Lecture3
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Some points to emphasize
English teaching
6-10 hours per week in addition to class
General Physics I
1
Today’s topics
My Laws of Motion!
General Physics I
Force is exerted on an object by other objects, either physically touched or at a distance. Force is a vector with both a magnitude and a direction.
y x
a
General Physics I
11
Mass
The mass of a body is an intrinsic characteristic that relates a force exerted on the body to the resulting acceleration.
General Physics I
6
Newton’s Epitaph by Pope
“Nature and Nature’s laws lay hid in night: God said, Let Newton be! And all was light.”
---- Alexander Pope
Magnitude:
Fg mg
Direction: points towards the center of Earth Weight: The weight W of a body is equal to the magnitude of the gravitational force on the body.
a
General Physics I
10
Inertial Reference Frame
A reference frame at rest or with constant velocity is an inertial frame, or is it?
Ground is usually assumed as an inertial frame, neglecting Earth’s astronomical motion.
At very large speeds (an appreciable fraction of the speed of light c), Newtonian mechanics must be replaced by Einstein’s special theory of relativity. If objects under study are very small (at atomic scale, ~10-10 or 10-9 m), Newtonian mechanics must be replaced by quantum mechanics.
Mass is a scalar. It is a measurement of an object’s inertia. The greater an object’s mass, the more the object resists being accelerated.
General Physics I
General Physics I
16
Solution FA FB FC m(0) 0 FB FA FC
Force components in x-axis:
FBX FAX FCX FB cos( 90 ) FA cos133 FC cos 0 ( 220 N) (cos133 ) (170 N) cos
( 220 N ) (cos 133 ) 1 cos 28.04 170 N
General Physics I
17
Force components in y-axis:
FBy FAy FCy FB sin ( 90 ) FA sin 133 FC sin , FB (220 N) (sin133 ) (170 N) sin 28.04
When a body presses against a surface, the surface (even a seemingly rigid surface) deforms and pushes on the body with a normal force that is perpendicular to the surface.
General Physics I
8
Newton’s First Law: Law of Inertial
General Physics I
9
Inertial Reference Frame
An inertial reference frame is one in which Newton's laws hold. An accelerating train is a non-inertial frame.
General Physics I
13
Unit of Force
In SI, the force unit is newton.
1 N (1 kg) (1 m / s ) 1 kg m / s
2
2
General Physics I
14
Free-Body Diagram (F.B.D.)
25
General Physics I
Newton’s Third Law
When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.
General Physics I
27
Applying Newton’s Laws
Objects stuck together, Objects connected through cord over pulley, Objects on an inclined plane, Scale reading in an elevator, ...
12
Newton’s Second Law
The net force on a body is equal to the product of the body's mass and the acceleration of the body.
Fnet ma (Newton' s second law) .
General Physics I
15
Sample Problem
In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of the figure.
2
Force and Motion
Q: What is the cause for the change of motion status (acceleration) of an object?
A: Force
General Physics I
3
Force
Force causes acceleration of an object.
General Physics I
7
Newtonian Mechanics
Newtonian Mechanics describes the relation between force and motion based on the laws by Isaac Newton (16421727).
General Physics I
20
Einstein Asks…
General Physics I
21
The Gravitational Force
Newtonian Mechanics
General Physics I
Einstein’s General Relativity
22
The Normal Force
Third-law force pair:
FBC FCB
General Physics I
26
Conceptual Question
How dose a horse try to use physics to escape work!
A horse refuses to pull a cart. He reasons:“According to Newton’s third law, whatever force I exert on the cart, it will exert an equal and opposite force on me, so the net force will be zero and I will have no change of accelerating the cart.”
General Physics I
4
Force is Vector
principle of superposition fI
5
Net Force Net force is the sum of all forces on a body. It is an effect, NOT a real force. In the case Fnet = 0, the forces cancel one another. But each individual force still exists. Only the net effect on the body is like no forces on it at all.
F.B.D.
General Physics I
23
Frictional Force
General Physics I
24
Tension
The tension force pulls on a body along a taut cord. The cord is often assumed to be massless and not stretchable. A string has a single tension force (magnitude). The direction depends on the body on which this force acts upon. We usually assume pulleys to be frictionless and massless. The tension forces on two sides of a pulley are the same in magnitude.
Therefore,
FB 241N
General Physics I
18
Some Particular Forces
Gravitational force
Normal force
Frictional force Tension
General Physics I
19
The Gravitational Force
The acceleration component along a given orthogonal axis is caused only by the sum of the force components along that same axis, and not by force components along any other axis.
