Chapter 6 Forces

1. Chapter 6 Forces 6.1 Force and Motion A object that experiences a push or a pull has a force exerted on it. The object is called the system The world around the object that exerts forces on it is called the environment. Force (F)is a vector quantity that has magnitude (F) and direction.

2. The Two Types of Forces CONTACT FORCE: acts on an object only by touching it. LONG RANGE FORCE: is exerted without contact. For example the force of gravity is an attractive force that exists between all objects without touching, Electric Forces and Magnetic forces.

3. Newton’s Second Law of Motion The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object being accelerated. Fnet = m × a a = Fnet/m The unit of force in the SI unit is the Newton 1N = 1kg.m/s2

4. Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced.As the net force increases, so will the object's acceleration. However, as the mass of the object increases, its acceleration will decrease 

5. Practice: A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass. Two forces, 225 N and 165 N are exerted in opposite directions on a crate, what is the net horizontal force on the crate? Indicate the direction of the net force. The 225-N force is exerted on the crate toward the north and the 165-N force is toward the east. Find the magnitude and direction of the net force.

6. Newton’s First Law of Motion or Law of Inertia An object that is at rest will remain at rest or an object that is moving will continue to move in a straight line with constant speed, if and only if the net force acting on that object is zero.

7. Inertia: is the tendency of an object to resist change. Equilibrium: if the net force on an object is zero, then the object is in equilibrium.

9. The second law is not true for velocities close to the speed of light, nor for objects the size of atoms. Einstein’s theory of relativity and quantum mechanics should be used instead. The weight (or gravitational) force is: Fg = mg (g is the acceleration the object would have if it was falling freely) Weights vary from planet to planet, but masses will not change. 6.2 Using Newton’s Laws

10. The forces acting upon the sled from point B to point C would be the normal force (the snow pushing up on the sled) and the gravity force

11. Example # 1 Weighing Yourself in an Accelerating Elevator (pg 128) Your mass is 75 kg. You stand on a bathroom scale in an elevator. Going up! Starting from rest, the elevator accelerates at 2.0 m/s2 for 2s, then continues at a constant speed. What is the scale reading during the acceleration? Is it larger than, equal to, or less than the scale reading when the elevator is at rest? Weightlessness: doesn’t mean that your weight is zero, but that there are no contact forces pushing up on you. It means that you apparent weight is zero.

12. Example # 2Lifting a bucket A 50-kg bucket is being lifted by a rope. The rope is guaranteed not to break if the tension is 500 N or less. The bucket started at rest, and after being lifted 3.0 m, it is moving at 3.0 m/s. Assuming that the acceleration is constant, is the rope in danger of breaking?

13. The Friction Force Static Friction Force: is exerted on one surface by the other when there is no relative motion between the two surfaces. Kinetic Frictional Force (Ff,kinetic): is the force exerted on surface by the other when the surfaces are in relative motion. Friction depends on the surfaces in contact, but not on the area of the surfaces nor the speed of their relative motion. Ff,kinetic = ?K FN Where ?K is proportionality constant called the kinetic coefficient of friction. FN is the normal force Static Friction Force 0? Ff,static ? ?s FN? is the maximum static friction force that must by balanced before motion can begin.

14. Typical Coefficients of Friction

15. Practice #1 An applied force of 50 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)

16. Practice #2 An applied force of 20 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the coefficient of friction (µ) between the object and the surface, the mass, and the acceleration of the object. (Neglect air resistance.)

17. Practice #3 A 5-kg object is sliding to the right and encountering a friction force which slows it down. The coefficient of friction (µ) between the object and the surface is 0.1. Determine the force of gravity, the normal force, the force of friction, the net force, and the acceleration. (Neglect air resistance.)

18. Falling with Air Resistance As an object falls through air, it usually encounters some degree of air resistance. Air resistance is the result of collisions of the object's leading surface with air molecules. Air resistance encountered by an object depends upon the speed of the object and the cross-sectional area of the object. Increased speeds result in an increased amount of air resistance. Increased cross-sectional areas result in an increased amount of air resistance.

19. Terminal Velocity The constant velocity that is reached when the drag force equals the force of gravity is called the terminal velocity. Object Terminal velocity Tennis ball in air 9 m/s Basketball 20 m/s Baseball 42 m/s

20. The feather quickly reaches a balance of forces and thus a zero acceleration (i.e., terminal velocity). On the other hand, the elephant never does reach a terminal velocity during its fall; the forces never do become completely balanced and so there is still an acceleration. If given enough time, the elephant would finally accelerate to high enough speeds to encounter a large enough upward air resistance force in order to achieve a terminal velocity.

21. As the skydiver falls, he encounters the force of air resistance. The amount of air resistance depends upon : the speed of the skydiver, and the cross-sectional area of the skydiver. A skydiver in the spread eagle position (or with open parachute) encounter more air resistance than a skydiver who assumes the tuck position or who falls feet (or head) first. The greater cross-sectional area of a skydiver in the spread eagle position leads to a greater air resistance and a tendency to reach a slower terminal velocity

22. Periodic Motion A plucked guitar string continues to move rapidly back and forth in simple harmonic motion. Whenever the object is pulled away from its equilibrium position, the net force becomes nonzero and pulls it back toward equilibrium. If the force that restores the object to its equilibrium position is directly proportional to the displacement of the object, the motion that results is called simple harmonic motion. Simple harmonic motion is described by two quantities: The period is the time needed to repeat one complete cycle of motion, and amplitude is the maximum distance the object moves from equilibrium

23. Other example of harmonic motion is pendulum, a metal block bobbing up and down on a spring. The swing of the pendulum demonstrates simple harmonic motion. The period of a pendulum (T) is given by the following equation: This formula is valid only for small angles (less than 15?) l is the length of the pendulum in meters and g is the acceleration due to gravity. Period depends only upon the length of the pendulum and the acceleration due to gravity, not on the mass of the bob or the amplitude of oscillation.

24. A simple pendulum consists of a string, cord, or wire that allows a suspended mass (called bob) to swing back and forth. The longer the pendulum, the longer is the time of its swing

25. The forces acting on the mass are gravity and the tension in the string.  Only gravity provides a restoring force towards the equilibrium position.  The magnitude of this force Fnet= FT + Fg =mgsin?

26. 6.3 Interaction Forces Newton’s Third Law “For every action, there is an equal and opposite reaction." In every interaction, there is a pair of forces acting on the two interacting objects. The size of the force on the first object equals in size and opposite to the direction of the force on the second object.

27. A bird flies by use of its wings. The wings of a bird push air downwards. In turn, the air reacts by pushing the bird upwards. The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite to the direction of the force on the bird (upwards)