Chapter 4 – Forces and Newton’s Laws of Motion

Newton’s First Law (aka Law of Inertia) Objects maintain their state of motion unless acted on by a net external force.

Inertia – resistance to change in motion. Mass – measure of an object’s inertia (in kg)

The net force is the total (vector) force on the object Newton’s Second Law mass acceleration net force (m/s2) (Newtons) (kg) The net force is the total (vector) force on the object

Newton’s Second Law in words… The net force on object equals the mass of the object x it’s acceleration. The acceleration of an object is inversely proportional to its mass. Given the same net force, a small mass will accelerate more than a larger mass.

Units for Mass, Acceleration, and Force System Mass Accel. Force SI kg m/s2 newton (N) CGS g cm/s2 dyne (dyn) BE slug foot/s2 pound (lb)

Weight – force of gravity on a mass (Newtons) F = ma W = mg A 1 kg object has a weight of W = mg W = (1 kg)(9.8 m/s2) W= 9.8 N

Newton’s Third Law Forces always occur in pairs. For every action there is an equal and opposite reaction. Forces always occur in pairs.

Fhammer on nail = -Fnail on hammer Newton’s Third Law Fhammer on nail = -Fnail on hammer

Newton’s Third Law If one object exerts a force on another, then the second object also exerts a force on the first; these forces are equal in magnitude and opposite in direction. FA on B = -FB on A Remember that the forces act on different objects and DO NOT cancel out! When determining the motion of an object, only consider the forces acting ON the object.

An unfortunate box elder bug splatters against the windshield of a moving car. Compared to the force of the car on the bug, the force of the bug on the car is a. larger b. smaller c. the same d. need more information to say c. the same Compared to the deceleration of the car, the deceleration of the windshield-hitting bug is a. larger b. smaller c. the same d. need more information to say a. larger

A box weighing 600 lbs is pushed along a horizontal floor at constant velocity with a force of 250 lbs parallel to the floor. What is the net force on the box? The net force is zero since the velocity is constant (no accel.) A car weighs 2193 lb. What is the weight of the car in N? What is the mass of the car in kg ? (a) 9754 N (1 lb = 4.45 N) (b) 995 kg (W = mg, g = 9.8 m/s2)

ASSIGN: Chapter 4 #1-13 (odds), p. 121 Due Thursday

Chapter 4 Conceptual Questions #1-18 Page 118

An object must be moving for it to have inertia. FALSE In a tug of war, the person who pulls with the most force wins. FALSE If the net force on an object is zero, it can’t be moving. FALSE In order for you to jump off the ground, you need to exert a force on the floor that is greater than the force the floor exerts on you. FALSE Constant velocity requires that the acceleration be zero. TRUE As a ball falls freely, the distance it falls each second is the same. FALSE If a horse pulls on a wagon at rest, the wagon pulls back equally as much on the horse. TRUE When given the same force, a heavy mass will have a larger acceleration than a lighter mass. FALSE Neglecting air resistance, all objects fall at the same rate. TRUE

If a horse pulls on a wagon at rest, the wagon pulls back equally as much on the horse. Will the wagon be set into motion? a. No, because the forces cancel each other out. b. Yes, because there is a net force acting on the wagon. c. Yes, because there is time delay between action and reaction. d. Yes, only if the horse’s pull on the wagon is larger than the wagon’s pull on the horse. b. Yes, because there is a net force acting on the wagon. An object of mass 5 kg is acted upon by exactly four forces, each of magnitude 10 N. Which of the following could NOT be the resulting acceleration of the object? a. 0 m/s2 b. 2 m/s2 c. 4 m/s2 d. 8 m/s2 e. 10 m/s2 e. The maximum net force would be 40 N; 40N/5kg = 8 m/s2

Clearly state Newton’s Three Laws of Motion in your own words. First Law – Objects maintain their state of motion until acted upon by a net external force. Second Law – Given the same force, a more massive object will have a smaller acceleration than a less massive object. F = ma Third Law – Every force has an equal and opposite force.

