Physics 218 Review

1. Physics 218Review Dr. David Toback Physics 218, Review

2. Thought of the day… Physics 218, Review

3. Problem Choices • Ball rolling down a hill • Ice Skating • Apollo 11 • Mass moving in a circle • Hunter in the forest • Simple harmonic motion derivation • Ski Vacation • Rocket Launcher Physics 218, Review

4. Ball Rolling Down a Hill You are the technical advisor on the new movie: “The Matrix – Refrozen.” The script has a giant spherical ice ball, I = 2/5 mr2, where you have measured m and r. It rolls down a hill (without slipping) starting from rest right at Morpheus who is at the bottom. You know the length of the slope (L) and its angle to the horizontal (q) and the ball starts from the top of the hill • Your job is to calculate the speed of the ice ball at the bottom of the hill (you want to make sure it’s fast enough to look cool) and • The time it takes to get down the hill so Morpheus knows exactly when to dive out of the way. Physics 218, Review

5. Ice Skating You decide to take up ice-skating and, being athletic, want to learn all the moves. You are proud of the fact that you have learned to spin in place on the ice. Your friends video tape you spinning and then bringing your arms in close to your body. From the tape you are able to measure your initial and final moments of inertia, I0, and If = Io/3, as well as your final angular speed, wf. In terms of I0 and wf, find: • Your final angular momentum • Your initial angular speed • Your initial kinetic energy • How much work you have to do to bring in your arms. At the end of your spin, you put your foot down and dig your toe into the ice and come to a stop. You measure the time it takes to stop to be t seconds. Assuming constant negative angular acceleration: • What is the torque your toe exerts? Physics 218, Review

6. Mass Moving in a Circle A puck of mass M, attached to a massless string, moves in a circle of constant radius R about a small hole on a frictionless, horizontal table. The end of the string is connected to a small block of mass m through the hole as shown. At t=0 the puck is at (R,0) and moving in the positive Y-direction. The block and puck may be treated as particles. • Draw the force diagram for the puck including the magnitude and direction of each force. • Find the speed (v1) of the puck in terms of g, R, M and m • Is this Simple Harmonic Motion? If so, what is the Amplitude and w? What is the equation of motion in the X-direction? • A woman pulls the block (of mass m) down by ½R. Find the resultant speed, v2, of the rotation in terms of v1. Hint: Use conservation of angular momentum Physics 218, Review

7. Hunter in the Forest d A hunter aims directly at a target which is a distance R away. Note that the gravitational acceleration near the earth’s surface is g. Ignore air friction. • If the bullet leaves the gun at a speed of V0, by how much (vertically) will it miss the target? In other words, on the diagram what is the value of d. • Assuming the bullet leaves at the same speed, at what angle should the gun be aimed so that the target will be hit? Hint: 2sinqcosq = sin2q Physics 218, Review

8. Simple Harmonic Motion A block of mass m sits on a frictionless surface attached to a spring with spring constant k. We can write down • Hooke’s law: F=-kx • Newton’s law: F = ma =md2x/dt2. • Given that the general equation of motion for the position, x, as a function of time t is x(t) = Asin(wt+f), show that this equation is a solution of Hooke’s law and Newton’s law with w2= k/m. • At time t=0, the spring is compressed to the position -x0 and released from rest. Using your previous results, find the amplitude. You may NOT just write down the solution, rather you must show it to be true mathematically. • For the same system, find the phase of the motion Physics 218, Review

9. Ski Vacation You take a ski vacation to Vale, Colorado. While at the summit of a large slope, you start from rest and then ski over two successively lower hills with known heights H1 = 2H2. The lowest hill is essentially a semi-circle centered at the 0 level. You want to leave the lowest hill at its top and fly through the air. Assume no friction and air resistance. The magnitude of gravity = g. How far up the slope must you be when you start down the hill? Put your answer in terms of g and H2. Physics 218, Review

10. Rocket Launcher You want to simulate the muzzle velocity of a missile fired by the shoulder-fired “Red-eye launcher.” To simulate this, you build a small model and test-fire a bullet of mass M1 and unknown speed directly into a wooden block of mass M2. The block is suspended by wires from the ceiling and is initially at rest. The bullet embeds in the block and the block swings up to a maximum height (Hmax) above its initial position. Magnitude of gravity = g. Ignore air friction. • What is the speed of the bullet, when fired? • What is the change in mechanical energy after the bullet gets stuck in the block? • Is this an elastic or inelastic collision? Why? Physics 218, Review

11. That’s it… • It’s been a pleasure • I hope you’ve enjoyed it as well and perhaps even learned something ;) • Make sure you get your homework and labs turned in • Best of luck on the final… Physics 218, Review

12. End of Lecture Notes Physics 218, Review