Newton’s First Law – Law of Inertia
• An object at rest will remain at rest
– and an object in motion will continue in motion at a
constant velocity (Magnitude and Direction)
– unless acted upon by a nonzero net external force.
•
Inertia – The tendency of a body to maintain its state of rest or constant
velocity.
•
Equilibrium - A condition during which the velocity of an object is constant
or the object is at rest. The net force acting on the object is zero.
•
Inertial Reference Frame
– Place where Newton's Laws are valid. (at rest or constant velocity)
– Non-inertial reference frames are accelerating.
Weight and Mass
• Mass - A term used to quantify/measure inertia.
–
–
–
–
Has SI units of kilogram.
The amount of a substance.
The quantity of matter.
Scalar
• Weight - Force exerted on an object while it is under the
influence of a gravitational field.
– Vector
• Density - The amount of a substance per unit volume.
Newton’s Second Law
• The acceleration of an object is
– directly proportional to the net force acting on it
– and inversely proportional to its mass.
– The direction of the acceleration is in the
direction of the net force acting on the object.
F

a
m
 F  vector sum of all forces
 F  ma
Units
Physical
Quantity
Length
Dimension
Symbol
[L]
SI MKS
SI CGS
m
cm
US
Customary
ft
Mass
[M]
kg
g
slug
Time
[T]
sec
sec
sec
Acceleration
[L/T2]
m/s2
cm/s2
ft/s2
dyne
g-cm/s2
pound (lb)
slug- ft/s2
Force
[M-L/T2] newton (N)
kg-m/s2
1 lb  4.45 N
Alternate Statement of the Second Law
• Momentum - The quantity of an object’s
motion. The product of an object’s mass and
velocity.
p  mv
• The time rate of change of the momentum of an
object is equal to the resulting net external force
acting on the object.
dp
 F  dt
Weight and Mass
• Mass - A term used to quantify/measure inertia.
–
–
–
–
Has SI units of kilogram.
The amount of a substance.
The quantity of matter.
Scalar
• Weight - Force exerted on an object while it is under the
influence of a gravitational field.
– Vector
FG  mg  mgjˆ
• Density - The amount of a substance per unit volume.
Example 1
• What constant net force must be used to
bring a 1500 kg car to rest from a speed of
100 km/hr within a distance of 55 m?
Newton’s Third Law
• If two objects interact (contact or at a distance),
• the force exerted on body 1 by body 2 (F12)
On By
• is equal and opposite the force exerted on
body 2 by body 1 (- F21 ).
Cautions on the Third Law
• The forces of an action-reaction pair always act on
different bodies. They do not combine to give a
net force and cannot cancel each other.
Model Assumptions
• Surfaces are frictionless (*)
• The mass of a rope or string is zero.
• The tension in a rope is the same everywhere in
the rope. (The force(s) it exerts is(are) on the object(s) it
is attached to).
• Ropes are non-extensive (do not get longer)
• A pulley has no friction or mass (*). It simply
redirects the tension in another direction.
Problem Solving Approach
•
•
•
•
Read the problem. Several times if necessary.
Write down the information that is given or looked up in a table.
Write down what is to be found.
Draw a picture or sketch. Draw and label with forces, velocities, accelerations,
etc. Isolate the object(s) of interest.
– Free body diagram.
– Specify your coordinate system.
– Resolve forces along these coodinate axes.
• Write down the fundamental relationships/definitions/formula you need to solve
the problem.
–
•
•
•
•
Apply Newton’s laws in component form along coordinate axes.
Manipulate the equations. # Equations = # Unknowns.
Check that your answer makes sense.
Actually plug in numbers at the very end. Include unit analysis.
Box your final answer. Include units and check for significant digits.
Big Picture
• If the object is at rest
or moving at a
constant velocity it is
in equilibrium and the
1st Law applies.
• If the the forces don’t
seem balanced the
object will accelerate
and the second law
applies
F  0
 F  ma
Example 2
• A 10 kg box is sitting
on the table.
• You pull up with a
string attached to the
box and apply 40 N.
• What is the normal
force applied by the
table on the box?
Example 3
• Two boxes are connected
by a cord and pulled by a
second cord attached to
the first box with a force
of 40.0 N
• The two boxes have
masses of 12.0 kg and
10.0 kg as shown.
• Find the acceleration of
each box and the tension
in the cord
Example 4 – Hanging Objects
2
1
T2
T1
1
2
mg
m
F  0
Resolve into components
T1
1
T2 sin 2
T1 sin 1
T2
2
T2 cos 2
T1 cos 1
mg
mg
F  0  T cos   T cos 
F  0  T sin   T sin   mg
x
y
1
1
1
1
2
2
2
2
Block on a smooth incline plane
FN
mg sin 
mg cos 

mg

F  0  F  mgcos 
F  ma  mgsin 
y
N
x
Atwood’s Machine (a pulley)
Object 1: Elevator Car
F
y
 FT  m1g  m1a
Object 2: Counterweight
F
y
 FT  m2g  m2a
Incline plane (no friction)
• m2 = 7 kg
• Which way do
blocks move?
• What is
acceleration?
• What is tension
in cord?
Inside the elevator (non-inertial frame)
While moving up at constant velocity:
F
y
 FN  mg  0
Scale reads correctly
While slowing down:
F
y
 FN  mg  ma
Scale reads light!