AP Physics Monday 14.10.20 Standards: Kinematics 1D & 2D: Big Idea 3 Warm Up Free Standards: 3a3 A force exerted on an object is always due to the interaction of that object with another object I –Independent Resilient Individuals RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… Learning Goal: SWBAT score 4 on their multiple choice test Agenda: Warm Up Kinematics Retest Homework NA

AP Physics Tuesday 14.10.14 Warm Up 17N Standards: 3a3 A force exerted on an object is always due to the interaction of that object with another object 40N 20N I –Independent Resilient Individuals RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… 7N Learning Goal: SWBAT use free body diagrams to solve Newton’s 2nd Law Find Fnet & the angle. Agenda: Warm Up Review HW Net Force & Drawing FBD’s Homework FAP #2

AP Physics Wednesday 14.10.15 Standards: 3a3 A force exerted on an object is always due to the interaction of that object with another object RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… Warm Up 12N 2N 19N Learning Goal: SWBAT interpret situations involving forces using Free Body Diagrams 31N Agenda: Warm Up Review HW Net Force & Drawing FBD’s Homework FAP #2

AP Physics Thursday 14.10.16 Standards: 3a3 A force exerted on an object is always due to the interaction of that object with another object RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… Warm Up Draw a free body diagram of a 20kg car at rest on a ramp angled at 30 degrees to the ground. Learning Goal: SWBAT draw free body diagrams of different physics situations Agenda: Warm Up Finish Free Body Diagrams of Physics Situations Begin HW FAP#2 Homework FAP#2

AP Physics Friday 14.10.17 Standards: 3a3 A force exerted on an object is always due to the interaction of that object with another object RST.11-12.4 Meaning of symbols, key terms, technical jargon Problem Solvers Warm Up Draw the free body diagram and write the net force expression in the y direction if the object is sitting on a table at rest. Learning Goal: SWBAT solving problems using Free Body Diagrams Agenda Warm Up Stamp HW K14-FAP#2 Problem Solving Homework FAP #3

FAP #1 Finding Net Force Preview Fnet=ma W=mg 1. In 1994, Vladimir Kurlovich, from Belarus, set the record as the world’s strongest weightlifter. He did this by lifting and holding above his head a barbell whose mass was 253 kg. Kurlovich’s mass at the time was roughly 133 kg. Calculate the normal force exerted on each of Kurlovich’s feet during the time he was holding the barbell. 1.89x103N upward on each foot

Types of Forces Force Symbol Definition Direction Friction f or Ff Resistive Force. Comes from rubbing against or sliding across surfaces. Parallel to the surface and opposite the direction of sliding Normal N or FN The force exerted on an object by the ground, a table, a platform, or any surface. Perpendicular to and away from the surface. Spring Fsp Restoring Force. The push or pull a spring exerts on an object. Opposite the displacements of the object at the end of the spring. Tension T or FT The pull exerted by a string, rope, or cable when attached to something. Away from the object and parallel to the string, rope, or cable at the pont of attachment. Thrust Fthrust A general term for the forces that move objects such as rockets, planes, cars and people. In the same direction as the acceleration of the object. Weight W or Fg Attractive Force of two objects due to gravity. Usually Earth and and object Straight down towards the center of the earth. Air Resistance/Drag FAR Resistive Force, comes from air/wind hitting moving objects Opposite of Motion Electric FE Force between atoms with electric charge (protons & electrons) Like charges repel + Opposite charges attract - Magnetic FB Force between magnetic poles & force created when electric current is in flux. Same Pole repels Opposite Pole Attracts Applied Force FAP A Force applied by a person, thing, or individual that does not fall into any of the above categories any

Free Body Diagrams Reflection: How to draw a free body diagram. 1. Represent the object of interest with a dot. Make an arrow for every Force acting on that object in the direction that the Force is pointing. Only include Forces in this type of diagram. This is separate from previous diagrams we have used to solve problems. The Arrows should never point towards the object. Label the Forces. Reflection: 1.How might doing this help you solve problems? 2.This can help you make which type of equations? Fap 30° W

Free Body Diagram Stations Force Stations: For each situation in front of you, draw a free body diagram that includes all of the forces acting, then create an expression for the Net Force in the x direction and the Net Force in the y direction Example: Ball rolling down ramp. (This is a hard one and we’ll be going over this situation individually) Coffee filter in freefall A mass on a table A ball between 2 strings A loaded mousetrap Levitating cylinder A pith ball sticking to a van de graff generator N f Fnet ll=Wsinθ-f=ma Fnet _l_=N-Wcosθ=0 W θ

