Unit Two: Dynamics Section 1: Forces
Look in glossary of book … • What is the difference between dynamics and kinematics? • What is a force? What can a force do? What causes a force? • Key Terms: • Dynamics Kinematics • Force Gravitational Force • Strong Nuclear Force • Inertia Net Force • Normal Force Weight Mass
What is dynamics??? • Kinematics: The study of how objects move (velocity, acceleration) • Galileo performed experiments that allowed him to describe motion but not explain motion. • Dynamics: The study of why objects move. • The connection between acceleration and its cause can be summarized by Newton’s 3 Laws of Motion (published in 1687) • The cause of acceleration is FORCE.
Forces • What is a force? • A push or a pull • Some forces cause acceleration • Example: gravity • Some forces cause stretching, bending, squeezing • Example: spring force
The 2 Main Types of Forces • Contact Forces: are forces that result when two objects are physically in contact with one another Example: push/pull, normal force, friction, spring force, tension, air resistance Non-contact Forces: forces that result when two objects are not in physical contact Example: gravitational force, nuclear force, magnetic force, electrostatic force (electric charge)
Newton’s First Law of Motion- Newton’s Law of Inertia • An object at rest or in uniform motion (ie, constant velocity) will remain at rest or in uniform motion unless acted on by an external force. • Section 5.1 in text (pages 154 to 159) • Reworded: An object at rest will remain at rest until a force is applied. An object moving at a constant velocity will continue to move at a constant velocity if no force is applied (ie, no acceleration).
Inertia • the natural tendency of an object to remain in its current state of motion (either moving or at rest)
Where did this come from? • Galileo performed many experiments and speculated that if a perfectly smooth object were on a perfectly smooth horizontal surface it would travel forever in a straight line. • Newton developed this idea.
Newton’s First Law Example • If an apple is sitting on Mrs. Evans’ desk, it will remain there until the desk is removed (so gravity acts on it) or someone lifts it up (applied force). • If a car is driving along a straight road at 100km/h, it will continue to do so (given the car still has gas!) until the brakes are applied (applied force), there is a turn or the road surface changes (more or less friction).
Net Force • The sum of all vector forces acting on an object. • Example: What are the forces acting on a stopped car? Draw a labeled diagram. • Example: What are the forces acting on a car moving at 100km/h [N]?
Normal Force • A force that acts in a direction perpendicular to the common contact surface between two objects • Example Diagram:
Quick Experiment • Materials – cup, card, penny or coin • What to do: • Set up the card on top of the cup and the penny on the card in the middle. • Flick the card. What happens to the card? The penny? Why?
Questions 1. To which object was a force applied by the flick and which object was not acted upon by the flick? • 2. Why did the penny fall into the cup and not fly off with the card? • 3. What force held the penny in place while the card was flicked out? What force brought the penny down into the cup? • 4. Would the penny move in the same way if sandpaper was used instead of the card?
Summary • The inertia of every object resists the change in motion. In this case, the inertia of the penny held it in place while the card was flicked out from under it. The force acting on the card was not applied to the penny. After the card was moved from under the coin, gravity supplied the force to bring the penny down into the cup. If a force had been applied to both the card and the penny, then both would have moved and the penny would not have fallen into the cup.
Check Your Learning • 1. Why does a package on the seat of a bus slide backward when the bus accelerates quickly from rest? Why does it slide forward when the driver applies the brakes? • Use as many physics terms as possible and describe in detail.
The bus is initially at rest, as is the package. In the absence of any force, the natural state of the package is to remain at rest. When the bus pulls forward, the package remains at rest because of its inertia (until the back of the seat applies a forward force to make it move with the bus). • From the point of view of someone on the bus, it appears that the package is moving backward; however, someone watching from outside the bus would see the bus move forward and the package trying to stay in its original position. • Once the package is moving with the bus, its inertia has now changed. It now has a natural tendency to be moving forward with a constant speed. When the bus slows down, the package continues to move forward with the same constant speed that it had until some force stops it.
Force • Symbol: F • Formula: F=ma • Force = mass x acceleration • Units: kg x m/s2 = Newtons (N)
Gravitational Forces • Example: Consider the following information and then compare the gravitational force on the SAME OBJECT in each case. • A man standing near the equator (distance from Earth’s centre = 6378 km) • A man standing near the North pole (distance from Earth’s centre = 6357 km) • A man standing in the International Space Station (distance = 6628 km) • A man in a space ship past Pluto
Gravitational Forces • Gravitational force decreases as we increase how far we are from the centre of the Earth • It is a non-contact force
Weight Vs. Mass • Weight and mass are NOT THE SAME. • Weight = the force of gravity acting on a mass. Weight can change. It is measured in Newtons (force). • Weight = mass x gravitational force • Fg = mg • Mass = the quantity of matter an object contains. Mass for the same object is constant. It is measured in kg.
