AP Physics Monday 13.10.28 Standards: b2b Newton’s 2 nd Law Objective: SWBAT solve Newton’s 2 nd Law Problems

1. Warm Up Draw a free body diagram of a 600kg car braking on the way down a hill with a 5° incline. AP PhysicsMonday 13.10.28Standards: b2b Newton’s 2nd LawObjective: SWBAT solve Newton’s 2nd Law Problems Agenda • Warm Up • Review Free Body Diagrams. • Newton’s 2nd Law of Motion Homework Newton’s 2nd Law Practice 3C

2. Warm Up Find the Force applied by a jet engine of a 20,000 kg plane on the runway that experiences 5200 N of Friction and 9000 N of Air Resistance, and accelerates of 6 m/s2. AP PhysicsTuesday 13.10.29 Standards: b2b2 write down vector equation that results from Newton’s 2nd LawObjective: SWBAT correct their mistakes from the Kinematics Test Agenda • Warm Up • Review N’s 2nd Law • Correct Test Mistakes Homework Finish 3C Practice Finish Correcting Test Questions

3. AP PhysicsWednesday 13.10.30Standards: b2b2 write down vector equation that results from Newton’s 2nd LawObjective: SWBAT solve 2D force problems. Warm Up An 2kg object moves 20,000 m from rest in 10s. (No friction involved) What is the applied Force? Agenda • Warm Up • Review Homework • 2D Force Sample Problem • 2D Force Practice Homework Homework #3d Finish Test Corrections by Monday

4. Warm Up A person pulls a 20 kg box with a force of 20N at an angle of 20° to the horizontal. If friction is 12N, is the person able to move the box? If so, what is the box’s acceleration? AP PhysicsThursday 13.10.31Standards: B2c analyze 2D situation with multiple forces acting on an objectObjective: SWBAT analyze situations involving inclined planes to find the acceleration of the object. Agenda • Warm Up • Review #3c • Inclined Planes Homework 1. Quiz Friday – Force Basics: Equations, symbols, definitions, and basic force problems. 2. #3e, 3. #3d will be reviewed friday

5. Warm Up AP PhysicsFriday 13.11.01Standards: B2 Dynamics of a single particle recap.Objective: SWBAT solve an AP free response problem involving an inclined plane. 30kg Agenda • Warm Up • Quiz 6 • AP Inclined Plane Free Response 45° Find the normal Force ? Homework Packets Due Monday: 3a-3f & Test Corrections

6. How to complete the lab write Up • Come up with a question or hypothesis that you think you can prove. : ex. hyp. The 3 equations of motion will predict the motion of a following marble enabling us to break an egg. • Write down materials & procedures used and write down your procedure for setting up the experiment and implementing the experiment. (Do not include anything about calculations in this section) • Data: Use the scant information that you have to make a parabolic graph that represents the position of the marble. We do not have time data so we will just graph vertical and horizontal position y vs. x • Questions you will need to answer in your Calculations portion of the lab: • 1. What was the projectile’s initial velocity? • 2. How long was the projectile in the air before it hit the egg? • 3. Find the components of velocity of the marble as it goes through each of the three rings and as it hits the egg • 4. What was the projectile’s final speed and angle as it hits the egg? • Analysis: In this section just justify your results using data. This entails evaluating your hypothesis as true, false, or inconclusive and provide it with actual data. One thing you might try proving is that the motion is parabolic. It may help depending on whether you are arguing for true, false, or inconclusive. • Conclusion: Summarize your results: Include important data that you got from the lab. Talk about and name some sources of error. Talk about and name any design changes or improvements you’d make to the lab.

7. Types of Forces among others

8. Free Body Diagrams 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. Fap 30° W

9. Free Body Diagram Practice #3b For each of the following problems create a free body diagram. Where asked, answer questions. • 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.

10. Newton’s 2nd Law Practice #3c • A car is accelerated east with a 2000 N Force. Friction resists the car’s motion with 120N 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 200N. This only accelerates the bike at 1m/s2. If s/he and the bike have a combined mass of 150kg, how much resistive Force was acting on the bike? • How much is A different car with a mass of 750 kg accelerates at a rate of 2m/s2. If Friction resists the motion with 180 N of force and air resistance with another 35 N, how much Force was applied by the engine? • A toy 0.5 kg toy car is accelerated from rest with a 20 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? • 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 #9 #10

11. Newton’s 2nd Law 2D – #3d 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. 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? θ2 θ1 Toad goes here

12. 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?

13. 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 FF θ W=mg 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.

14. 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 FN ϕ β Ff ϕ β β ϕ β ϕ β ϕ ϕ β W=mg β ϕ θ Now that we can see that the two situations are analogous, we’ll solve our problem.

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

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

17. Inclined Plane Problems #3e 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? 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? FN=? FF=20N Find m?, FN, and a? 45° W=800 N

18. 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.