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 distanceof 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 kilo-grams 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.

• Answer: 100 N

Question 4

• What is the mass of a 100-N Weight?

Solution 4

• 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

Answer

• Choice D

• The greater the mass, the more inertia.