FAP#2 Free Body Diagram Practice For each of the following problems create a free body diagram. Where asked, answer questions. Write an expression for Net Force in the x and y direction for each A piano falls from the sky and air makes it reach terminal velocity A cart from an amusement park ride is accelerated up at an angle θ. Assume friction is negligible, but air resistance is significant. The cart from problem 2 drops at a very steep angle of ϕ. A 70kg rock falls from the cliff and the air provides an upwards force of 30N. A 65kg skydiver opens her parachute. Air resistance to her body is 20 N and the Lift Force is 617N. What is the Net Force acting on her? A 25kg child rolls down a hill angled 60° to the horizontal. Friction is significant. A 15kg chandelier is attached to the ceiling using a cable. A 25kg child is hanging stationary from monkey bars. One arm is angled at 30° and the other arm is angled at 60°. **A cart is sitting on a table and attached to a pulley by a string. The other side of the pulley has a mass M attached to the bottom. Both objects are stationary. Find the free body diagram of the cart and of the mass separately.

FAP #3 USING FBD’s to Solve Net Force Problems A car is accelerated east with a 2.0x103 N Force. Friction resists the car’s motion with 1.20 x102 N and air resistance contributes another 35 N. What is the net Force acting on the car? A bike rider pushes his/her bike pedals with a Force of 2.0x102 N. This only accelerates the bike at 1.00 m/s2. If s/he and the bike have a combined mass of 1.50x102 kg, how much resistive Force was acting on the bike? A car with a mass of 7.50x102 kg accelerates at a rate of 2.00 m/s2. If Friction resists the motion with 1.8x102 N of force and air resistance with another 35.0 N, how much Force was applied by the engine? Net Force with the equations of motion A toy 0.50 kg toy car is accelerated from rest with a 20.0 N force for 3 seconds. How far did the car travel? A child is on a table flicking marbles to see how far they will fly. A 0.25 kg marble is flicked from rest by the child. The child applies 4 N of Force with her finger that lasts 0.5 seconds. Afterwards, if the marble travels at a constant velocity until it flies off of the 2 m high table (assume no friction), how far away from the table did the marble land?

FAP #4 Net Force Problems 2 A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength of the rope is 50 N. The largest acceleration that can be given to the block by pulling up on it with the rope without breaking the rope is most nearly what? A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chains at each end. A person weighing 500 N is sitting on the board. The tension in the right chain is 250 N. What is the tension in the left chain? The cart of mass 10 kg shown above moves without frictional loss on a level table. A 10 N force pulls on the cart horizontally to the right. At the same time, a 30 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart? A 100 N weight is suspended by 2 chords as shown above. The Tension on the slanted chord is? When an object of weight W is suspended from the center of a massless string as shown above, the tension at any point in the string is? #6 #8 #10 #9

Newton’s 2nd Law 2D – #3d θ1=45° θ2=45 θ2 θ1 Net Force Review in 2D (break into x and y components) p.34 About 50 years ago, the San Diego Zoo, in California, had the largest gorilla on Earth: its mass was about 3.10x102 kg. Suppose a gorilla with its mass hangs from two vines, each of which makes an angle of 30.0° with the vertical. Draw a free-body diagram showing the various forces, and find the magnitude of the force of tension in each vine. What would happen to the tensions if the upper ends of the vines were farther apart? Newton’s 2nd Law 1&2D p.35 In 1994, a Bulgarian athlete named Minchev lifted a mass of 157.5 kg. By comparison, his own mass was only 54 kg. Calculate the force acting on each of his feet at the moment he was lifting the mass with an upward acceleration of 1.00 m/s2. Assume that the downward force on each foot is the same. In 1991, a lobster with a mass of 20.0 kg was caught off the coast of Nova Scotia, Canada. Imagine this lobster involved in a friendly tug of war with several smaller lobsters on a horizontal plane at the bottom of the sea. Suppose the smaller lobsters are able to drag the large lobster, so that after the large lobster has been moved 1.55m its speed is 0.550 m/s. If the lobster is initially at rest, what is the magnitude of the net force applied to it by the smaller lobsters? Assume that friction and resistance due to moving through the water is negligible. A person pulls a 10kg box across the ground with a force of 20 N at an angle of 35°. How fast will the box accelerate if air resistance is negligible and the force of friction is 12N? Will the person be able to lift the box in the air? The largest toad ever caught had a mass of 2.65kg. Suppose a toad with this mass is placed on a metal plate that is attached to two cables, as shown in the figure below. Toad goes here θ1 θ2 θ1=45° θ2=45 An average newborn blue whale has a mass of 3.00x103kg. Suppose the whale becomes stranded on the shore and a team of rescuers tries to pull it back to sea. The rescuers attach a cable to the whale and pull it at an angle of 20.0° above the horizontal with a force of 4.00kN. There is, however, a horizontal force opposing the motion (Friction) that is 12% of the whale’s weight. Calculate the magnitude of the whale’s net acceleration. A hot-air balloon with a total mass of 2.55x103 kg is being pulled down by a crew tugging on a rope. The tension in the rope is 7.56x103N at an angle of 72.3° below the horizontal. This force is aided in the vertical direction by the balloon’s weight and is opposed by a buoyant force of 3.10x104N that lifts the balloon upward. A wind blowing from behind the crew exerts a horizontal force of 920 N on the balloon. a. What is the magnitude and direction of the net force? b. Calculate the magnitude of the balloon’s net acceleration. c. Suppose the balloon is 45.0m above the ground when the crew begins pulling it down. How far will the balloon travel horizontally by the time it reaches the ground if the balloon is initially at rest?

