Kinematics and Dynamics

AP PHYS 1 Test Review Kinematics and Dynamics Name: Other Useful Site: http://www.aplusphysics.com/ap1/ap1- supp.html

2015-16 AP Physics: Kinematics Study Guide The study guide will help you review all chapter concepts as well as prepare you for AP style test questions. The Basics: Motion o Uniform Constant acceleration o Non-Uniform Changing acceleration Kinematic Variables: o Scalars: (only have magnitude) Time Speed Distance o Vectors: (have magnitude and direction) Displacement Δx Remember, position (can be x or y) is measuring the location with respect to an origin. Velocity v = Δx t Acceleration a = Δv t Motion Graphs o Position vs. Time Graphs REMEMBER!!! Δ (Delta) Delta means the change in. The variable after the delta is what we are finding the change in. LIKE THIS: Change in Position Δx = x f x i The change in a variable is always the final minus the initial. Staying still = any horizontal line Constant velocity = any straight line with a non-zero slope To find velocity, find the slope of the line Acceleration = curved line o Velocity vs. Time Graphs

Constant velocity = any horizontal line Accelerated motion = any straight line with a non-zero slope To find acceleration, find the slope of the line Distance covered = area under the line Displacement = adding the total area KEEPING negative area in mind NOT REQUIRED Any curved line on a V vs T graph is a change in acceleration (Jerk) Our Kinematic Equations o o o o v f = v i + at x f = x i + v i t + 1 2 at2 v f 2 = v i 2 + 2ad Δx = 1 2 (v i + v f )t As the AP Test will give you: SUB NOTATIONS!!! We use sub notations to distinguish from different variables with the same letter. You can see in Grant AP Physics, we use the sub notations with i and f. These stand for initial and final respectively. However, the AP Test will use a sub notation such as 0. This stands for initial, and there is no sub notation for final. Projectile Motion We both use sub notations like x and y, occasionally, to distinguish in which direction our variable is. o Free fall Any object in free fall is only being acted on by gravity If it is dropped from rest, use: t = 2h 9.8 If it is thrown up and returns to its original height, use: t = 2v iy 9.8

o Type 1 (Horizontal projectiles) Launched with a 0 degree angle. Vertical motion depends on gravity (9.8m/s 2 ) and initial height (find t like finding an object dropped from rest) t = 2h 9.8 Horizontal motion depends on BOTH velocity in the x direction, and time of flight Δx = v x t o Type 2 (Horizontal and vertical components) Vertical motion depends on gravity, initial height, AND initial velocity. (find time like you would find an object thrown up and returns to its original height) t = 2v iy 9.8 Horizontal motion depends ONLY on horizontal velocity and time Δx = v x t o Type 3 (y i y f ) Same as a type 2 projectile except the final height is not the same as the initial height Find t by: Δy = v iy t + 1 a 2 yt 2 Find x by: Δx = v x t REMEMBER!!!! The quadratic equation must be used to solve for variables in second degree polynomials! It goes like this: For functions that look like this: For Physics it looks like this: x = b ± b2 4ac 2a 0 = ax 2 + bx + c (now we solve for t instead of x) 0 = 1 2 (a)t2 + v i t + ( Δx)

CH 4 Forces Equations and Fact Sheet Forces symbols/names/information: Forces are a push or pull applied to an object. The standard units for force are N (Newtons) or kgm/s 2 Fa = Force applied o Usually a given value FN = Normal Force o Normal force is the force perpendicular to a surface. It is Newton s 3 rd law in action. (the surface pushing back on an object so that it doesn t fall through it) o F N = mgcosθ The angle in this equation is for when you are on an incline. Remember a horizontal surface has a θ = 0 so cos(0) = 1 FT or T = Tension o Tension can be solved for in Atwood problems, or it can be given to you. Fg or W = Weight (force of gravity) o Always points toward the center of the planet o W = mg where g = (+9.8m/s 2 ) Ff = Force of friction o Friction always opposes the direction of motion o F f = μf N OR F f = μmgcosθ Fsp = Spring force o We do not have spring force problems in our AP physics curriculum at the moment, but you should still know how to solve it. o F sp = kx k is the spring constant in units of (N/m) or (N/cm) It tells you how many Newtons you have to pull or compress in order to move a certain distance. X is the displacement of the object on the spring from the equilibrium point (where the spring doesn t apply a force) This can be in either (m) or (cm) depending on if your k value is in (N/m) or (N/cm) Continue to next page:

What do we do if we have an inclined plane problem??? We need to tilt our frame of reference so that it is along the direction of motion (matches the angle of the slope). You must find the components of the weight vector. W x = mgsin(θ) W y = mgcos(θ) F N = W y = mgcos(θ) Wy θ Wx Steps to any Newton s 2 nd Law problem o 1: Draw a Free Body Diagram Solve for any x and y components o 2: Chose to sum your forces in either the x or y direction (you may have to do both directions, but do them separately) ΣF x = ma x OR ΣF y = ma y o 3: Decide whether or not your object is accelerating If it s not, your (ma) side goes to 0, if it is, the (ma) side stays o 4: Replace ΣF with the forces from your Free Body Diagram EX: For the problem above (W x = ma x ) o 5: Substitute any forces with given values or with equations for the forces EX: For the problem above (mgsin(θ) = ma x ) o 6: Calculate all forces and solve for the final answer

KINEMATICS 1. An object is sitting motionless for days on end, what is its acceleration? 2. An object is falling down without air friction, what is its acceleration? 3. An object is being tossed upward without air friction, what is the acceleration? 4. An object is moving in a circle at a constant speed. Does it have an acceleration? 5. If you walk 5 meters forward, and then 7 meters backwards, what is the distance you traveled? What is your displacement? 6. A train moves to the right at 30 m/s for 5 minutes, then it moves to the left at 30 m/s for 5 minutes. What is the average speed? What is the average velocity? 7. If an object is being accelerated at a rate of 6 m/s 2 for 15 seconds, how much does the velocity increase between 11 and 12 seconds? 8. If a ball is thrown in the air with an initial velocity of 25 m/s, how high does the ball get? a. How is the height affected when the initial velocity is cut in half? b. if initial velocity doubles? 9. A hotwheels car rolls off of a lab table 0.92m high. It hits the ground about 2m away from the edge of the table. a. How long was the car in the air? b. What was the car s initial velocity? 10. An object slows from 100 m/s to 90 m/s while covering a distance of 50 m. How many seconds does this take? 11. An object moves from 20 m to 100 m while accelerating from 5 m/s to 8 m/s. How long does this take?

12. A train is moving according to the equation X = 3t 2 + 5t 9. A bus moves according to the equation X = -2t 2 + 4t + 10. a. What is the initial location of the train? b. What is the initial location of the bus? c. What is the initial velocity of the bus? d. What is the initial velocity of the train? e. Which way is the bus moving? f. Which way is the train moving? g. What is the acceleration of the bus? h. What is the acceleration of the train? i. Is the train speeding up or slowing? j. Is the bus speeding up or slowing? k. When does the train pass the bus? 13. An object is thrown upward, from ground level, with an initial speed of 60 m/s. At the same time (t=0) a second object is thrown downward with an initial speed of 15 m/s at a height of 75 m from the ground. At what height do the objects pass each other? 14. Draw a particle model for the motion of an object with a constant speed. 15. Draw a particle model for the motion of an object with a slower constant speed than in #14. 16. Draw a particle model for the motion of an object speeding up then slowing down.

17. Draw a position vs time graph for an object that object that starts at rest 5m in front of a motion detector. After 1 second, the object moves at a constant velocity towards the detector. At 3 seconds, when the object is 1 m away, the object stops moving towards the detector and immediately accelerates away from it. 18. The equation for range of a projectile where y f=y i is R = v i 2 sin2θ. A cannon always launches the ball with the same initial velocity. Besides 36 o what other angle would allow the cannoneers to shoot the same distance? g 19. A football is kicked at an angle and travels 50 yards down field and attains a height of 30 yards. A soccer ball is kicked at an angle and travels 40 yards down field and attains a height of 45 yards. Which was in the air longer? 20. Look at the graph below. How would you describe the motion in section A? in section B? in section C? Section D?

21. Find the total displacement of the object graphed below: V 3 m/s 0 2 6 t (s) -2 22. Using the following position vs. time graph. Create a velocity vs. time graph. a. Find the acceleration from 7 to 9 s. b. Find The total distance traveled and the total displacement from t=0 to t=10. c. Which direction is the average acceleration for the entire duration of the motion?

23. A bouncy ball is thrown at a wall with a speed of 15 m/s. It bounces straight back from the wall with a speed of 10 m/s. The bouncy ball was in contact with the wall for 0.05 s. a. What was the change in velocity of the bouncy ball? b. Find the acceleration of the bouncy ball during the interaction with the wall. c. If the ball hit an interesting bump on the wall, and took off with an angle of 10 0 to the horizontal and bounced 3 meters high on the wall, how far would the ball go before hitting the ground? Assume air resistance is negligible.