English teaching
6-10 hours per week in addition to class
General Physics I
1
Today’s topics
My Laws of Motion!
General Physics I
Force is exerted on an object by other objects, either physically touched or at a distance. Force is a vector with both a magnitude and a direction.
y x
a
General Physics I
11
Mass
The mass of a body is an intrinsic characteristic that relates a force exerted on the body to the resulting acceleration.
General Physics I
6
Newton’s Epitaph by Pope
“Nature and Nature’s laws lay hid in night: God said, Let Newton be! And all was light.”
---- Alexander Pope
Magnitude:
Fg mg
Direction: points towards the center of Earth Weight: The weight W of a body is equal to the magnitude of the gravitational force on the body.
a
General Physics I
10
Inertial Reference Frame
A reference frame at rest or with constant velocity is an inertial frame, or is it?
Ground is usually assumed as an inertial frame, neglecting Earth’s astronomical motion.
At very large speeds (an appreciable fraction of the speed of light c), Newtonian mechanics must be replaced by Einstein’s special theory of relativity. If objects under study are very small (at atomic scale, ~10-10 or 10-9 m), Newtonian mechanics must be replaced by quantum mechanics.
Mass is a scalar. It is a measurement of an object’s inertia. The greater an object’s mass, the more the object resists being accelerated.
General Physics I
General Physics I
16
Solution FA FB FC m(0) 0 FB FA FC
Force components in x-axis:
FBX FAX FCX FB cos( 90 ) FA cos133 FC cos 0 ( 220 N) (cos133 ) (170 N) cos
( 220 N ) (cos 133 ) 1 cos 28.04 170 N
General Physics I
17
Force components in y-axis:
FBy FAy FCy FB sin ( 90 ) FA sin 133 FC sin , FB (220 N) (sin133 ) (170 N) sin 28.04
When a body presses against a surface, the surface (even a seemingly rigid surface) deforms and pushes on the body with a normal force that is perpendicular to the surface.
General Physics I
8
Newton’s First Law: Law of Inertial
General Physics I
9
Inertial Reference Frame
An inertial reference frame is one in which Newton's laws hold. An accelerating train is a non-inertial frame.
General Physics I
13
Unit of Force
In SI, the force unit is newton.
1 N (1 kg) (1 m / s ) 1 kg m / s
2
2
General Physics I
14
Free-Body Diagram (F.B.D.)
25
General Physics I
Newton’s Third Law
When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.
General Physics I
27
Applying Newton’s Laws
Objects stuck together, Objects connected through cord over pulley, Objects on an inclined plane, Scale reading in an elevator, ...
12
Newton’s Second Law
The net force on a body is equal to the product of the body's mass and the acceleration of the body.
Fnet ma (Newton' s second law) .
General Physics I
15
Sample Problem
In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of the figure.
2
Force and Motion
Q: What is the cause for the change of motion status (acceleration) of an object?
A: Force
General Physics I
3
Force
Force causes acceleration of an object.
General Physics I
7
Newtonian Mechanics
Newtonian Mechanics describes the relation between force and motion based on the laws by Isaac Newton (16421727).
General Physics I
20
Einstein Asks…
General Physics I
21
The Gravitational Force
Newtonian Mechanics
General Physics I
Einstein’s General Relativity
22
The Normal Force
Third-law force pair:
FBC FCB
General Physics I
26
Conceptual Question
How dose a horse try to use physics to escape work!
A horse refuses to pull a cart. He reasons:“According to Newton’s third law, whatever force I exert on the cart, it will exert an equal and opposite force on me, so the net force will be zero and I will have no change of accelerating the cart.”
General Physics I
4
Force is Vector
principle of superposition fI
5
Net Force Net force is the sum of all forces on a body. It is an effect, NOT a real force. In the case Fnet = 0, the forces cancel one another. But each individual force still exists. Only the net effect on the body is like no forces on it at all.
F.B.D.
General Physics I
23
Frictional Force
General Physics I
24
Tension
The tension force pulls on a body along a taut cord. The cord is often assumed to be massless and not stretchable. A string has a single tension force (magnitude). The direction depends on the body on which this force acts upon. We usually assume pulleys to be frictionless and massless. The tension forces on two sides of a pulley are the same in magnitude.
Therefore,
FB 241N
General Physics I
18
Some Particular Forces
Gravitational force
Normal force
Frictional force Tension
General Physics I
19
The Gravitational Force
The acceleration component along a given orthogonal axis is caused only by the sum of the force components along that same axis, and not by force components along any other axis.