Practice Final Note: THIS TEST IS LONGER THAN THE ACTUAL TEST. It is a sample and does not include questions on ever topic covered since the start of the semester. Also be sure to review homework assignments on WebAssign Whiteboard problems worked out in class Problems from tests 1 - 3 Exercises, Examples, and Review Questions (at the end of each chapter) in your textbook Some general rules: • Read all problems carefully before attempting to solve them • Your work must be legible, and the organization must be clear • You must show all your work, including correct vector notation • Correct answers without adequate explanation will be counted as wrong • Incorrect work or explanations mixed in with correct work will be counted as wrong o Cross out anything you don’t want us to read! • Make explanations complete but brief. Do not write a lot of prose. • Include diagrams! • Show what goes into a calculation, not just the final number: a ! bc ! d=8 " 10#3( )5 " 106( )2 " 10#5( )4 " 104( )= 5 " 104 • Give standard SI units with your results Unless specifically asked to derive a result, you may start from the formulas given on the formula sheet, including equations corresponding to the fundamental concepts. If a formula you need is not given, you must derive it. If you cannot do some portion of a problem, invent a symbol for the quantity you can’t calculate (explain that you are doing this), and use it to do the rest of the problem.Problem 1. A baseball of mass 0.025 kg is released from rest at a location 3.5 m above the ground. You will calculate its speed at the instant it hits the ground. (a) Choose a system to analyze, and list the objects in your chosen system. (b) Write out the energy principle as it applies to the system you have chosen. Solve for the speed of the baseball when it hits the ground.Problem 2. In transitions between vibrational energy levels of the diatomic molecule HI (hydrogen iodide), photons are emitted with energy 4.4e-20 J, twice this energy, three times this energy, etc. Because the mass of the iodine nucleus is much larger than that of the hydrogen nucleus, it is a good approximation to consider the iodine nucleus to be always at rest; you can think of the H atom as being attached by a “spring” to a wall. What is the effective stiffness of the HI bond? Show your work.Problem 3. The neutron has a mass of 1.6749e-27 kg. The neutron is unstable when removed from a nucleus, and it decays into a proton, electron and antineutrino. The proton’s mass is 1.6726e-27 kg, the electron’s mass is 9.1e-31 kg, and the antineutrino has nearly zero mass. Assume that the original neutron was at rest. What is the total kinetic energy of the proton plus electron plus antineutrino when they are far apart? Show all work.Problem 4. You apply a force of <10, -25, 8> N on an object while the object moves from position <-4, 3, 6> m to position <-1, 6, 2> m. How much work do you do?Problem 5. By “weight” we usually mean the gravitational force exerted on an object by the Earth. However, when you sit in a chair your own perception of your own “weight” is based on the contact force the chair exerts upward on your rear end rather than on the gravitational force. The smaller this contact force is, the less “weight” you perceive, and if the contact force is zero, you feel peculiar and “weightless” (an odd word to describe a situation when the only force acting on you is the gravitational force exerted by the Earth!). Also, in this condition your internal organs no longer press on each other, which presumably contributes to the odd sensation in your stomach. (a) How fast must a roller coaster car go over the top of a circular arc for you to feel “weightless”? The center of the car moves along a circular arc of radius R = 20 m. Include a carefully labeled force diagram. (b) How fast must a roller coaster car go through a circular dip for you to feel three times as “heavy” as usual, due to the upward force of the seat on your bottom being three times as large as usual? The center of the car moves along a circular arc of radius R = 20 m. Include a carefully labeled force diagram.Problem 6. An electron is moving with constant speed 0.97c, where c is the speed of light. (a) What is its rest energy? (b) What is its total energy? (c) What is its kinetic energy?Problem 7. At t = 532.0 s after midnight a spacecraft of mass 1400 kg is located at position <3e5, 7e5, -4e5> m, and an asteroid of mass 7e15 kg is located at position <9e5, -3e5, -12e5> m. There are no other objects nearby. (a) Calculate the (vector) force acting on the spacecraft. (b) At t = 532.0 the spacecraft’s momentum was !pi. At t = 532.4, the spacecraft’s momentum was !pf. Calculate the (vector) change in momentum !pf!!pi.Problem 8. (a) A package of mass m sits on an airless asteroid of mass M and radius R. We want to launch the package straight up in such a way that its speed drops to zero when it is a distance 4R from the center of the asteroid, where it is picked up by a waiting ship before it can fall back down. We have a powerful spring whose stiffness is ks. How much must we conpress the spring? Show your work. (b) Starting just after the launch, for the system consisting of the asteroid plus package, graph the gravitational potential energy U, the kinetic energy K and the sum K+U, as a function of the distance between the centers of the asteroid and package. Label each curve clearly.Problem 9. One mole of nickel (6 ! 1023 atoms) has a mass of 59 grams, and its density is 8.9 grams per cubic centimeter. You have a long thin bar of nickel, 2.2 m long, with a square cross section, 0.1 cm on a side. (a) You hang the rod vertically and attach a 104 kg mass to the bottom, and you observe that the bar becomes 1.12 cm longer. Calculate the effective stiffness of the interatomic bond, modeled as a “spring”. (b) Next you remove the 104 kg mass, place the rod horizontally, and strike one end with a hammer. How much time !t will elapse before a microphone at the other end of the bar will detect a disturbance?Problem 10. A block of mass 0.07 kg is attached to the end of a vertical spring whose relaxed length is 0.23 m. When the block oscillates up and down in the lab room, it takes 1.29 s to make a