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Chapter 4: Newton's Laws Forces We are now concerned with the causes of motion (dynamics) Force ( F or F ): an action exerted on an object which may change its state of rest or motion. Examples: o Push o Pull o Air resistance o Friction Two types of forces: 1. Contact Force: results from physical contact between two or more objects; physical. 2. Field Force: results from no physical contact; objects don’t touch. Less is known about field forces Magnetism, force fields, etc. are examples. The Four Fundamental Forces of Nature The four natural forces are all field forces They are not fully understood (special relativity, quantum mechanics, string theory….scientists are still working on these!) The Four Fundamental Forces of Nature 1) Nuclear Force (or the Strong Force): holds the subatomic particles together. Acts as atomic glue within an atom: (shouldn’t those positive charges be fighting to get away from one another?) The Four Fundamental Forces of Nature 2) The Weak Force: repelling force that causes radioactive decay; dissolves the Nuclear Force. 3) Electromagnetic Force (EM): Positive and negative charge interactions; North and South pole interactions. Can be attractive or repulsive 4) Gravitational Force: Gravity; anything that has mass has an attractive force. Strength Can we rank the four forces in terms of strength? Strongest 1. Nuclear 2. EM Range 3. Weak Can we rank the four forces in terms of range? 4. Gravity Weakest Longest Range 1. Gravity 2. Weak 3. EM 4. Nuclear Shortest Range THE LAW OF UNIVERSAL GRAVITATION m1 m2 r m1m2 F 2 r •The gravitational force is proportional to the masses of the objects. •The force is inversely proportional to the distance between them, squared. m1m2 F G 2 r 11 G 6.67 x10 N m / kg 2 2 4 units 3 units 2 units 1 unit Let’s look at the inverse-square nature for the force of gravity. Gravity is the most dominant, far-reaching force in nature. Yet it is the weakest! Gravity is caused by MASS….yet there is more gravity than mass to explain it…. THE MASS Every object possesses inertia. Inertia is the tendency of a body at rest to remain at rest, and of a body in motion to continue in motion or Inertia is the sluggishness of an object to changes in its state of motion. Mass - a measure of the inertia of an object Inertia is what causes the injury in a car accident: If a body is travelling at 50 mph and it hits a wall, the body tries to continue moving at 50 mph! The seatbelt, dashboard, windshield, etc will work against this forward motion. Mini Lab – Inertia of a coin and the spinning egg Perform the mini-labs, then sketch and write an explanation in your notes about what you did! Homework: You’re the Attorney…. You are an attorney defending a bus driver on a personal injury case. The plaintiff claims that she was sitting in the back of a moving bus when the driver suddenly applied the brakes, causing a suitcase from the front of the bus to fly back and hit her. She is suing the driver and the bus company for pain and suffering. How would you defend your client? Recap: Inertia Inertia is Newton’s First Law of Motion: “An object at rest stays at rest, and an object in motion stays in motion unless acted upon by an outside force.” Recap: Force In general force is the agency of change. In mechanics forces cause accelerations. It is a vector. It is an action exerted on a system. Newton’s Second Law of Motion The Second Law of Motion states that the acceleration of an object is proportional to the force, and is inversely proportional to its mass. Huh? F a m The total of all forces that act on an object is the net force. (Only the net force is shown in the figures on this slide.) F m a F m a This symbol means proportional to The acceleration of an object is directly proportional to the net force. a F F m a Consider the same net force applied to different m mass objects. F a m m m F The acceleration is m a inversely proportional to the mass of the object. a 1 m So in other words…. ∑F = ma “Sigma” – means the sum of, or total Force Mass Acceleration SI Units: F = ma = (kg) (m/s2) So the unit of force is kg m/s2 which equals a newton (N). 1 N = 1 kg m/s2 THE STANDARD KILOGRAM The standard kilogram is an object whose mass is defined to be one kilogram. Abbreviation is kg. There is an English unit of mass. The slug. A slug weighs 32.2 lb. THE NET EXTERNAL FORCE The net force (∑F) is the total of all of the forces acting. Sometimes it’s just one force, and sometimes there are many. You must add them all up to find the net force. Direction is important! They are all vectors, after all…. THE NET FORCE Have you ever played Tug-of-War? You have to find out who is winning, and by how much, before you can solve problems with the equation F = ma. If 65-kg Ramiro pulls to the left with 250 N of force, and 50-kg Maria pulls to the right with 200 N of force, what is the net force? What is the acceleration of the loser? F1 = -250 