1. A sensitive accelerometer is placed inside a falling cannonball to measure the effect of air resistance on the ball's motion when it is dropped from the leaning tower of Pisa. A curve is fit to the data as a function of time and the equation from the fitted data is: a(t) = g - Ct where g = 9.800-2 is the acclerateon due to gravity and C = 1.500 x 10-3_ $ 4 (a) What are the absolute errors in the ball's position dy (in units of m) and velocity ov (in units of m/s) after 2.00 s if air resistance is neglected? (b) What is the fractional error in position (Sy/y) and velocity (Sv/v)? (c) Assuming that air resistance conditions were similar for Galileo, could he safely neglect air resistance for the cannonball? 2. A point particle moving in one dimension has initial position xo = 5.00m, initial velocity vo = 12.0 %, and is accelerating uniformly at 3.00 -2. (a) Write equations for the position, velocity, and acceleration of the particle as a function of time. (b) Sketch graphs of: position versus time, velocity versus time, and acceleration versus time. Label the axes and label important values. 3. William Tell, legendary archer and hero of Swiss independence was forced to shoot an apple placed on his son's head. If Tess must stand 13.0 m from his son and he launches the arrow with speed vo = 58.0 %, at what angle 0 above the horizontal should he point the arrow? Assume the arrow starts at the same height as the apple and neglect air resistance. 4. A monkey is hanging from a branch in a tree 3.00 m away from a zookeeper and 2.00 m above the zookeeper's hand. The zookeeper knows that the monkey always lets go of the branch just as a banana is thrown to it. (a) At what angle must the zookeeper throw the banana for the monkey to catch it? (b) At what is the minimum speed that the zookeeper must throw the banana at for the monkey to catch the banana? . A roller coaster passes the bottom of a drop at a speed of 20.0 m/s. The radius of curvature of the track at the bottom is 20.0 m. What acceleration do the passengers experience at the bottom of the drop? 6. A small aircraft must land at an airspeed of 31.0 m/s (this is the speed of the plane relative to the air just before landing). The runway direction is West. Wind is blowing in a direction that is 30 North if East. In what direction should the plane head to fly parallel to the runway? 7. An aircraft mass 2.00 x 105 kg is flying at 1.00 x 102 m/s. The pilot banks the aircraft at 0 = 30 in order to make a turn. (a) What is the magnitude of the lift force? (b) What is the radius of the turn? (c) How long does it take the aircraft to make a 360 turn?(15 3. (10 pts) A 0.250 kg ball is travelling at 18.0 m/s to the left when a variable force F(t) directed to the right acts on it for 0.100 s. What is the final velocity of the ball? F(t) = 20,000 - t2 + 5.00 N Draw meaningful diagrams: What physics principle(s) will you apply? Show your work: Uf = Direction (circle one). right left neither4. (15 pts) A solid disk with mass M and radius R, rolls without slipping up an incline to a maximum height h. What was the angular velocity of the disk at the bottom of the incline? (a) Draw a labelled diagram. (b) Find a general equation for the angular velocity. This should be an algebra equation. answer : (c) Find the angular velocity if M = 0.20 kg, R = 0.100 m, and h = 0.400 m. Give a numeric answer with 3 significant figures and units. answer:6. (20 pts) Three point masses are located (3.00, 0), (0,4.00) and (-3.00,0). All measurements are in meters. Each mass is 2.00 kg. (a) Calculate the center of mass of the system of masses. XCM = yCM = (b) Calculate the moment of inertia for rotation around the y axis. 1 = CONTINUED NEXT PAGE!c) Suppose that the two masses on the x axis are held fixed and the mass at (0,4.00) is released. What is the velocity of the released mass when it is at the origin? O 1 = (d) Describe the motion of the released mass after it passes through the origin. (You may find it helpful to sketch the potential energy of the particle as a function of location, U(x).)9. (15 pts) A ball, which is a hollow sphere with m mass m = 0.500 kg and radius R = 10.0 cm is moving at speed v1 = 3.00 m/s to the right when it is on top of a hill at height h1=2.00m It h1 rolls without slipping down the hill then slips hz through a long muddy flat section that has a length d = 2.00m and coefficient of kinetic friction MK = 0.200. The ball then rolls without slipping up the ramp that makes an angle 0 = 30.0 with the horizontal. It is still rolling when it reaches height h2=1.50m (a) Find an algebra expression for the angular velocity @2 of the ball when it reaches height h2. Use given variables and accepted constants. Meaningful, labelled diagram(s) General Equation(s) or name of physics principle(s) you will apply: Show/justify your process. w2 = Calculate W2 W2 =10. (10 pts) A 0.250 kg ball is hit with a tennis racquet with a variable force F(t) directed to the right that acts on the ball for 0.100s. The ball is initially moving to the left. The final velocity of the ball is 20.0 m/s towards the right. What is the initial velocity of the ball? F (t) = (40,000 -2) t2 + 8.00 N Draw meaningful diagrams, labelled with important variables: What physics principle(s) will you apply? Show your work: vi =12. (15 pts) A safe that weighs 25,000N is hung from a boom that consists of a cable Cable and a uniform steel rod that has a weight of 30,000N. 0 = 30. (a) Find the tension in the cable, T. (b) Find the x and y components of the Beam com Rope reaction force F at the hinge. Draw free body diagrams and show your work for full credit. Hinge M 11 1 114. (15 pts) The diagram shows a double pulley which is made of two solid cylinders (mass m, radius r; and mass M, radius R) that are rigidly attached to one another. There are two wires. One wire is wound around the small radius r of the pulley, and is attached to a weight W that is moving upwards with acceleration a. The other wire is wound around the large radius R of the pulley and a force F is exerted on the wire as shown in the diagram. Derive an equation for the magnitude of the acceleration of mass m as a function of given variables and known constants such as g. You must justify each step to receive credit. F W a =