Section 4.7 – The Gravitational Force Newton’s Law of Universal Gravitation All masses attract each other with a force determined by masses (in kg) force of attraction (in N) distance b/w mass centers (m)

Universal Gravitational Constant (G)

The force of gravity between masses depends on The value of each mass The distance between their center of masses

Inverse Square Law – The force of gravity becomes 4x less when r doubles.

True or False – TRUE! TRUE! TRUE! You exert the same amount of force on the earth as it exerts on you. TRUE! 2. If you threw something fast enough it would never land. TRUE! 3. The sun exerts more of a force on you than the moon. TRUE! How many more times?

Weightlessness – feeling experienced during free-fall due to lack of support force. Apparent Weight – Weight read by a scale; reaction force applied to the person. True Weight – Actual weight due to gravitational force. Zero g or micro g – Zero acceleration of gravity experienced by astronaut; Not zero gravity, gravity holds them in orbit!

True or False – FALSE! FALSE! FALSE! There is barely any gravity in an orbiting space shuttle. FALSE! 2. The earth exerts the same gravitational force on a falling penny as it does on a ton of bricks. FALSE! 3. Neglecting air resistance, a falling ton of bricks will fall faster than a falling penny. FALSE!

Weight of objects on the surface of the earth g = 9.80 m/s2

ASSIGNMENT: Ch. 4 #18, 20, 24, 30 Due Friday

Section 4.8 – The Normal Force The normal force (FN) is a support force that a surface exerts on an object. FN = W since net force on box is zero.

Section 4.8 – The Normal Force FN > W since box is being pressed down.

Section 4.8 – The Normal Force FN < W since box is being lifted up.

Section 4.8 – The Normal Force FN is always perpendicular to the surface.

Section 4.8 – The Normal Force Apparent Weight – weight read by the scale. True Weight – weight due to gravity.

Section 4.8 – The Normal Force True Weight Apparent Weight

Friction – force that opposes motion. Section 4.9 – Friction Friction – force that opposes motion. Depends on 1. Types of surfaces in contact 2. Amount of force pressing surfaces together (the normal force) Does NOT depend on contact surface area (according to the books)

Static Friction (fs) – friction holding an object in place. Kinetic Friction (fk) – friction while object is moving.

ASSIGNMENT: Read 4.8 – 4.9 Chapter 4 #34 – 39 (p. 123)

Help with solving problems… 1. Draw a picture of the object; include all forces drawn with the correct direction. 2. Write an expression for the net force (ΣF). Have a separate expression for the horizontal (x) and vertical (y) direction. 3. Set the net force expression equal to ma. 4. Try substituting to eliminate the number of variables. Keep trying!!

Tension (T) – the reaction force of a pulling on an object. Pull w/ 100 N, box pulls back / 100 N. Tension in rope is 100 N, not 200 N

What does spring scale read now? Spring scale reads 100 N What does spring scale read now? 100 N

Applying Newton’s 2nd Law Equilibrium (a = 0) ΣFx = 0 ΣFy = 0 Non-Equilibrium (a ≠ 0) ΣFx = max ΣFy = may

Don’t forget that ΣF = ma Free-Body Diagrams – Show relative magnitudes and directions of all forces acting on an object. Free-Body Diagrams help to visualize all the forces acting to determine the net force. Don’t forget that ΣF = ma

Free-Body Diagram Examples… A book is at rest on a table top. A girl is suspended motionless from the ceiling by two ropes.

Free-Body Diagram Examples… A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance.

Free-Body Diagram Examples… A car is coasting to the right and slowing down. An leave is free-falling from a tree. Neglect air resistance.

Free-Body Diagram Examples… A block on an inclined plane.

ASSIGNMENT: Ch. 4 #46,47,50,51,53,58,63,67 due Tuesday