Chapter 5 Forces Forces in One Dimension Objectives

Chapter 5 Forces (Forces in One Dimension)

Objectives for Section 5. 1 n n n n Describe how force affects the motion of an object. Identify different types of forces. Interpret and construct free-body diagrams. Explain the relationship between the motion of an object and the net external force acting on the object. Calculate the net force. State Newton’s three laws of motion and how they are applied. Use Newton’s Second Law to calculate the acceleration of an object.

A. Forces and Motion - study of dynamics 1. Force - a push or a pull it can change the motion of an object, start or stop movement, and change shape of object 2. Four basic types a. gravitational - weakest, attractive force between objects, acts over very large distances b. electromagnetic - results from basic property of particles. Large compared to gravitational, but over smaller distances

c. strong nuclear forces - holds nucleus together, limited in range to diameter of nucleus d. weak nuclear forces - deals with radiation – alpha, beta, gamma 3. forces act & cause things to occur 4. Forces can be in contact or act over distances - field forces (long-range forces) a. contact forces – an object from the external world touches a system and exerts a force on it b. field forces – an object is pushed or pulled by a force without actual touching (gravity, magnetic or electrostatic force)

Force and Motion n What is a force? n n A push or pull on an object (system) How does it affect the motion of the object it acts on? n It changes it’s motion or shape (starts, stops, changes motion, it causes acceleration) System: the object being manipulated n Agent: cause of the force n

Types of Forces n Contact force n n Example: Your book laying on the desk Field force n Example: You drop your textbook onto the floor.

Free-body Diagrams

n n Balanced & Unbalanced Forces With a Balanced force – opposite and equal forces acting on the same object result in NO motion of the object Unbalanced forces – two or more forces of unequal strength or direction acting upon on an object results in the motion of the object

A. Force n Balanced Forces (Equilibrium) n forces acting on an object that are opposite in direction and equal in size n no change in velocity

A. Force n Net Force n unbalanced forces that are not opposite and equal n velocity changes (object accelerates) Fnet Ffriction Fpull N W N

Newton’s Laws of Motion “If I have seen far, it is because I have stood on the shoulders of giants. ” - Sir Isaac Newton (referring to Galileo)

A. Newton’s First Law n Newton’s First Law of Motion n An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.

Newton’s 3 Laws of Motion Newton’s 1 st Law of Motion: n AKA The Law of Inertia n n which states an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity until acted on by another force. Remember: The greater the mass of an object the greater the inertia

Newtons’s 1 st Law and You Don’t let this be you. Wear seat belts. Because of inertia, objects (including you) resist changes in their motion. When the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 m/hour.

2 nd Law

Newton’s Second Law n The acceleration of an object is equal to the sum of the forces acting on the object (the net force) divided by the mass of the object. n a = F / m F = ma

Newton's Second Law: a. F = m a but more easily understood by a = F / m b. Acceleration is directly proportional to force and inversely proportional to mass of an object c. Second law is a vector equation - direction of acceleration is the same direction as the net force d. Greater the force, the greater is the acceleration the mass experiences

Unit of Force is the Newton (N) n One newton is the force required to give a mass of one kilogram an acceleration of one meter per second squared. 2 n 1 N = 1 kg-m/s (a derived unit)

Net Force n Sum of all forces acting on an object n Equilibrium (when the net forces balance or equal zero) n Can you have equilibrium when an object is moving?

Combine all forces acting on object to determine the net force acting on the object n n n (1) sum of all forces is the net force. (2) net force can replace all forces acting on object and have the same result (3) forces added using vector math – more later on the process (4) net force will have magnitude and direction – critical to remember (5) Net force - combination of all forces acting on an object

Calculating Net Force

Check Your Understanding n 1. What acceleration will result when a 12 N net force applied to a 3 kg object? 12 N = 3 kg x 4 m/s/s 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s 2. Determine the mass. 16 N = 3. 2 kg x 5 m/s/s n n 3. How much force is needed to accelerate a 66 kg skier 1 m/sec? 66 kg-m/sec or 66 N n 4. What is the force on a 1000 kg elevator that is falling freely at 9. 8 m/sec? n 9800 kg-m/sec or 9800 N

Newton’s Third Law n Newton’s Third Law of Motion When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first. n The magnitudes of the forces are always equal. The two forces are know as actionreaction forces or action-reaction pairs. n

Newton’s 3 Laws of Motion n Newton’s 3 rd Law of Motion: n n n For every action there is an equal & opposite reaction. If an object is not in motion, then all forces acting on it are balanced and the net force is zero! Friction – the force that one surface exerts on another when the two rub against each other. Sliding Fluid friction Rolling

5. 1 Concept Review n You exert a force on a black box and measure its acceleration and then exert the same force on a brown box and find its acceleration is three times greater. What can you conclude? n Mass of the brown box is 1/3 that of the black box n What is a Newton? n Force require to accelerate 1 kg by 1 m/s 2 2 n 1 N = 1 kg-m/s n How can you feel the inertia of a pencil or your text book? n By changing it’s motion (accelerating it)

Objectives for Section 5. 2 Describe the relationship between the mass and weight of an object using Newton’s 2 nd Law n Demonstrate an understanding of frictional forces and the use of coefficients of friction n Be able to calculate acceleration based on net force n Define free fall and terminal velocity due to air resistance n

Weight Force n Using Newton’s Second Law you can derive the formula for weight force.