DYNAMICS 24. A 45 kg block has 2 forces acting on as shown below. What is the magnitude and direction of net force? 30 o 50 N 40 70 N 25. A 100 N force accelerates a sled on a frictionless surface. An acceleration results. Later, the force is tripled. What happens to the acceleration? 26. A small trailer/load is 400 kg mass. It is accelerated by a small force. Later, the total mass of the trailer/load is increased to 1200 kg. The applied force is the same. What happens to the acceleration? 27. A 100 N force accelerates a sled on a frictionless surface. An acceleration results. Later, the force is cut in half. What happens to the acceleration? 28. An elevator is suspended by a cable. The elevator is moving downward and slowing to a stop. Draw the free-body diagram 29. An elevator is suspended by a cable. The elevator is moving upward and speeding up. Draw the free-body diagram 30. An elevator is suspended by a cable. The elevator is moving downward and speeding up. Draw the free-body diagram 31. A small car is pulling a big tow-truck. Which of the following statements is true? a) The car exerts a force on the truck, but the truck doesn t exert a force on the car b) The truck exerts a force on the car, but the car doesn t exert a force on the truck c) The car exerts just as much force on the truck as the truck exerts on the car d) The truck exerts a larger force on the car than the car exerts on the truck e) The car exerts a larger force on the truck than the truck exerts on the car f) None of the above 32. A wad of paper is tossed up and it falls back down to the ground. The direction of the force of air friction is a) Down, then up b) Up, then down c) Always up d) Always down

33. A block is pushed across a horizontal surface by the forces F1 and F2 shown. If the block moves with an acceleration of 3m/s 2, F1 = 100N, F2 = 6N and M = 8kg, which of the following is an approximation of the coefficient of kinetic friction between the block and the surface? 34. A block of mass M is pushed across a rough surface by force F. Force F is applied at an upward angle of O (like a rope pulling a sled). Friction force of f exists. What is the coefficient of friction in terms of F, and other constants? 35. Two masses M and m are hung from the ends of a rope over a pulley (M>m). Ignore friction. Find the acceleration of the masses and the tension. 36. Two masses M and m are hung from the ends of a rope over a pulley. (M>m). Mass M is on a ramp with angle O. Everything is frictionless. Find the acceleration of the masses. 37. Two masses M and m are hung from the ends of a rope over a pulley. (M>m). Mass M is on a horizontal track with no friction. Find the acceleration of the masses. 38. A box of mass M starts stationary on the top of a rough ramp with angle O. Coefficient of friction = µ. Find the acceleration 39. Three masses (4 kg, 8kg, 12 kg) are connected by ropes. A third rope pulls all three in a train with a force of 24 N. What is true? a) The acceleration of each block will vary according to the masses. b) the acceleration of each block will be the found by F/m or 8/4 c) the net force acting on block 12 kg is 3 times greater than the net force acting on the 4 kg. d) the net force acting on each block is the same. e) the 8 kg pulls back on the 12 kg more than the 12 kg pulls on the 8 kg. f) the net forces acting on the masses add up to 24 N. 40. Two masses, 5m and 2m, are touching but not connected (box train). They are pushed by a force F applied to the 2m. What is the magnitude of the force between the masses?

41. A mass hangs from two ropes at unequal angles, as shown below. Which of the following makes correct comparisons of the horizontal and vertical components of the tension in each rope? Rope A Rope B m Horizontal tension Vertical tension a. Greater in rope B greater in rope B b. Equal in both ropes greater in rope B c. Greater in rope A greater in rope A d. Equal in both ropes equal in both ropes e. Greater in rope B equal in both ropes 45. A mass hangs from two ropes at unequal angles, as shown below. Which of the following makes correct comparisons of the horizontal and vertical components of the tension in each rope? Rope A Rope B m Horizontal tension Vertical tension f. Greater in rope B greater in rope B g. Equal in both ropes equal to mg in rope B h. Greater in rope A greater in rope A i. Equal in both ropes equal in both ropes j. Greater in rope B equal in both ropes 46. A person stands on a scale in an elevator. He notices that the scale reading is higher than his usual weight. Which of the following could possibly describe the motion of the elevator? (choose all that apply) a. It is moving down at constant speed. b. It is moving down and slowing down. c. It is moving up and slowing down. d. It is moving up and speeding up. e. It is moving up with constant speed. 47. A person stands on a scale in an elevator. He notices that the scale reading is lower than his usual weight. Which of the following could possibly describe the motion of the elevator? (choose all that apply) f. It is moving down at constant speed. g. It is moving down and slowing down. h. It is moving up and slowing down. i. It is moving down and speeding up. j. It is moving up with constant speed.