4. Using her measured quantities, what must she graph to linearize the graph so that the slope of the line is the acceleration due to gravity?

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1 Linear Kinematics 1. A student wants to determine the height of an unreachable object. The materials available include a protractor and tape for measuring small distances. Describe a procedure that can be used to achieve the objective and what quantities can be graphed to determine the height of the object by calculating the slope of the best-fit line. 2. An object is dropped on the surface of a different planet where the acceleration due to gravity is not -9.81m/s 2. The object free-falls a distance of 2.3m in 1.2s, calculate the acceleration AND velocity of object before impacting the ground. Assume no friction Questions 3-4: A student wishes to confirm the acceleration due to gravity on Earth (9.81 m/s 2 ). The materials available to her are two meter-sticks, a timer, and small ball to drop. She drops the ball from different heights and records the time of fall. 3. Describe what type of function she will get if she plots a graph of distance vs time. 4. Using her measured quantities, what must she graph to linearize the graph so that the slope of the line is the acceleration due to gravity? Questions 5-7: Consider a rally car going around two curves: For segment A it s going at 25 m/s for 3s; B at 35 m/s for 4s; and C at 30 m/s for 3s. Diagram not shown to scale. 5. Calculate the average speed of the car over the three segments? 6. Calculate the distances for each segment and total distance. 7. Qualitatively distinguish between the total distance and displacement.

2 Questions 8-10: An object is thrown upwards on a different planet. The velocity is depicted on the following graph. 8. What quantity can be found by doing the slope of function? What quantity can be found by doing the area-under the curve? 9. Calculate the acceleration due to gravity on this planet. 10. Calculate the total displacement of the object. Questions 11-13: Consider two rocks of different masses thrown horizontally off a building: Rock 1 has mass 2M and lands 20m away from the base of the building, while rock 2 has mass M and lands 40m away from the base. 11. Qualitatively compare the time of flight for the rocks. 12. Qualitatively compare the launch speed for each rock. 13. Compare and contrast the vertical and horizontal components of each rock.

3 14. The following graphs depict the motion of an object starting from rest and moving without friction. Describe how you would calculate the object s acceleration, instantaneous speed, and distance at time p from each graph (slope, area-under-curve, etc.). 15. An object is launched at an angle of 45 0 from the ground of a mystery planet. The object hits the ground 20m away after a total flight time of 4.0s. Assume no air resistance. a. What are the initial vertical and horizontal velocities? b. Calculate the acceleration due to gravity. c. Draw graphs to quantitatively represent the vertical and horizontal velocities for the entire 4.0s of flight.

4 Linear Dynamics AP Physics 1: Semester 1 Exam 1. A block of mass 3 kg, initially at rest, is pulled along a frictionless, horizontal surface with a force shown as a function of time by the graph above. Calculate the acceleration and speed after 2s. Questions 2-4: Two blocks of masses M and m, with M > m, are connected by a light string. The string passes over a frictionless pulley of negligible mass so that the blocks hang vertically like Atwood s machine. The blocks are then released from rest as shown above. 2. Draw a free-body diagram for each mass. Compare and contrast the tension on each. 3. Compare and contrast the net-force acting on each block. 4. Draw a free-body diagram for the string holding the pulley. Explain whether the force increases, decreases, or remains the same as the blocks accelerate.

5 Questions 5-6: A ball is released from the top of a curved hill as shown above; the hill has sufficient friction so that the ball rolls as it moves down the hill. 5. What can be inferred about the ball s linear acceleration and speed as the ball goes from the top to the bottom? (Increase, decrease, or remain the same) 6. Draw a free-body diagram for each location in the diagram to compare the weight, normal, and friction forces as it rolls down hill. Questions 7-8: Consider the above block sitting on a smooth tabletop. It is connected by a light string that passes over a frictionless and massless pulley to a pulling force of 30N downward. 7. Use Newton s 2nd Law to determine what will happen to the net force, mass, and acceleration of the entire system if the pulling force of 30N is replaced with another block weighing 30N. 8. What will happen to the tension on each body?

6 9. The following circular object is suspended by two cables in two different designs as shown. Assume the object has the same weight in each case and the cables have no mass, compare the tension between cable T1 vs T3 and T2 vs T A plastic hollow ball is released onto a metal wedge as shown. The wedge sits on a frictionless floor. After impact, the plastic ball breaks into four pieces with the center of mass moving straight to the right. Use Newton s Laws to qualitatively describe the force and acceleration acting on each object during the collision. Questions 11-12: Two masses are pressed together with a massless-spring between them as shown above; m 2 is twice as massive as m 1. The masses are then released and move in opposite directions on a frictionless horizontal surface. 11. Compare and contrast the magnitude of the force, acceleration, and velocity provided by the spring to each block when it is released. 12. Draw a free-body diagram of each object when the spring is extending and after the blocks are far apart. Compare and contrast the forces on each object for each case.

