Download Lecture 2 Newton`s laws of motion

© Copyright FIRST EDUCATION 2011
0430 860 810 Nick Zhang
Lecture 2 Newton's laws of motion
Momentum
When explaining changes in motion, it is necessary to consider the mass of the object as well as the velocity.
Imagine an unknown object is moving really fast towards you, say at a speed of 20 m/s or 72 km/h. You
probably would choose to get out of the way, but what if it is a mosquito? Imagine again an unknown object
is travelling towards you at a slow speed of 5 m/s. You may choose to stay, but you are now told that it is an
elephant. Therefore, velocity itself is no longer sufficient to describe the effect of change in motion.
P is used to denote momentum and P = mv . The unit of momentum is kg m/s.
Momentum is also a vector quantity that has the same direction as that of the velocity.
Newton's First Law of Motion (Law of Inertia)
Every object continues in its state of rest or uniform motion unless made to change by a non-zero net force
The inertia of an object is its tendency to resist changes to motion, mass is the only measure of the inertia of
an object. In other words, the greater the mass, the more difficult an object could change its motion.
The net force is denoted by Fnet
and mathematically, Fnet = 0 implies that the object is stationary or
moving at a constant velocity (Note constant velocity means both magnitude and direction are not changed).
Example
The small triangular block is placed on the big one, the surface between the two blocks is frictional and the
top surface of the small triangular block is smooth. A smooth ball is placed on the surface of the small
triangular block and the small triangular block is released from rest, what will be the path of the motion of
the ball?
Newton's Second Law of Motion
The rate of change in momentum is directly proportional to the magnitude of the net force and is in the
direction of the net force.
∆P m∆v
Mathematically Fnet =
=
= ma , the net force has the same direction as that of the acceleration.
∆t
∆t
Drawing diagrams and force analysis are critical to solving problems of Newton's Second Law.
Newton's Third Law of Motion
Whenever an object applies a force (an action) to a second object, the second object applies an equal and
opposite force (a reaction) to the first object
distinction
similarity
Physics
A pair of equilibrium forces
A pair of action-reaction forces
Acting on the same object
Acting on two different objects
Equal in magnitude and opposite in direction
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© Copyright FIRST EDUCATION 2011
0430 860 810 Nick Zhang
Example
A person standing on the ground is trying to raise an object by pulling down a rope over a pulley as shown in
the diagram below. The mass of the person is 70 kg and the mass of the object is 20 kg. The object is
accelerating uniformly at 0.5 ms-2. The friction between rope and pulley is negligible. Find the normal
reaction force that the ground exerted on the person.
Example
Two students are conducting an experiment in which a block, m1, of mass 0.40 kg is being pulled by a string
across a smooth surface. The string is attached over a smooth pulley to another mass, m2, of 0.10 kg. The
second mass, m2, is free to fall vertically. This is shown in the figure below:
The block is released from rest.
What is the acceleration of the block m1?
m1
m2
Example
A block of mass 0.20 kg is held at point A against a spring which has been compressed by 10 cm as shown in
the diagram below. The block is released, and is pushed by the spring across a smooth surface. When the
block leaves contact with the spring at point B the block has a speed of 5.0 ms-1.
At point C the block still has a speed of 5.0 ms-1. At point C the block encounters a rough surface that
provides a constant friction force that brings it to rest at point D. The distance C to D is 2.0 m. What is the
magnitude of the friction force?
Physics
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© Copyright FIRST EDUCATION 2011
0430 860 810 Nick Zhang
A ball hangs in a lift and rest against the smooth wall of the lift as shown in the diagram below. The mass of
the ball is 2.0 kg and the angle made between the string and the wall is 37º. If the lift is accelerating upwards
uniformly at 2.0 ms-2, what will be the tension in the string? (Assume g = 10 ms-2)
θ
A tractor, including the driver, has a mass of 500 kg and is towing a trailer of mass 1000 kg as shown in
figure below. The tractor and trailer are accelerating at 0.50 ms-2. Ignore any retarding friction forces and the
mass of the towing rope. The tractor and trailer start from rest.
What is the magnitude of the net force on the system of the tractor and trailer?
What is the tension in the rope connecting the tractor and trailer?
How far does the tractor move in the first 6.0 s?
Physics
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© Copyright FIRST EDUCATION 2011
0430 860 810 Nick Zhang
Apparent weight
The apparent weight is equal to the magnitude of the normal reaction force acting on a person. It can be
considered as the perceived weight and in some cases different from the actual weight of a person.
The actual weight is the universal gravitational force exerted by a reference planet on the person.
Note the difference between apparent weightlessness and actual weightlessness
Apparent weightlessness occurs when the
normal reaction force acting on the person is ZERO
i.e. N = 0
Actual weightlessness occurs when the gravitational
weight force acting on the person is ZERO, only
possible in deep space. i.e. W = 0
Typical apparent weight problems
1. Free falling
Helen is carried up on a platform to the top. At the top, a trapdoor in the platform opens and Helen free falls.
Approximately 100 m below the release point, a net catches Helen.
Helen has a mass of 60 kg, the platform travels vertically upward at a constant speed of 5.0 ms-1.
What is Helen's apparent weight as she travels up?
As the platform approaches the top, it slows to a stop at a uniform rate of 3.0 ms-2.
What is Helen's apparent weight as the platform slows to a stop?
Physics
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© Copyright FIRST EDUCATION 2011
0430 860 810 Nick Zhang
Helen then drops through the trapdoor and free falls. Ignore the air resistance.
During her fall, Helen experiences 'apparent weightlessness'. Explain what is meant by apparent
weightlessness by making mention of gravitational weight force and normal reaction force.
2. In an accelerating lift
N
N
Going up
Speeding up
Going up
Slowing down
W
Since N > W, the person will feel heavier
W
Since N < W, the person will feel lighter
3. At the top or bottom of a circular track
N
W
N
W
N
W
If N = 0, the person will
experience apparent
weightlessness
and maximum safe speed
occurs when N = 0.
If N = 0, the person will
experience apparent
weightlessness
and minimum safe speed
occurs when N = 0.
N is always greater than W
and the person would feel
heavier.
NOTE: This type is closely related to circular motion, so must be reviewed after completing circular motion.
Physics
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© Copyright FIRST EDUCATION 2011
0430 860 810 Nick Zhang
Inclined plane problems and force analysis
Force analysis is critical to finding the net force acting on an object and hence deciding the motion of the
object. General steps as below should be followed closely:
1. Choose two perpendicular directions into which minimum number of forces acting on an object need to
be resolved.
2. Perform vector addition on each resolved direction and determine the net force acting on the object.
3. According to Newton's Second Law of Motion Fnet = ma , determine the acceleration of the object.
4. Other important physical quantities such as displacement, time interval, initial velocity or final velocity
could be found given the motion is of uniform acceleration.
N
N = W cosθ
Fnet = W sinθ - Fr = ma
Fr
W cosθ
W sinθ
θ
W
W is the only force needs to be resolved into two perpendicular directions, one is parallel to the slope and the
other is perpendicular to the slope.
Example
Nick is riding his sled on snow. Nick and the sled have a total mass of 80 kg. He travels downhill from A to
B. The sled starts form rest. The angle of the slope is 30� .
A is a vertical height of 12.8 m above B. At B he then travels along a horizontal snowfield to point C. From
A to C (on snow) there is no friction force.
What is the momentum of Nick and his sled at point C?
At point C he runs off snow onto grass where there is now a constant friction force and he slows to a stop at
D after a time of 6.0 s.
What is the magnitude of the friction as he travels from pont C to point D?
Physics
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