2D Force Sample Problem How do we find the acceleration of an object that is subject to a 2D Force? Example A 50 kg object is pulled by a rope with a 100 N of force at 30° to the horizontal. Friction resists the forward motion with 30 N. What is the acceleration of the block moving across the ground? Will the block be pulled up or will it leave the ground? If not, what would be the magnitude of the normal force on the box?

Forces & Inclined Planes Inclined planes are very common but the geometry involved makes this type of problem confusing. Here is the free body diagram of an object sliding down an inclined plane. FN W=mg FF θ Our procedure for dealing with this or any kind of Force problem is: Fnetx=? , Fnety=? But this is kind of tricky because the only Force that has no components is Fg. So either we need to find the components of Ff and FN or we need to try a different approach.

Inclined Planes Continued Our different approach sounds strange. We are going to do something called shifting our coordinate system. All it entails is some geometry though. Remember this ϕ β ϕ β FN W=mg Ff β ϕ β ϕ β ϕ ϕ β β ϕ θ Now that we can see that the two situations are analogous, we’ll solve our problem.

Inclined Planes Continued FN W=mg Ff θ Φ 90-θ ϕ=90-θ mgsinθ 2. Break Gravity into components perpendicular to the inclined plane instead of breaking up FN,and FAP θ mgcosθ 90-θ Fnet||=mgsinθ-Ff mgsinθ Fnet =FN- mgcosθ

What you have to remember is… FN W=mg Ff θ mgsinθ θ Fnet||=mgsinθ-Ff mgcosθ Fnet =FN- mgcosθ mgsinθ

Inclined Plane Problems #3e FN=? W=800 N FF=20N 45° 1. 2. A 10 kg mass slides down a 20° frictionless incline. What will be the acceleration of the mass, and how much normal force is opposing gravity? Find m?, FN, and a? 3. The largest squash ever grown had a mass of 409 kg. Suppose you want to push a squash with this mass up a smooth ramp that is 6.00 m long and that makes a 30.0° angle with the horizontal. If you push the squash with a force of 2080 N up the incline, what is… the net force exerted on the squash? the net acceleration of the squash? the time required for the squash to reach the top of the ramp?

Free Response Question #3f B2007B1. An empty sled of mass 25 kg slides down a muddy hill with a constant speed of 2.4 m/s. The slope of the hill is inclined at an angle of 15° with the horizontal as shown in the figure above. a. Calculate the time it takes the sled to go 21 m down the slope. b. On the dot below that represents the sled, draw/label a free-body diagram for the sled as it slides down the slope c. Calculate the frictional force on the sled as it slides down the slope. d. Calculate the coefficient of friction between the sled and the muddy surface of the slope. e. The sled reaches the bottom of the slope and continues on the horizontal ground. Assume the same coefficient of friction. i. In terms of velocity and acceleration, describe the motion of the sled as it travels on the horizontal ground. ii. On the axes below, sketch a graph of speed v versus time t for the sled. Include both the sled's travel down the slope and across the horizontal ground. Clearly indicate with the symbol t the time at which the sled leaves the slope.