Mass and Weight a. weight - due to gravitational force (1) w = m g (F = m a) (2) direction is downward b. mass - amount of matter in an object. c. gravitational mass (a) measured using a balance to compare weights of two objects (b) unknown mass on one side, known mass on the other d. Inertial mass: measured by the force is required to accelerate the mass: m = F/a e. weight is a vector, mass is a scalar

Friction is the name given to the force that acts between materials that touch as they move past each other. • Friction is caused by the irregularities in the surfaces of objects that are touching. • Even very smooth surfaces have microscopic irregularities that obstruct motion. • If friction were absent, a moving object would need no force whatever to remain in motion.

More on Friction…………… 1. Force that opposes motion between two surfaces in contact. 2. Amount depends on: a. Kinds of surfaces in contact – this determines the coefficient of friction ( ) b. Amount of force pressing surfaces together – the normal force (More weight more friction) 3. Expressed as Ff = FN

3. Friction is caused by microwelds 4. Types of friction: a. Static (usually the greatest) b. Sliding c. Rolling (usually the least) d. Fluid Friction (air or water resistance)

Drag Force n The friction force exerted by a fluid on the object moving through the fluid. n Example: Air resistance

Air resistance (drag force) 1. Force that opposes motion of objects through air 2. Pushes up on falling objects 3. Affected by object’s speed, size, shape

4. Without drag force, all objects fall at the same rate 5. Terminal velocity is the max speed at which an object can fall

n Objects with similar air resistance fall at the same rate. Everything falls at the same rate of speed in a vacuum. n That rate is the gravitational constant. n n On earth (-9. 8 m/sec²)

n Video! Falling Objects, Gravity, Air Resistance, on the moon with Apollo. n http: //www. youtube. com/watch? v=KDp 1 ti. Us. Z w 8

Terminal Velocity n The constant velocity that is reached when the drag force equals the force of gravity. n What reaches a terminal velocity faster, a heavy, compact object or a light object with larger surface area?

Objectives for Section 5. 3 Net Forces Identify forces acting on an object and calculate net forces n Determine acceleration based on the net force n Find the direction and magnitude of normal forces. n

B. Using Newton’s Second Law 1. Free body diagrams - critical for solving problems a. Sketch object under consideration b. Draw and label all external forces acting on object c. Assume a direction for each force. If your selection ends up negative(-) means it goes the other way

n Combine all forces acting on object to determine the net force acting on the object n (1) sum of all forces is the net force. n (2) net force can replace all forces acting on object and have the same result n (3) forces added using vector math n (4) net force will have magnitude and direction – critical to remember n (5) Net force - combination of all forces acting on an object

Tension Force

Practice Problem A 50. 0 kg bucket is being lifted by a rope. The rope will not break if the tension is 525 N or less. The bucket started at rest, and after being lifted 3. 0 m, it is moving at 3. 0 m/s. If the acceleration is constant, is the rope in danger of breaking? Remember Fg = mg = 50 kg(9. 8 m/s 2 )= 490 N Ftension Fnet = Ftension – Fg or Ftension = Fnet + Fg Fnet = ma; use Vf 2 = Vi 2+2 ad or a = Vf 2 -Vi 2/2 d Fg 2 2 2 a = (3 m/s) -(0 m/s) /2(3 m) = 1. 5 m/s Fnet = 50 kg(1. 5 m/s 2) = 75 N Ftension = Fnet + Fg = 75 N + 490 N = 565 N, yes it is in danger!

The Normal Force

Weight & Normal Force n In which figure is the box’s weight equal to the normal force in magnitude? n n In which figure is the magnitude of the normal force greater than the weight of the box? n n The magnitude of the normal force is greater than the weight of the box in Figure b. Are mass and gravity the only factors that contribute to the normal force of an object? n n The weight of the box and the magnitude of the normal force are equal in Figure a. External forces other than gravity and the mass of the object may change the normal force that an object exerts. In which figure (or figures) does the box have an apparent weight different from that caused by its mass and the effect of gravity alone? n The box’s apparent weight is different from the weight caused by its mass and gravity in Figures b and c.