Examples of Weight Problems • Mrs. Evans’ dog Pi has a mass of 17kg. What would Pi’s weight be: • A) On Earth? • B) On Jupiter (where g = 25.9 m/s2) • C) On the Moon (where g = 1.64 m/s2)
Examples of Weight Problems • A student standing on a scientific spring scale on Earth finds that he weighs 825N. Find his mass.
Practice • Page 137, #1, 2, 3, 4
Friction • A contact force • Electromagnetic Force (between surface atoms of objects touching)
Friction • There are 2 types of friction: • Static Frictional Force • When you start to move an object from rest • Larger than Kinetic Frictional Force due to Inertia • ųs • Kinetic Frictional Force • Exists when the object is moving • ųK
Friction • The strength of friction depends on… • Surface materials • Magnitude of forces pressing surfaces together • The strength of friction DOES NOT depend on… • Surface area • Velocity of object moving • See page 140, table 4.5 for a list!
Coefficient of Friction • “Stickiness value” • ų (symbol mu) • ų has no units • Page 140, table 4.5 • Formula: Ff = ųFN • Remember: FN = - Fg
Friction Example • During the winter, owners of pickup trucks often place sandbags in the rear of their vehicles. Calculate the increased static force of friction between the rubber tires and wet concrete resulting from the addition of 200. kg of sandbags in the back of the truck. • Use the table of coefficients of friction on page 140.
Friction Example 2 • A horizontal force of 85N is required to pull a child in a sled at constant speed over dry snow to overcome the force of friction. The child and sled have a combined mass of 52 kg. Calculate the coefficient of kinetic friction between the sled and the snow.
Practice Friction Problems • Page 144 • Questions 5, 6, 7, 8 • Weight Problems • Page 137, #1, 2, 3, 4
Tug of War • Sometimes we have more than 1 force acting on an object (like in a tug of war). • What are the forces at work in a tug of war? • What direction are the forces? • If your team wins, what does that mean about the forces? • If your team loses, what does that mean about the forces? • What other forces are there on the players?
Free Body Diagrams • We usually use a box or small circle to represent the object. • The size of the arrow is reflective of the magnitude (SIZE) of the force. • The direction of the arrow reveals the direction in which the force acts. • Each force arrow in the diagram is labelled to indicate the type of force. • Use math symbols to show equality if needed.
A free body diagram will be used in most dynamics problems in order to simplify the situation In a FBD, the object is reduced to a point and forces are drawn starting from the point Free Body Diagrams FN Fa Ff Fg
Free Body Diagram Examples • 1. A book is at rest on a table top. Diagram the forces acting on the book. • Refer to sheet in class with 10 examples!
The Net Force • The net force is a vector sum which means that both the magnitude and direction of the forces must be considered • In most situations we consider in Physics 11, the forces will be parallel (ie, up and down, etc) and perpendicular
The Net Force • In most situations, there is more than one force acting on an object at any given time • When we draw the FBD we should label all forces that are acting on an object and also determine which would cancel each other out • Ones that do not completely cancel out will be used to determine the net force
Newton’s Second Law • Newton’s first law states that an object does not accelerate unless a net force is applied to the object. • But how much will an object accelerate when there is a net force? • The larger the force the larger the acceleration. • Therefore acceleration is directly proportional to mass. • Acceleration also depends on mass. • The larger the mass, the smaller the acceleration. • Therefore acceleration is inversely proportional to mass. • We say that a massive body has more INERTIA than a less massive body.
Newton’s Second Law- Newton’s Law of Motion • Force = mass x acceleration • Fnet = ma • The acceleration is in the same direction as the force.
Newton’s Second Law Examples • Ex. 1: What net force is required to accelerate a 1500. kg race car at +3.00m/s2? • Draw a FBD to show the net force.
Practice Problems • Page 163, Questions 1, 2, 3
Putting it All Together • Now that we have considered Newton’s Second Law, you can use that to analyze kinematics problems with less information than we have used previously • We can either use dynamics information to then apply to a kinematic situation or vice versa
Newton’s Second Law Examples • Ex. 2: An artillery shell has a mass of 55 kg. The shell is fired from a gun leaving the barrel with a velocity of +770 m/s. The gun barrel is 1.5m long. Assume that the force, and the acceleration, of the shell is constant while the shell is in the gun barrel. What is the force on the shell while it is in the gun barrel?
Practice Problems • Page 168, questions 4 to 8
An Example • A 25kg crate is slid from rest across a floor with an applied force 72N applied force. If the coefficient of static friction is 0.27, determine: • The free body diagram. Include as many of the forces (including numbers) as possible. • The acceleration of the crate. • The time it would take to slide the crate 5.0m across the floor.