Journal #21 9/30/09 Most missed question from Chapter 3 Test: A gazelle is running in a straight line path at a constant velocity of 1340m/min. A cheetah can accelerate from 0m/min to 1820m/min in 3 seconds. What is the average acceleration of the cheetah?

Forces and Newton’s 3 Laws of Motion Chapter 4 Forces and Newton’s 3 Laws of Motion

Isaac Newton (1642-1727)

Isaac Newton (1642-1727) Isaac Newton is without a doubt one of the most influential men in history. Just a few of his accomplishments: Built the first practical reflecting telescope Developed a theory of color including the idea that white light is composed of all colors of the rainbow Studied the speed of sound Developed calculus from scratch! Defined the 3 Laws of Motion that govern all objects Studied the effects of gravity (story about the apple)

Force A force is a push or a pull. Force is not a thing in itself, but rather an interaction between two objects. Force is a vector quantity… direction matters in the answer!

Common Forces

Newton’s First Law “The Law of Inertia” A body remains at rest or moves in a straight line at a constant speed unless acted upon by a net force. Objects do not accelerate unless a net force is applied.

Newton’s First Law Inertia is a property of an object most closely related to it’s mass (not to be confused with momentum) that explains why objects with greater mass resist a change in motion more than those with a lesser mass.

Net Force Net force is the vector sum of ALL forces acting on an object. If there is zero net force, then there is zero acceleration (constant velocity), this is a special case called equilibrium. If there is a net force, there will be an acceleration. That means that the object will be speeding up, slowing down, or changing direction.

Free Body Diagrams A Free Body Diagram is a simple drawing that shows the magnitude and direction of all of the force vectors acting on an object. The length of the arrows in relation to each other is VERY important Each arrow must point away from the “free body” and be labeled appropriately The system, the object the force is applied to, is drawn as a shaded circle

The book is drawn as a ball Free Body Diagrams Here is an example of a FBD of a book at rest on a table top. Fg is acting downward but is “balanced” by FN acting upward. Results in no net force and zero acceleration FN The book is drawn as a ball Fg

Common Forces

Free Body Diagrams Here is an example of a FBD of a box being pulled by a rope at a constant speed on a flat surface. Fg and FN are still opposite and equal. FT and Ff are also opposite and equal. FN Ff FT Fg Object is in motion, but not accelerating

Balanced Forces (zero net)

Free Body Diagrams Here is an example of a FBD of a ball under free fall conditions. Fg is the only force acting on this object. The net force is down and the object is accelerating. Fg Object is in motion and accelerating

Unbalanced Forces (non-zero net)

HW Questions: P. 89 #1-5 Draw a FBD for the following situations: A flowerpot falls freely from a windowsill. (Ignore any forces due to air resistance.) A sky diver falls downward through the air at constant velocity. (The air exerts an upward force on the person.) A cable pulls a crate at a constant speed across a horizontal surface. The surface provides a force that resists the crate’s motion. A rope lifts a bucket at a constant speed. (Ignore air resistance.) A rope lowers a bucket at a constant speed. (Ignore air resistance.)

Answers to HW #1 #2 Fg Ff Fg

Answers to HW #3 #4 Fg FN FT Ff Fg FT

Answers to HW #5 Fg FT

Journal #22 10/1/09 Draw a free body diagram for the following situations: A car accelerates from rest on a flat road (there is both friction from the air and the ground). The space shuttle just after launch is accelerating upward (include friction from the air)

Newtons’ Second Law The accel. of an object is directly proportional to the net force acting on the object, and inversely proportional to the mass of the object. a m Fnet

Newton’s Second law of Motion …mathematically Net Force = (mass)(accel) Fnet = ma

NEWTON'S 2nd LAW a F m a F a M

Mass Mass is the amount of matter in an object (not to be confused with weight) Also considered a measure of the inertia of an object measured in SI unit of kilograms (kg)… if mass is given in grams you must convert!

Weight Weight is the downward force upon an object due to acceleration caused by gravity weight = mass (kg)  accel. due to gravity (m/s2) Fg = mg measured in Newtons (N)

The weight of a 10 kg brick is... A) 98 N B) 10 kg C) 9.8 kg D) 10 N E) 98 kg

Newton’s 2nd Law Practice Two horses are pulling a 100-kg cart in the same direction, applying a force of 50 N each. What is the acceleration of the cart? 2 m/s2 1 m/s2 0.5 m/s2 0 m/s2

Answer B Reason: If we consider positive direction to be the direction of pull then, according to Newton’s second law,

Journal #23 10-02-09 Two friends Mary and Maria are trying to pull a 10- kg chair in opposite directions. If Maria applied a force of 60 N and Mary applied a force of 40 N, in which direction will the chair move and with what acceleration? The chair will move towards Mary with an acceleration of 2 m/s2. The chair will move towards Mary with an acceleration of 10 m/s2. The chair will move towards Maria with an acceleration of 2 m/s2. The chair will move towards Maria with an acceleration of 10 m/s2.

