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Due On: _______________ Name: _________________________ AP Physics 1: Review Packet 04 Problem 1: Each part shows a set of energy bar graphs that are in sequence. Explain a situation where the energy of a system could be represented by that sequence of bar graphs. Draw a diagram to help your explanation. As you explain the energy transformations, reference the diagrams using (1), (2), etc. If the total energy of the system changes, explain what external force does work to change the energy of the system. Note that KT represents translational kinetic energy, Ug represents gravitational potential energy, and US represents the potential energy of a spring. Diagram (a) (1) (2) (3) Diagram (b) (1) (2) (3) Diagram (c) (1) (2) (3) 04-1 Diagram (d) (1) (2) (Repeat 1 and 2 over and over) Diagram (e) (1) (2) (Repeat 1 and 2 over and over) Diagram (f) (1) (2) (3) (1, then 2, then 3, then 2, then 1, then 2, then 3, then 2, then 1, then 2, …) Diagram (g) (1) (2) (3) 04-2 Problem 2: A student wishes to determine the spring constant k of the spring inside of a marble launcher. The student builds the experimental set-up shown in the diagram, where the marble launcher will project the ball horizontally after the spring is compressed a distance x. The student measures the spring compression x for five trials, and for each trial the student also measures the horizontal distance D that the ball travels once it becomes a projectile. The student also measures the height from which the ball is launched to be H = 0.8 m and the mass of the ball to be 0.03 kg. Use g = 9.8 m/s2. (a) Write two equations that relate D and H to the initial speed of the ball as it becomes a projectile and the time that the ball is a projectile. (b) Write a conservation of energy equation that relates the initial speed of the ball as it exits the launcher to the compression of the spring. (c) Combine all three equations into a single expression that relates D, x, g, H, and k. (d) What quantities should be graphed in order to yield a straight-line relationship to the data? What would the slope represent? (e) Fill in the blank data table with those quantities that need to be graphed and plot the quantities on the grid below. Label each axis with symbol, units, and an appropriate scale. Draw a best-fit line. Spring Comp. x (m) Horiz. Dist. D (m) 0.10 1.24 0.10 1.24 0.15 1.90 0.15 1.90 0.20 2.61 0.20 2.61 0.25 3.14 0.25 3.14 0.30 3.84 0.30 3.84 04-3 (f) From your best-fit line, determine the spring constant of the marble launcher. To get a different measurement of the spring constant, the student removes the spring from the marble launcher and hangs it vertically. The student hangs different amounts of mass on the spring and measures the length of the spring when the objects are in equilibrium. (g) Select two quantities that can be graphed such that the slope of the line is the spring constant. Fill in the second data table with those values. Graph those quantities. Hanging Mass m (kg) Spring Length L (m) 0.2 0.163 0.4 0.231 0.6 0.300 0.8 0.359 1.0 0.428 (h) State this new measurement of the spring constant. Calculate a percent error from your two spring constant measurements. (i) Explain what the intercept of your graph represents. 04-4 Work, Energy, and Power Review IMPORTANT QUANTITIES Name Symbol Units Work J W Kinetic Energy K J Potential Energy (Spring) Us J IMPORTANT EQUATIONS Name Basic Equation W Fx|| K 12 mv 2 p2 2m U s 12 kx 2 Name Energy Potential Energy (Gravity) Symbol E Units J Basic Equation None Ug J U g mgh Power P W P Equation Given? Work done by Friction (also energy lost to friction) W f Ff x No Conservation of Energy Ki Ui K f U f No Power in terms of Force and Velocity P Fv|| Yes IMPORTANT GRAPHS Name Graph (Shape) Energy time Notes Friction takes some energy out of the system. Note that energy lost to friction becomes heat, so sometimes this is referred to as thermal energy. The sum of all different energies before equals the sum of all different energies after. These could be kinetic, potential, thermal, etc. energies. Note that dot products imply that you are multiplying the two vectors and the “cosine of the angle between them”. Notes The area under a force vs. displacement graph is work. Force vs. Displacement (Could be anything) IMPORTANT CONCEPTS NO WORK IS DONE IF FORCE IS PERPENDICULAR TO AN OBJECTS MOTION!!! USE ENERGY EQUATIONS IF YOU ARE ASKED FOR VELOCITY IN TERMS OF POSITION, OR POSITION IN TERMS OF VELOCITY! Note that the equations W Fx|| and P Fv|| are equivalent to W F|| x and P F|| v and W Fx cos and P Fv cos . Cosine does the job of finding the parallel component for you. Work is a transfer of energy from one form to another. If energy goes from kinetic to potential, potential to kinetic, kinetic to thermal, kinetic to another object’s kinetic, etc., work was done. A force does positive work if the force is in the same direction as displacement. Likewise a force does negative work if the force is opposite displacement. A force does positive work if the potential energy related to that force decreases. Likewise, a force does negative work if the potential energy related to that force decreases. A force does positive work if the kinetic energy of the object increases. Potential energy increases if an object is forced to do “the opposite of what it wants to do.” Likewise, potential energy decreases if an object is allowed to do “what it wants to do.” o Objects want to fall down. So raising an object up increases its potential energy. o Springs don’t like to be stretched or compressed. Therefore, compressing or stretching a spring (away from its equilibrium position) increases its potential energy. o Objects in space want to attract each other due to gravity. Therefore, moving objects apart in space increases their potential energy. o Like charges want to move away from each other. Therefore, pushing like charges near each other increases their potential energy. o Opposite charges want to move toward each other. Therefore, pulling opposite charges apart increases their potential energy. o Like poles of magnets want to move away from each other. Therefore, pushing like poles near each other increases their potential energy. o Opposite poles of magnets want to move toward each other. Therefore, pulling opposite poles apart increases their potential energy. Example: I lift a book from a low shelf to a high shelf. I do positive work because the force I exert (up) is in the same direction as displacement (up), and my potential energy decreases because I had to burn calories to lift the book. On the other hand, gravity did negative work because the force of gravity (down) was opposite the direction as displacement (up), and gravitational potential energy increased. NO WORK IS DONE ON AN OBJECT IN ANY UNIFORM CIRCULAR MOTION (the speed doesn’t change, so no work is done because no energy is transferred). THIS INCLUDES A CHARGE CIRCLING IN A MAGNETIC FIELD OR A PLANET IN CIRCULAR ORBIT. Big concept: Use energy whenever are given a position and asked for a velocity, OR given a velocity and asked for a position. Example: A block is released from rest at the top of the incline (point A) as shown. If the incline is frictionless, how fast does the block move at point B? Potential energy becomes kinetic energy mgh 12 mv 2 v 2 gh 210 15 = 17.3 m/s If the incline has a coefficient of friction 0.11, what is the speed at point B? P.E. becomes K.E. AND energy lost to friction mgh 12 mv 2 F f x (where F f FN mg cos ) mgh 12 mv 2 mgx cos v 2 gh 2gx cos 21015 20.111025 20 25 v = 16 m/s If the incline and horizontal plane have a coefficient of friction of 0.11, what is the distance x traveled along the horizontal surface to point C? The speed at the bottom is v = 16 m/s from before. All of this kinetic energy becomes energy lost to friction: 2 1 2 mv mgx (no cosine because this is flat) 1 2 162 0.1110x x = 116 m