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2.2   forces and dynamics
 

2.2 forces and dynamics

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An overview of the concepts of force and momentum. This relates to Newton's Laws

An overview of the concepts of force and momentum. This relates to Newton's Laws

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    2.2   forces and dynamics 2.2 forces and dynamics Presentation Transcript

    • Topic 2 – Mechanics 2.2 – Forces and Dynamics
    • Force Diagrams
      • In order to solve dynamics problems we usually require a diagram.
      • In general there are two types of diagram we can use.
        • System diagrams – These are a “realistic” picture of the whole system.
        • Free body diagrams – These show only one object and only the forces acting on it.
      • Both types of diagram are useful in different situations.
    • Free Body Diagrams
      • Consider a box, mass m, that is sliding down a rough ramp of angle 30 o
      • The system diagram showing the external forces looks like this:
        • W is the box's weight acting vertically downwards from the centre of mass.
        • F is the surface friction force acting along the surface from the point of contact .
    • Free Body Diagrams
      • Consider a box, mass m, that is sliding down a rough ramp of angle 30 o
      • The free body diagram for the box looks like this:
        • W is the box's weight acting vertically downwards from the centre of mass.
        • R is the normal reaction force of the ramp on the box acting perpendicular to the surface of contact from the point of contact .
        • F is the surface friction force acting along the surface from the point of contact .
    • Free Body Diagrams
      • Often the only way to properly describe all the forces acting on an object is to draw a free body force diagram.
      • This will help identify Newton's third law paired internal forces and help solve the problem.
    • Weight due to Gravity
      • Gravity is not a force.
      • Gravity is a field. The slope of that field is the gravitational field strength.
      • The effect of the field on an object's mass is called the object's weight due to gravity.
      • Weight is a force and is measured in newtons.
      • Mass is a measure of an object's linear inertia and is measured in kilograms.
        • Inertia is the resistance of an object to change its state of motion.
    • Weight due to Gravity
      • Weight due to gravity is calculated by:
        • W = mg
          • W : weight in N
          • M : inetial mass in kg
          • g : gravitational field strength Nkg -1
      • For object's in a uniform gravitational field (i.e. close to the Earth's surface) g is a constant.
      • G = 9.81 Nkg -1 or 9.81 ms -2
    • Newton's First Law
      • An object in equilibrium will remain in equilibrium if no external forces act.
        • OR
      • If the resultant force on an object is zero, then the velocity of that object will be constant.
        • If the resultant forces on an object are zero then the object is in translational (linear) equilibrium.
        • The velocity is constant or zero
        • There is no change in direction.
    • Newton's First Law
      • All of the objects below are in equilibrium. Determine the magnitude and direction of the unknown force.
      30 0 m=6kg m=4kg m=8kg
    • Newton's Second Law
      • An object that is not in equilibrium experiences an acceleration proportional to the nett force on the object.
        • Σ F = ma
          • Σ F : the vector sum (nett) force acting in N
          • m : the inertial mass of the object in kg
          • a : the acceleration of the object in ms -2
      • This is only true if m remains constant.
      • The acceleration will be in the same direction as the nett force.
    • Newton's Second Law
      • Calculate the acceleration of each of the objects below:
      m=6kg m=8kg m=4kg
    • Linear Momentum
      • The linear momentum of an object is the product of its inertial mass and its velocity.
        • It is a sort of measure of how difficult it is to stop the moving object.
      • p = mv
        • p = momentum in kgms -1
        • m = inertial mass in kg
        • v = velocity in ms -1
      • Momentum is a vector quantity.
        • It has direction
      • Momentum is a conserved quantity.
        • There is always the same amount of momentum in a system if no external forces act.
    • Linear Momentum
      • Calculate the momentum of the following objects.
        • A 70kg man running with a velocity of 10ms -1 to the right.
        • A 1000kg car travelling at 30ms -1 to the left.
        • A 50,000kg rocket travelling at 80ms -1 upwards.
    • Newton's Second Law
      • Newton's second law can also be stated as:
        • The nett force is equal to the time rate of change of momentum.
    • Impulse
      • In most situations such as collisions, Σ F is not a constant and is applied over a very short time Δ t.
      • The product of force and time is called impulse and is measured in Ns
      • Impulse = Δ F Δ t = Δp = m(v-u)
        • It is the total impulse of a kick that affects the change in momentum of a ball, not the force or time individually.
        • The total impulse is found in reality by measuring the area under an F-t graph
    • Impulse
      • A model rocket motor has a total impulse of 246Ns. The rocket has a mass of 500g and is fired from rest. What is the rocket's velocity when the motor burns out?
      • A cricket ball has a velocity of 130kmh -1 when bowled. The batsman applies an impulse of 350Ns to the 160g ball. What is the speed of the ball after striking?
    • Principle of Conservation of Linear Momentum
      • The Principle of Conservation of Linear Momentum states that:
        • In a collision the total momentum of the system is conserved if no external forces act.
      • i.e. p final = p initial OR Σ mv = Σ mu
    • Simple Collisions
      • Consider a car of mass 1500kg travelling at 50kmh -1 . It strikes a stationary van (no brakes) of mass 2500kg. After the collision both vehicles move off together. Calculate the speed.
    • Simple Collisions
      • Two marbles (A and B) of equal mass (100g) roll towards each other. A has a speed of 2.5ms -1 . B has a speed of 4.0ms -1 . After the collision both marbles roll away with the same speed. Calculate the speed.
    • Newton's Third Law
      • Newton stated that:
        • If body A exerts a force on body B then body B exerts an equal and opposite force on body A.
      • This is a consequence of the law of conservation of momentum.
        • The two objects in a collision, are subject to the same impulse during a collision for the same time. The forces must therefore be equal
      • These forces are internal to the system. You can only see them in free body diagrams.
      • You can not “measure” these forces, but you can calculate them.
    • Newton's Third Law
      • Forces due to Newton's third law always occur in pairs.
        • The pair of forces act:
          • On different bodies
          • Are of the same type (contact, gravitational etc)
          • Are of the same magnitude
          • Are of opposite directions.
      • e.g. Bob pushes to the left on the wall.
        • The wall pushes to the right on Bob
      • e.g. the Moon is attracted by the gravitational pull of the Earth.
        • The Earth is attracted by the gravitational pull of the Moon.
    • Newton's Third Law
      • Two boxes (A and B) have masses 4kg and 9kg respectively and are in contact on a smooth floor. A force of 10N is applied to the 4kg box to cause an acceleration.
        • What is the acceleration of the 9kg box?
        • What is the magnitude of the force exerted on Box B by box A?