# Kinematics – the study of how things move Dynamics – the study of why things move Forces (the push or pull on an object) cause things to move Aristotle.

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Kinematics – the study of how things move Dynamics – the study of why things move Forces (the push or pull on an object) cause things to move Aristotle believed that anything that moves must have forces being applied Galileo argued that objects can move at constant speeds without forces being applied. Forces are what cause objects to accelerate.

English Physicist, Astronomer, Theologian 1643 - 1727 Isaac Newton picked up where Galileo left off. Lived during the bubonic plague in England. During that time, he: Invented calculus Proposed a law to describe gravity Proposed a theory to explain color Proposed Three Laws of Motion.

Mass A measurement of an object’s quantity of matter A measurement of an object’s inertia Inertia – the tendency of objects to maintain their state of rest or to maintain constant velocity Example: car slams on brakes and items on seat fall to floor

Objects with a larger mass have a greater inertia. Therefore, they are harder to accelerate (speed up or slow down)

Inertia can give the impression that forces are being applied. Force is not being applied to rider. Rider is moving at constant velocity because of inertia.

Newton’s First Law – an object at rest tends to stay at rest and an object in uniform motion tends to stay in uniform motion (constant velocity) unless acted upon by a net external force Newton’s First Law is also known as the Law of Inertia.

A free body diagram (FBD) shows all of the forces that are present on an object both in the horizontal and vertical direction. In a FBD, angled forces are resolved into horizontal and vertical components Net force (ΣF) – the sum of all forces that act on an object.

Four Basic Forces Applied force (F a ) – a force that is done by an external cause (agent). It can be any direction. Gravitational force (F g or W) -- the force caused by gravity (weight). It always acts downward. Frictional force (F f ) -- a force that opposes motion and slows down objects. It is always parallel to the surface. Normal force (F n ) – the force exerted by a surface on which an object is resting. It is always perpendicular to the surface.

Example: book being pushed on table Σ F x = F a - F f Σ F y = F n - F g FaFa FfFf FnFn FgFg book FBDNet Force Equations

Forces at Angles book 40° FaFa F ax = F a cos40 F ay = F a sin40 Σ F x = F ax - F f Σ F y = F n + F ay - F g FfFf FnFn FgFg book FBDNet Force Equations F ax F ay

Newton’s Second Law – the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass Newton observed some things about accelerating objects: The bigger the force, the greater the acceleration The larger the mass, the smaller the acceleration

Σ F = ma F = force (Newtons) m = mass (kg) a = acceleration (m/s 2 )

What net force is required to bring a 1500-kg car to rest from a speed of 28 m/s within a distance of 55 m?

A 70-kg person traveling at 100 km/hr strikes a parked car. At the instant of impact, the seat belt restrains the person with a force of 21,000 N bring them to rest in the car. How far does the person travel before coming to rest?

When a force is applied to an object, it is always exerted by another object. Examples: a hammer hits a nail a child pulls a sled an apple is pulled to the Earth Newton believed that the “force-providers” also are “force-receptors.” Examples: the nail pushes back on the hammer the sled pulls back on the child the Earth is pulled to the apple

If every force has an equal and opposite force, why dos objects ever move? The forces are NOT exerted on the same object. Newton’s Third Law – Whenever one object exerts a force on an second object, the second exerts an equal force in the opposite direction on the first Evidence: Hammer causes the nail to accelerate (+ force) while the nail causes the hammer to decelerate (- force) Example: If a hammer exerts a 50-N force on a nail, the nail exerts a 50-N force on the hammer in the other direction.

Weight A measure of the gravitational force on an object Always directed downward (toward the center of the Earth F g = mg A person’s mass does not change, but his weight does depending on the magnitude of gravitation force.

An average man has a weight of 686 N on the Earth. What would his weight be if he was standing on the moon (a g = 1.6 m/s 2 )

A person pulls upward on string attached to a box with a force of 150 N. The box has a mass of 12 kg. Does the box move upward and if so, with what acceleration does it move?

Normal Force A contact force that is perpendicular to the surface The force that pushes up on the object resting on the surface Since the statue is at rest F N is equal and opposite to F G. F N has another equal and opposite force (F’ N is reaction force on table)

A 65-kg woman descends in an elevator that briefly accelerates at 0.20g downward. She stands on a scale that reads in N. What is her weight and what does the scale read? What does the scale read when the elevator descends at a constant speed of 2.0 m/s? Should the scale read the same, more or less than her weight?

Resultant Force and Equilibrium Multiples forces on an object must be broken down into x and y components to find the resultant force. What is the resultant force (magnitude and direction) acting on the boat by workers A and B?

An object is stationary when all forces acting on it cancel out. This situation is called equilibrium. What are the tensions in F A and F B ?

Pulleys Pulleys utilize ropes or cables which have a constant tension force throughout their length If multiple lengths of rope extend from the mass being lifted, the tension force pulls up for each extension.

A mover is trying to lift a piano up to a second story apartment. If the piano is 2000 kg, what force does he need to apply to lift the piano at a constant speed? If he fatigues and only can lift with 500 N of force, what will be the acceleration of the piano?

Friction Caused by a rough surface. Object on a rough surface actually has to move up and down because the two rough surfaces catch on each other. Because energy is used to move the moving object up and down, less energy is used to move the moving object forward. Friction is the resistance that an object experiences when moving.

The force of friction is influenced by two factors – the surface on which an object is moving and the weight (gravitational force) of the object. F f = μF n Coefficient of friction (μ) – indicates the “roughness” of the surface. Unique to each surface. Typically, the normal force of the object is just equal and opposite to the gravitational force (but not always).

Two Types of Friction Static (Stationary Object) If an object is at rest, an applied force has to exceed the maximum static frictional force of the object for it to move F fs = μ s F n Kinetic (Moving Object) If an object is moving, there is a kinetic frictional force that opposes motion (always less than static frictional force) F fk = μ k F n applied static friction box at rest appliedkinetic friction box in motion

When an object is at rest, friction is equal to the force applied to an object until the maximum static force is attained. Beyond that maximum force, the object moves and friction reduces to the constant kinetic friction force.

A 10.0-kg box rests on a horizontal floor. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is 0.30. Determine the maximum static frictional force and the kinetic frictional force. Would the box move if a 10 N force was applied? If so, what would be its acceleration? Would the box move if a 40 N force was applied? If so, what would be its acceleration?

Inclined Planes Inclined planes are unique because gravity is the accelerating force, but the motion is not vertical (not free-fall). Friction Normal Gravity Friction Normal Gravity To solve, rotate the object so the majority of forces are in x and y directions (gravity is not).

Friction (F f ) Normal (F n ) FgFg F gx F gy Gravity (F g ) Σ F x = F gx - F f = ma Σ F y = F n - F gy = 0 Resolve gravity into the new x and y components. y x Write net force equations

A skier with a mass of 85 kg begins to descend a 30 degree slope. Assuming the coefficient of kinetic friction is 0.10, calculate his acceleration.

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