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 DYNAMICS Newton’s 2 nd Law of Motion Newton’s 1st Law of Motion Newton’s 3rd Law of Motion Newton’s Second Law of Motion states that the rate of change of momentum of a body is directly s proportional to the resultant force acting on it, and it acts in the same direction as the resultant force. Newton’s First Law of Motion states that every object will continue in its state of rest or uniform motion in a straight line unless a resultant force acts on it. If there is a net resultant force acting on a body, it will change its state of motion. 𝑑𝑝
𝑑𝑡
𝑑𝑝
(SI units) 𝑑𝑡
Inertia is defined as the reluctance to a change in the state of motion of an object. It is proportional to mass. 𝑑𝑚
Can also be expressed 𝐹
=
𝑣
+ 𝑚𝑎 (By pdt rule) like this: 𝑑𝑡
𝐹∝
𝐹=
Newton’s Third Law of Motion states that for every action force acting on a body, there is an equal and opposite reaction force acting on the opposite body. Characteristics action-­‐reaction forces: 1)
2)
3)
Weight & Weightlessness Hence, the net force acting on an object is defined as the rate of change of momentum of an object. Principle of Conservation of Linear Momentum •
Principle of Conservation of Linear Momentum states that if there is no resultant external force acting on a system of When the mass of the body is constant, the equation reduces to 𝑭 = 𝒎𝒂. bodies, the total linear momentum of the system always remain constant. Linear Momentum & Impulse Types of Collisions Linear momentum, 𝒑, is the product of its mass and -­‐1
velocity. (Vector, kgms ) Elastic 𝑝 = 𝑚𝑣 1) 𝐼 = 𝐹!"# ∆𝑡 2) 3) 𝐼 = ∆𝑝 4) Conservation of Linear Momentum (PCOM) Conservation of Kinetic Energy (COE) Conserved Conserved !!
𝐼 = ! 𝐹 𝑑𝑡 !!
Perfectly Inelastic Conserved Not Conserved Conserved Not Conserved 𝐼 = Area under 𝐹𝑡 graph 263 Tanjong Katong Road, #01 – 07 S437050 |Tel: 67020118 | mulberryeducation.sg •
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Particles coalesce (stick together) after the collision. They move together with the same velocity. Elastic collisions between 2 bodies with 𝒖𝟏 = 𝒖, 𝒖𝟐 = 𝟎 Special cases Result 𝒎𝟏 = 𝒎𝟐 𝑣! = 0, 𝑣! = 𝑢 𝒎𝟏 ≪ 𝒎𝟐 𝑣! ≈ −𝑢, 𝑣! ≈ 0 𝒎𝟏 ≫ 𝒎𝟐 𝑣! ≈ 𝑢, 𝑣! ≈ 2𝑢 Weight of an object is defined as the gravitational force acting on the object. The sensation of feeling weightlessness refers to apparent weightlessness whereby the object experiences no contact forces. Free-­‐Body Diagrams (FBD) Relative Speed of Approach (RSA) = Relative Speed of Separation (RSS) Inelastic Impulse, 𝑰, is the product the average force acting on an object and the time interval that the force is being applied. (Vector, Ns) •
Types of 2 body collisions The forces are of the same nature. They are equal in magnitude and opposite in direction. Action and reaction act on different bodies. Identify and isolate the body. Draw all the physical forces acting on the body clearly. Length of arrow represents the magnitude of the force. Take note of the relative magnitude of forces. Ensure correct point of application of force. Label all drawn forces. Friction • Friction is a resistive force which opposes impending motion. • It is directly proportional to normal contact force, 𝑁. • Can be separated into static and kinetic friction. 𝑓! ≤ 𝜇! 𝑁 𝑓! = 𝜇! 𝑁 (Increases linearly) (constant)