Answer: C Reason: Since the force is applied in opposite direction, if we consider Maria’s direction of pull to be positive direction then, net force = 60 N – 40 N = 20 N . Thus, the chair will move towards Maria with an acceleration.

Location Mass Weight Earth 18.4 kg 180 N Moon 18.4 kg 30 N Orbiting 1/6 of Earth’s Orbiting Earth 18.4 kg 0 N

Mass and Weight On the Moon, the force of gravity is only 1/6 as strong as on the Earth. (approx. 1.63m/s2) While orbiting, you are practically weightless but your mass remains unchanged. Your mass does not depend on where your are. e.g. Earth, Moon, or space

Falling with Air Resistance Air resistance (drag force) increases with speed and increased cross-sectional area and can be effected by the size and shape of an object.

Acceleration << g Terminal Velocity Net Force Acceleration = g Velocity = 0 but motion is about to begin mg F Acceleration < g v increasing downward mg F Acceleration << g v still increasing downward just not as rapidly as before mg F Acceleration = 0 Terminal velocity mg

Terminal Velocity Terminal velocity occurs when the drag force of air resistance becomes large enough to balance the force of gravity. At this instant in time, there is no net force — the object stops accelerating (see D below); terminal velocity has been reached.

Friction The force that opposes the motion between two surfaces that are in contact. Friction is the "evil monster" of all motion. Regardless of which direction something moves in, friction pulls it the other way. Move something left, friction pulls right. Move something up, friction pulls down. It appears as if nature has given us friction to stop us from moving anything. Friction is actually a force that “appears” when there is relative motion between two objects. Although two objects might look smooth, microscopically, they're very rough and jagged.

Static (starting) Friction The force that opposes the start of the motion. Static means stationary ( not moving).

Kinetic (sliding) Friction The force between surfaces in relative motion For the same object, why is the force of kinetic friction less than the force of starting friction?

Newton’s Third Law Action-Reaction Law Two forces that make up an interaction pair of forces are equal in magnitude, but opposite in direction and act on different objects.

Newton’s Third Law For every action, there is always an equal (magnitude) and opposite (direction) reaction. By “action” or “reaction”, we mean a force. Action/reaction forces do not act on the same object.

Reaction: road pushes on tire Action: tire pushes on road

Reaction: gases push on rocket Action: rocket pushes on gases

Identify at least six pairs of action-reaction force pairs in the following diagram:

Question 1 The top of the rope, near the hook. If a stone is hung from a mass-less rope, at which place on the rope will there be more tension? The top of the rope, near the hook. The bottom of the rope, near the stone. The middle of the rope. The tension will be same throughout the rope.

Answer 1 Answer: D Reason: Because the rope is assumed to be without mass, the tension everywhere in the rope is equal to the stone’s weight .

Question 2 In a tug-of-war event, both teams A and B exert an equal tension of 200 N on the rope. What is the tension in the rope? In which direction will the rope move? Explain with the help of Newton’s third law.

Answer 2 Team A exerts a tension of 200 N on the rope. Thus, FA on rope = 200 N. Similarly, FB on rope = 200 N. But the two tensions are an interaction pair, so they are equal and opposite. Thus, the tension in the rope equals the force with which each team pulls (i.e. 200 N). According to Newton’s third law, FA on rope = FB on rope. The net force is zero, so the rope will stay at rest as long as the net force is zero.

Journal#24 10/5/09 You place a watermelon on a spring scale at the supermarket. If the mass of the watermelon is 4.0kg, what is the reading on the scale in Newtons?

Journal#25 10/6/09 A train engine is accelerating while pulling two box cars of equal mass of 1.0x104-kg. If the acceleration of the cars is 2.0m/s2, with what force must the engine be pulling. (ignore friction from the rails and the air)

Journal#26 10/7/09 A train engine is accelerating while pulling two box cars of equal mass of 1.0x104-kg. There is an opposing frictional force of 2.0x104N acting against the motion. What will be the acceleration of the cars if the engine uses a force of 3.0x104N?

Journal#27 10/8/09 Two train engines are accelerating while pulling two box cars of equal mass of 1.0x104-kg. If EACH engine uses a force of 3.0x104N and the acceleration of the cars is only 2.0m/s2, what is the opposing frictional force acting against the motion?

I Respond Questions # 1 Draw a FBD for the following situations: A flowerpot falls freely from a windowsill. (Ignore any forces due to air resistance.) #2 #3 #4 Fg FN FT Ff Fg Ff Fg FT Fg #1

I Respond Question # 2 A sky diver falls downward through the air at constant velocity. (The air exerts an upward force on the person. #2 #3 #4 Fg FN FT Ff Fg Ff Fg FT #1 Fg