### Force and Newton Laws

```Force and Newton Laws
Aqeel Mohamed &Christian Martinez
Dynamics
• Observation of objects in nature
• If a body is not under the influence of force, it
is at rest or a natural state. - Aristotle
• Claim is refuted by Newtonian Law
Motion
• Change in the location of an object over a
period of time.
• Speed and direction is maintained of an object
is in motion.
• Newton’s Three Laws help in our
understanding of the properties of motion.
Newton’s First Law: Inertia
• Matter would resist a change in motion.
• If a force acts upon an object, it would
continue to move indefinitely in the direction
the force acted in.
• The larger a mass, the more inertia (resistance
to change in motion) an object would have.
Newton’s Second Law:Acceleration
• An unbalanced force acting on an object
causes the object to accelerate in the
direction of the force.
• Acceleration is the change in magnitude of
velocity or direction.
• Situation occurs when resultant force or the
net force is NOT zero.
Formula
• Acceleration is directly proportional to the net
force.
• Acceleration is indirectly proportional to an
object’s mass
• a= F/m
• Where “a” is acceleration, “F” the net force,
and “m” the mass of the object
Force
• Expressed in Newtons (N)
• 1(N)= 1kg x m/s^2
• Net force can be represented as the product
of an object’s mass and accelaration
• F=ma
• Force is directly proportional to acceleration
Third Law of Motion
• For every reaction, there is an equal and opposite
reaction.
• Forces always occur in pairs when acting on an
object. Second object of two objects will exert a
force equal to the force the first object originally
exerted.
• Never act on the same object or could be
combined. (same magnitude but opposite in
direction)
Law of Universal Gravitation
• All objects have the ability to attract other
objects.
• Gravitational pull is proportional to mass. The
greater the mass, the greater the gravitational
pull.
Weight
• The “pull” felt by objects on Earth
• Product of acceleration due to gravity and an
object’s mass.
• Weight is a “force due to gravity”
• F= ma
g=a
• F=mg
• g= 9.81 m/s^2 (acceleration due to gravity
Gravitational Force of Two Objects
• Gravitational force between two objects is
inversely proportional to the square of their
distance and directly proportional to their
masses
• F=(Gm1m2)/r^2
• (G= 6.67 x 10 ^-11 N x m^2/kg^2)
• G represents the Universal Gravitational
Constant
Inverse Square Relationship
• Distance between masses increases,
gravitational force between objects decrease.
• Example: (if the distance
of two masses is doubled,
the force is reduced to
one forth the original value)
• 2^2 = 4 then Find reciprocal value = ¼
Question 1
• A 120-N net force acts upon a 68-kg cart at
rest. What acceleration results?
Solution 1
•
•
•
•
a=F/m
a= 120N/68kg
a=(120 kg x m/s^2)/ (68kg)
a=1.8 m/s^2
Question 2
• A force of F Newtons causes a mass of m kilograms to accelerate at 24 m/s^2. What
acceleration would occur in the following
conditions?
• -the force is doubled to 2F Newtons and mass
remains the same
• -The force F Newtons is constant and the mass
is tripled.
Solution 2
• Acceleration is directly proportional to an
object’s net force, therefore:
• a=2(24 m/s^2)= 48 m/s^2
• Acceleration is inversley proportional to mass,
when mass is tripled, there is a decrease in
acceleration, thefore:
• a= (24 m/s^2)/ 3 = 8 m/s^2
Question 3
• A 400-newton girl standing on a dock exerts a
force of 100 Newton's on a 10,000-newton
sailboat as she pushes it away from the dock.
How much force does the sailboat exert on
the girl?
• Mass of Earth= 5.98 x 10^24 kg
• Mass of moon= 7.35 x 10 ^22 kg
• Distance= 3.84 x 10 ^8 m
Solution 3
• Newton’s Third Law: For every action there is
an equal and opposite reaction.
• Since the girl is applying a force of 100 N on
the sailboat, the sailboat is applying a force of
100 N back to her.
Question 4
• What is the mass of a 100-N Weight?
Solution 4
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•
•
•
g= F/m
m=F/g
m= (100 kg x m/s^2)/(9.81 m/s^2)
m= 10.2 kg
Question 5
• Which cart has the greatest Inertia?
•
•
•
•
A-speed of 4 m/s and 1 kg load
B-Speed of 3 m/s and 2kg load
C-Speed of 1.5 m/s and 3 kg load
D-Speed of 1 m/s and 4kg load