Practice Problem Poloma hands a 13 kg box to a 61 kg Stephanie, who stands on a platform. What is the normal force exerted by the platform on Stephanie? FN FN = Fg(Steph) + Fg(box) FN = (m(Steph)+ m(box))g FN = (13 kg+ 61 kg)9. 8 m/s 2 FN = 725 kgm/s 2 or 725 N Fg(Steph) Fg(box)

2. Scales (Elevator Problems) a. weight on scale is from the normal force of the scale pushing back up on the object which is pushing down due to gravity b. with elevator at rest, a = 0 and Fnet = 0 = FN - W FN = W scale Scales reading is normal force true weight of object weight

c. elevator moving up so “a” is positive and the Fnet =m a Fnet = m a = FN - W FN = m a + W weight Scales reads an apparent weight – not true weight but net force normal force acting on object.

d. elevator moving down, “a” is negative and the Fnet = -ma weight normal force Fnet = -ma = FN - W FN = - m a + W

Practice Problem Your mass is 75. 0 kg, and you are standing on a bathroom scale in an elevator. Starting from rest, the elevator accelerates upward at 2. 00 m/s 2 for 2. 00 s and then continues at a constant speed. Is the scale reading during acceleration greater than, equal to, or less than the scale reading when the elevator is at rest? W = mg = 75 kg(9. 8 m/s 2) = 735 N, at rest Fnet = 0 so FN= W or FN = Fscale = 735 N But during upward acceleration……… Fnet = ma = FN - W or FN = ma+W= 75 kg(2 m/s 2)+(735 N) So FN = Fscale= 885 N (It reads greater during upward

Newton’s Third Law n All forces come in pairs and the forces in a pair act on different objects and are equal in strength and opposite in direction

Interaction Forces

Action - Reaction “For every action there’s an equal but opposite reaction. ” n If you hit a tennis ball with a racquet, the force on the ball due to the racquet is the same as the force on the racquet due to the ball, except in the opposite direction. n If you drop an apple, the Earth pulls on the apple just as hard as the apple pulls on the Earth. n If you fire a rifle, the bullet pushes the rifle backwards just as hard as the rifle pushes the bullet forwards.

Practice Problem When a softball with a mass of 0. 18 kg is dropped, its acceleration toward Earth is equal to g, the acceleration due to gravity. What is the force on Earth due to the ball, and what is Earth’s resulting acceleration? Earth’s mass is 6. 0 x 1024 kg. F Fball = ma =. 18 kg(9. 8 m/s 2) = 1. 76 N Fball = FEarth (Action-Reaction Pair) FEarth = 1. 76 N = ma; a = 1. 76 N/m. Earth a = 1. 76 N/6. 0 x 1024 kg = 2. 94 x 10 -25 m/s 2 ball Fg(Earth)

Earth / Apple How could the forces on the tennis ball, apple, and bullet, be the same as on the racquet, Earth, and rifle? The 3 rd Law says they must be, the effects are different because of the 2 nd Law! apple 0. 40 kg 3. 92 N Earth 3. 92 N 5. 98 1024 kg A 0. 40 kg apple weighs 3. 92 N (W = mg). The apple’s weight is Earth’s force on it. The apple pulls back just as hard. So, the same force acts on both bodies. Since their masses are different, so are their accelerations (2 nd Law). The Earth’s mass is so big, it’s acceleration is negligible.

Earth / Apple (cont. ) The products are the same, since the forces are the same. m Apple’s little mass a = Apple’s big acceleration m Earth’s big mass a Earth’s little acceleration

Lost in Space Suppose an International Space Station astronaut is on a spacewalk when her tether snaps. Drifting away from the safety of the station, what might she do to make it back?

n n n Fhand on bowling ball is the force that the hand exerts upward on the bowling ball. Fbowling ball on hand is the force that Earth exerts downward on the bowling ball. Fbowling ball on Earth is the force that the bowling ball exerts upward on Earth. Fhand on bowling ball and Fbowling ball on hand; FEarth on bowling ball and Fbowling ball on Earth. are interaction pairs because they are of equal magnitude and opposite direction and act on different objects. Fbowling ball on hand acts only on the hand, Fbowling ball on Earth acts only on Earth, and Fhand on bowling ball and FEarth on bowling ball act only on the bowling ball. The movement of the ball is due to unbalanced forces on it, not the balanced force of interaction pairs that act on each object.

Swimming Due to the 3 rd Law, when you swim you push the water (blue), and it pushes you back just as hard (red) in the forward direction. The water around your body also produces a drag force (green) on you, pushing you in the backward direction. If the green and red cancel out, you don’t accelerate (2 nd Law) and maintain a constant velocity. Note: The blue vector is a force on the water, not the on swimmer! Only the green and red vectors act on the swimmer.

Demolition Derby When two cars of different size collide, the forces on each are the SAME (but in opposite directions). However, the same force on a smaller car means a bigger acceleration!