 # Forces and the Laws of Motion Force, Mass, and Acceleration

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Forces and the Laws of Motion Force, Mass, and Acceleration
PVHS Physics

Objectives Students should be able to analyze situations in which a particle remains at rest, or moves with constant velocity, under the influence of several forces. Students should understand the relation between the force that acts on an object and the resulting change in the object’s velocity Students should understand how Newton’s Second Law, , applies to an object subject to forces such as gravity, the pull of strings, or contact forces Students should be able to analyze situations in which an object moves with specified acceleration under the influence of one or more forces Students should understand the significance of the coefficient of friction Students should understand the effect of drag forces on the motion of an object Students should be able to apply Newton’s Third Law in analyzing the force of contact between two objects that accelerate together

A little review… What is acceleration? What causes acceleration?
What are the types of forces?

What we know… Inertia… Mass is a measure of inertia
Is an object’s resistance to a change in motion it is the tendency of an object to maintain its state of motion Mass is a measure of inertia More mass… more inertia Less mass… less inertia

What we know… The Law of Inertia … “An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force”. Net Force… The vector sum of all the external forces acting on an object

What we know… Forces are Vectors Equilibrium…
The state in which there is no change in an object’s motion The sum of all forces equals zero

What we know… Finding the Net Force…
What happens when the Net Force is not zero? List givens and draw a free-body diagram Establish x-y axes (frame of reference) Resolve vector components Sum the vectors in each direction

F Forces and Motion Forces cause an object’s velocity to change…
Since acceleration is the rate of change in velocity… Force causes acceleration The acceleration is directly proportional to the force The bigger the force, the greater the acceleration The smaller the force, the smaller the acceleration F F

m Mass and Motion Inertia…
Is an object’s resistance to a change in motion Inertia resists acceleration Mass is a measure of inertia Acceleration in inversely proportional to mass More mass, less acceleration Less mass, greater acceleration m

Force, Mass, and Motion Combining the effects of mass and force…
This is Newton’s Second Law

SF=ma Newton’s Second Law
“The acceleration of an object as produced by a net force is directly proportional to the magnitude of the force, in the same direction of the force, and inversely proportional to the mass of the object” The 2nd Law is commonly written as: SF=ma “The sum of the forces on an object equals mass times acceleration” Note: it is the Net Force that causes the acceleration

Application… The net force on the propeller of a 3.5kg model airplane is 7.0N. What is its acceleration? A 2.0kg otter starts from rest at the top of an incline 85 cm long and slides to the bottom in 0.50s. What is the net force on the otter?

Who is pushing who?

Newton’s Third Law “For every action, there is an equal and opposite reaction” … Newton’s 3rd Law Forces always exist in pairs called Action-Reaction Pairs When two objects interact they exert forces on one another that are equal and opposite This includes field forces and physical forces Action-Reaction Pairs don’t cancel Each force acts on a different object… This law explains why both cars are dented in a car accident. (Can you think of any other examples of Newton’s Third Law?)

Newton’s Third Law

Newton’s Third Law

Friction always resists motion Two types of Friction Static… no motion/ stationary and forces in equilibrium Kinetic… object in motion, forces may or may not be in equilibrium Static friction force is greater than Kinetic friction force

Friction Do you think friction forces vary with the type of surface?
Do heavy objects have more friction than lighter objects? Why?

Friction Normal Force… the force perpendicular to the contact surface between two objects Normal Force (N) Normal Force (N) W W

Friction Friction is proportional to the normal force
m is the coefficient of friction and depends on the type of surface

Coefficient of Friction
Typical coefficients of friction… depends on the type of surface Coefficient of Friction Surfaces Static Friction Kinetic Friction Steel on steel (dry) 0.6 0.4 Steel on steel (greasy) 0.1 0.05 Teflon on steel 0.041 0.04 Brake lining on cast iron 0.3 Rubber tires on dry pavement 0.9 0.8 Metal on ice 0.022 0.02 Rubber tip of crutch on rough wood 0.7  -

Newton’s Laws and Friction
Useful Equations… Net force: SF = ma (units… newtons = kg m/s2) Gravitational force: W = mg Frictional force: Ffriction = mFnormal

Practice #1 An applied force of 50 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)

Practice #2 An applied force of 20 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the coefficient of friction (µ) between the object and the surface, the mass, and the acceleration of the object. (Neglect air resistance.)

Practice #3 A 5-kg object is sliding to the right and encountering a friction force which slows it down. The coefficient of friction (µ) between the object and the surface is 0.1. Determine the force of gravity, the normal force, the force of friction, the net force, and the acceleration. (Neglect air resistance.)

Practice #4 Demo… A 2.0 kg block accelerates down a 35 degree ramp. If it travels 2.0 m in 4 seconds, what is the coefficient of friction?

Practice #4 Do… A 1.0 kg block slides down a down a 30 degree ramp with a coefficient of friction of .15. How long will it take to slide 2.0m?

Air Resistance is a friction force In general, Air Resistance (aka Drag) is proportional to velocity or the square of velocity

What is Terminal Velocity?
As an object falls through a fluid, its velocity and Drag (air resistance) increases At a certain velocity, the drag equals the force of gravity and the object stops accelerating… equilibrium is reached and the net force is zero When equilibrium is reached the object has attained Terminal Velocity

Air Resistance and Terminal Velocity
Create qualitative x-t, v-t and a-t graphs of a falling object with air resistance…

What we know… How does force affect the motion of an object?
How do free-body diagrams help in analyzing forces and motion? What are Newton’s Laws of Motion? How can you determine forces required for equilibrium? How is mass related to motion? What are action-reaction pairs and why don’t they produce equilibrium? What is the difference between mass and weight? What is a normal force? How can you determine the force due to friction?

Questions?

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