7 13. A student wants to determine the coefficient of friction between different blocks and a wooden board as shown below. The blocks are of the same material but have different dimensions, masses, and densities. Describe a procedure for the experiment as well as what will and will not affect the coefficient of friction. 14. A coin sits on top of a playing card that is supported by the edges of a glass as shown above. The card is then removed by quickly flicking the card with the finger. The coin falls straight into the glass. Explain this observation using Newton s 1st Law, 2nd Law, and 3rd Law. 15. A 12,000N elevator is supported by a single vertical cable. Qualitatively describe the tension on the elevator when the elevator is at rest, moving at a constant velocity, accelerating down, and accelerating up.

8 Questions 16-17: Consider the following velocity-time graph for 3.0kg object. 16. Calculate the average velocity and average acceleration from 0s to 4s? 17. Calculate the net force acting on the object between 0s-2s, 2-4, and 4-6s.

9 Uniform Circular Motion & Universal Law of Gravitation 1. Consider a bicyclist on a curved segment of a horizontal road. Which of the following factors can be increased to allow the bicyclist to move at a higher speed without slipping or sliding off the track? (Mass of bicyclist, radius of curve, and/or coefficient of friction) 2. A child of mass M on a merry-go-round is standing a distance R from the center. If the child moved to half the distance, R/2, what will be the ratio of the centripetal accelerations (a1/a2)? 3. Qualitatively describe what force(s) are keeping each of the following objects in UCM. a. Child on a merry-go-round b. Ball whirled around a vertical circle with a string c. Race car on a banked curve 4. A 0.5kg ball is whirled around a vertical circle with a radius of 0.7m. a. If the speed of the ball at the bottom of the circle is 4m/s, calculate the tension on the string. b. What is the minimum speed to maintain the ball on the circle at the top of the path? 5. A satellite orbits around a planet on a circular path. Qualitatively describe what minimum measurements will be needed to calculate the satellites speed.

10 Work, Power, and Energy 1. Energy and Work are both scalar quantities. can be positive (in general, if it increases a system/object s energy) or negative. can be gained or lost by a system/object but the total mass-energy of the is constant. 2. The total energy of a system includes all of its kinetic (K) and potential (U s & U g) energy (together known as ), along with the system s internal energy. A or system exchanges no energy with the surrounding environment. An system can gain or lose energy. If positive work is done on a system, its total energy will. This could be done by the action of an, or by transfer of to the system (such as by adding heat). If a system loses energy to its surroundings, or does work on its surroundings, its total energy must. This happens when a non-conservative external force (usually ) acts on the system, or when a system gives off heat (or light, or sound, etc.). 3. +(Work done on a system) = -(Work ) 4. Work is energy (or the transfer thereof). They have the same units because doing 1.0 J of work on a system will its total energy by 1.0 J. Doing 1.0 J of work requires at least 1.0 J of energy (it requires more when efficiency is less than 100%, which is nearly always in the real world ). 5. is the ratio of net work (or useful output) done by a system or machine, versus the total used to do that work (or energy input). E.g.: if a motor does 500 J of useful work, but consumes 1000 J of electrical energy in the process, it is % efficient. Energy transformations in the real world are never 100% efficient, because of friction and heat-loss, which convert some input energy into non-mechanical types (like and ), rather than using it to do useful work. 6. In physics, an object is different from a system. An object is treated as having no. If positive net work is done on an object, its will increase. An object can only have potential energy through interaction with another object (e.g. for U g, or with a for U s)., when present, always does negative work on an object, transforming kinetic energy into energy (usually sound and heat), which is transferred to.

11 7. Work is only done on an object by the component of the external force that is to the object s displacement. Forces or components perpendicular to the direction of displacement cannot do work on the object, because they cannot increase or decrease its energy. 8. Power is the rate at which work is done, or energy is by a system or machine. The more powerful a machine, the less it takes to do a given about of work, but a given amount of work always requires the same amount of, regardless of power. 9. When Net Force is graphed versus displacement, the area under the curve is. 10. Draw lines on the graphs to show energy change vs. time for each of the following scenarios: a) An object accelerates at a constant rate on a level track. b) An object is thrown straight upward from ground level on Earth. c) An object oscillates on the end of a spring. d) An object swings back and forth on the end of a pendulum. e) An object is lifted upward at a constant speed by an external force.