N (because left is negative on the x-axis) F2 = +200 N ∑F = F1 + F2 = -250 N + 200 N = -50 N or 50 N to the left Since F = ma, a = F/m = (-50 N) / (50 kg) = - 1.0 m/s2 or 1.0 m/s2 to the left. Sorry Maria! Free Body Diagrams FBDs are drawn to isolate forces acting on a system FBDs are required and graded on the AP Test 1) Create a dot for the object of interest 2) Draw force vector arrows originating from the object of interest 3) Label the forces with subscripts When done with the FBD, you may draw additional diagrams showing components and net forces. FBD Example A crate is being pulled to the right 50 N by a rope. The force of gravity has an effect of 100 N (its weight) and the ground supports it with the same amount of upward force. Friction on the ground also provides 25 N of force opposing direction of motion. Draw a free body diagram showing all forces. Fsup Ffric Fr Fgrav The free body diagram is done! The next diagram: Component Diagram With the initial FBD complete, you can start filling in values and components: The labeled diagram allows us to easily solve Fsup = 100 N for the net force: ∑Fx = Fr + Ffric = 50N + (-25N) = 25N Ffric = 25 N Fr = 50 N ∑Fy = Fsup + Fgrav = 100N + (-100N) = 0N ∑F = √(Fx2 + Fy2) = 25 N Fgrav = 100 N A net force diagram would ∑F = 25 N be as follows: ∑F = 25 N If the crate had a mass of 10 kg, how quickly would it accelerate across the ground? F = ma → a = F/m = 25N/10 kg = 2.5 m/s2 Practice! Draw an FBD, a component diagram, and find the net force of each system: 1. An elevator’s cable provides a 1000 N force upward while the force of gravity (its weight) pulls down 600N. 2. A car is being towed by a 2000 N force at an angle of 15° from the horizontal. Friction is providing a 400 N force against the motion of the car along the horizontal. 3. A motor moves a boat through water with a 600 N force. The water provides 150 N of resistance. A strong wind blows in the direction of the boat’s motion with a force of 50 N. 4. Two students pull on a stubborn donkey as shown. How hard is the donkey pulling back? The Elevator Connected objects A 200 kg beam is connected by a cable to a 300 kg beam below it. The two are raised with an acceleration of 0.50 m/s2 by another cable attached to the 200 kg beam. Ignoring the masses of the cables, find the tension in each. Atwood’s Machine Problems If m1 is less than m2, solve for the acceleration of the system and for T (the tension in the string). Draw two FBD’s for the system: Combined objects in two dimensions (no friction) : Find the acceleration and tension. THE FRICTION FORCE It is a force acting on an object that opposes the sliding of that object on a surface. The friction force is parallel to the surface and opposite to the direction of motion. When an applied force exceeds the maximum static friction force (Fs), an object will begin to slide. When an object is already sliding, kinetic friction (Fk)is present. THE COEFFICIENT OF KINETIC FRICTION For surfaces in contact that are sliding, the coefficient of kinetic friction is the ratio of the friction force to the normal force. friction force Fk k normal force n THE COEFFICIENT OF STATIC FRICTION For surfaces on the verge of sliding the coefficient of static friction is the ratio of the maximum static friction force to the normal force. max imum static friction force Fs max s normal force n FRICTION Friction opposes the motion between surfaces in contact with one another. When there is a tendency for movement between two surfaces and yet there is no motion, the friction is static friction. Static friction has an upper limit. When there is motion between the two surfaces, the friction is kinetic (sliding) friction. FFA FA FA FA A F F F On the verge of slipping Sliding Maximum Static Friction Friction, F Kinetic (sliding) Friction Applied Force, FA A student pulls a rope attached to a 10.0 kg pumpkin and tries to move it across a field. If k between the pumpkin and the ground is 0.250, what is the force of friction? A witch tries to get her broom stick off the ground for a midnight flight. If the broom stick provides 200 N of force and the coefficient of friction is 0.15, what is her acceleration? The witch and her broom have a mass of 45 kg. You can keep a 3 kg book from dropping by pushing it horizontally against a wall. Draw force diagrams,and identify all the forces involved. How do they combine to result in a zero net force? Will the force you must supply to hold the book up be different for different types of walls? A hockey puck is given an initial speed of 20.0 m/s on a frozen pond and slides 120 meters before it stops. Find the coefficient of kinetic friction of the ice and puck. How much force is necessary to 5m pull the block up the ramp at constant velocity? 12 m Examine the pulley system on the front counter. If the cart has 4.0 kg of mass and the weight-hanger has 0.050 kg of mass, what is the acceleration? Assume the counter is frictionless. 4.0 kg 0.050 kg