AP Physics C! name 100pt TAKE HOME TEST - Chap 7 Work & Kinetic Energy 12/7/12 Show your work on the problems Box in answers No Naked Numbers! [ Yes! ] means that you get a card to help you on the test [ No. ] means that you do NOT get a card to help you. 1.) [ Yes! ] A 950 kg elevator starts from rest. It moves upward for 3.00 sec with constant acceleration until it reaches its cruising speed of 2.00 m/s a.) What is the average power of the elevator motor during this period? Required drawing: 1b.) [ Yes! ] What is the instantaneous power of the elevator motor during this constant cruising speed? 2.) [ No.] A small particle of mass m is pulled to the top of a frictionless half cylinder (of radius R) by a cord that passes over the top of the cylinder, as illustrated in the figure below. Show ALL the steps in the integration that determines the work done by the force in moving the particle at a constant speed from the bottom to the top of the half cylinder.!!!!!!!!! F m R Θ
3.) [ Yes! ] A crate of mass 22.0 kg is pulled up a rough incline with an initial speed of 2.00 m/s. The pulling force is 350 N and is at an incline of 25 to the incline, which makes an angle of 15 with the horizontal. The coefficient of friction is 0.300, and the crate is pulled 7.0 meters. a.)what is the speed of the crate after being pulled the 7.0 m? Required Drawing: b.) [ Yes! ] How much mechanical energy is converted to heat (Pac Man poop) during the 7.0 m pull? 4.) [ Yes! ] The ball launcher in a pinball machine has a spring that has a force constant of 2.00 N / cm. The suface on which the ball moves is inclined 10 with respect to the horizontal. If the spring is intially compressed 7.00 cm, find the launching speed of a 120 g ball when the plunger is released. The coefficient of friction between the ball and the inclined surface is 0.124
5.) [ No.] Show, by integrating from equilibrium to x max, each step of the derivation of the equation for the work done (W A ) by an applied force (F A ) on a spring. DO NOT COMBINE STEPS. Your final equation for W A must be in terms of the spring constant for the spring and x max.!!!!!!!!!! Also show the work done by the!!!!!!!!!! applied force in graphical form: 6.) [ No.] Derive the Work-Kinetic Energy Theorem starting with the general integral equation for work. Briefly state what you are doing along with each step. start here: W = x 2 x 1 F dx!!!!! Reason
s = ( 5.0ˆ i + 9.0 ˆ j )m 7.) [ Yes!] A particle moving in the xy plane undergoes a displacement while a constant force F = ( 4.0ˆ i + 3.0 ˆ j ) N acts on the particle. Calculate the work done by F over the displacement s by using unit vectors.!!!!!!!!! Draw the Force and position vectors below: y!!!! x 8.) [No.] The force acting on a particle varies as a function of position with the following equation: F(x) = 8x 2 + 3x + 16. Determine the amount of work done from x= 3 m to x= 9 m. 9a.) [No.] Below the corresponding spring,graph F s vs. x for the spring on the frictionless surface in the drawing below.!! - x max! equilibrium! +x max 9b.) [No.] Represent on the graph above the work done by the spring on the block in moving the block from max stretch to equilibrium. Is this positive work or negative work? Explain your choice.
10.) [Yes!] In a rifle barrel, a 40.0 g bullet is accelerated from rest to a speed of 620 m/s. Find the work that is done on the bullet by the expanding gases in the barrel. Caution: Watch your units! 11a.) [Yes!] A block of mass 4.0 kg is attached to a spring that has a force constant of 500 N/m The block is pulled 7.00 cm to the right of equilibrium and is then released from rest. Find the speed of the block as it passes through equilibrium if the coefficient of friction between the surface and the block is 0.20. Required Drawing: 11b.) [Yes.] What is the kinetic energy of the block! 11c.) [Yes.] What is the kinetic energy of the block when it is at maximum compression?!! as it passes through equilibrium? 12.) [Yes!] A proton (mass = 1.67 x 10-27 kg) screaming along the 17 mile circumference vacuum tube at the Large Hadron Collider moves at 90.0% the speed of light has a kinetic energy of 195 pj. Use the work kinetic energy theorem and the relativistic equation for kinetic energy at high speeds to find the work (in Nm) required to increase its speed to 0.980c c = 3.00 x 10 8 m/s
13.) [Yes!] Spring A has a k1 of 2.0 N/cm. Spring B has a k2 of 5.0 N/cm. Spring C has a k3 of 8.0 N/cm. a.) One end of spring A is connected to the ceiling and the other end hangs free. Spring B is connected to the bottom of spring A. Spring C is connected to the bottom of Spring B.. A 3.0 kg block is attached to the bottom of spring C and the block is allowed to slowly stretch the spring system until the system is in static equilibrium. How many cm will the block have moved down from where it was originally attached to the bottom of C to where it reaches static equilibrium? k1 k2 k3 b.) [Yes!] Now the 3.0 kg block is moved over to another set of three springs each with identical spring constants of 6.0 N/cm. These are in parallel with each other as in the set up below. The block is attached to the bottom bar as is shown in the figure. How many cm will the block stretch the springs when the system ireaches static equilibrium?
16.) [No.] An object of mass m is traveling at constant speed v in a circular path of radius r.how much work is done by the centripetal force during one half of a revolution? 15.) [Yes!] A 7000 kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs, as illustrated in the figure below. Both springs obey Hooke s law with k 1 = 1800 N/m and k 2 = 2800 N/m. After the first spring compresses a distance of 40.0 cm, the second spring (acting with the first) increases the force so that additional compression occurs. If the car is brought to rest 60.0 cm after first contacting the spring system, find the car s initial speed and draw a graph of total F s vs. compression distance. Show your work below:!!!!!!!!!!!!!!!! Draw the variable forces on the graph below:!!!!!! 1500 N!!!!!!!! 1000 N!!!!!!! 500 N!!!!!!! 10 20 30 40 50! cm