12 11. a) How much power is needed to lift a 50kg mass 10m in 10s? (g 10m/s 2 ) b) If that lift were performed by a motor in the real world, how much energy would the motor consume? Justify your answer. 12. Assume a car on a level road begins at rest and is subject to the following four forces: 1. Weight= 1.0 x 10 4 N downward 2. Normal F = 1.0 x 10 4 N upward 3. F from its engine = 1.2 x 10 3 N forward 4. Frictional F s = 4.0 x 10 2 N backward a) Diagram the situation here: b) How much net work does the engine do on the car in the first 10s of motion? c) How much work does Friction do on the car in the same time interval? Is the work positive or negative? Explain.

13 13. A 70kg skier begins at 2.0m/s atop a 10m tall hill. Friction is minimal. Find each of the following: a) The skier s Kinetic energy at the top of the hill. b) The skier s Potential energy at the top of the hill. c) The skier s total mechanical energy at the top. d) The skier s total mechanical energy at the bottom. e) The skier s Potential energy at the bottom. f) The skier s Kinetic energy at the bottom of the hill. g) The skier s speed at the bottom of the hill. h) Does the skier s speed depend on their mass? Why or why not?

14 14. A spring-powered launcher is used to accelerate a 100g pinball from rest up to 6.0m/s on a level surface. Find each of the following: a) The work done on the ball by the launcher. b) The force-constant (k) of the spring, assuming it was initially compressed 5.0cm. c) If the launcher were fired straight up instead, how high would the ball go? d) The launch-speed of the ball if the same spring-launcher was compressed 50% farther (x= 7.5cm). 15. A force that varies with distance as shown on the graph below acts on a 500g object that is free to move without friction on a horizontal track. a) How much work does this force do over the first 3.0m of displacement? b) What is the total increase in K for the object over the interval shown? c) If the object was moving at 1.0m/s at the 0.0m mark, how fast is it moving at x = 3.0m? 16. The engine of a 1000kg car consumes 1.76 x 10 3 kj of chemical energy (from gasoline) as it accelerates the car from rest up to 100km/hr in 4.6s. a) What is the output power of the engine? b) What is the engine s efficiency (as a percentage)? c) What happened to the missing energy in this case?

15 Linear Momentum & Collisions 17. Momentum (p = mv) is a vector quantity possessed by any object. Its direction is always the same as that of the object s. Because it is a vector, reversing directions involves larger changes in momentum. E.g.: A 1.0kg object moving at 2.0m/s to the right that reverses it s motion and travels at 1.5m/s to the left has experienced a Δp of kg*m/s (NOT -0.5 kg*m/s ; this is a very common error). 18. Changing the momentum of an object requires a(n) to act on it for some amount of. The product of force and time is called (j = Ft), and the - theorem says that Δp = Ft. For an object of a constant mass, this means that mδv = Ft. If the mass of the object changes, then m 2v 2 m 1v 1 = Ft. 19. Momentum is always conserved in collisions between objects. In collisions (such as those between individual atoms and molecules), is also conserved. In macroscopic collisions between everyday objects, K is not conserved (because energy is lost to the surroundings as and, or used to do work on the colliding objects, e.g. bending the metal panels of a car in a collision). For two objects: 20. If a collision is not head-on, it may involve conservation of momentum in two (or three) dimensions. In that case: o and, o 21. In perfectly inelastic collisions, the objects after colliding, combining their masses and travelling at a single velocity as one object. So for two objects, is not conserved in these collisions.

16 22. A 160g billiard-ball initially moving at 3.6m/s collides head-on with the rail of the table, and bounces straight back off at 3.1m/s. a) What is the ball s change in momentum? b) What impulse was exerted on the ball by the rail? c) If the ball was only in contact with the rail for 80ms, what average force did the rail exert on the ball? 23. A water-rocket has total mass of 500g (rocket + water) before launch. Upon launching, air-pressure blasts the water out the bottom, propelling the rocket upward with an average force of 40 N that lasts just 0.5 s. If the rocket hits 100m/s, what mass of water was ejected during the launch? 24. Two football players run straight at each other and collide. Player one has a mass of 85kg, and is initially running at 6.4m/s to the right. Player two has a mass of 105kg, and is initially running at 5.8m/s to the left. When they collide, player two wraps up player one, and the two move together briefly before hitting the field. a) What kind of collision is this? b) Which way do the players move immediately after the hit, and at what speed? c) Is kinetic energy conserved in this collision? If not, how much K is lost? What percentage of the K is lost?

17 25. The picture below depicts two 200g pucks colliding on an air-hockey table. a) If puck two moves at 3.5m/s at an angle of 50 below the +x axis following the collision, find v 1 (including θ 1). b) How much kinetic energy is lost in this collision? Where does it go? c) Is it necessary to know the mass of the pucks in a problem like this? Why or why not? 26. A particle of mass M is initially moving to the right at speed v. It has a head-on, elastic collision with a stationary particle of mass 9M. Find the speed and direction of each particle s motion immediately after the collision in terms of v.