Take as much time needed to answer every single question. Just be sure to answer ead h question correctly and will write a wor iew about you afterwards! Do not rush and use the correct amount of significant digts/figures for each questions. Thnak you. Question 1: A 53.0 kg circus performer oscillates up and down at the end of a long elastic rope at a rate of once every 4.00 s. The elastic rope obeys Hooke's Law. By how much is the rope extended beyond its unloaded length when the performer hangs at rest? Give your answer in meters. Question 2: A 40.0 kg block at rest on a horizontal frictionless air track is connected to the wall via a spring. The equilibrium position of the mass is defined to be at a = 0. Somebody pushes the mass to the position a = 0.350 m, then lets it go. The mass armonic motion with a period of 5.40 s. 00000M x -8.250m LLL 00000M 2a What is the position (in meters) of the mass 2.26 s after the mass is released? 2b What is the magnitude of the maximum acceleration the mass undergoes during its motion? Give answer in m/s2. Question 3: Two different simple harmonic oscillators have the same natural frequency of 9.20 Hz when they are on the surface of the Earth. The first oscil Ba If both systems are moved to the g = 1.67 m/s?), what is the new frequency of the pendulum in Hz? 3b Calculate the new frequency of the vertical spring and mass in Hz. Question 4: A 1.10 kg mass on a spring oscillates horizontally with little friction according to the following equation: = = 0.0700 cos(3.10t) where a is in meters and t in seconds. 4a Find the maximum en by stored in the spring during an oscillation. Give your answer in joules. 4b Find the maximum velocity of the mass in m/s Question 5: A simple pendulum is 5.60 m long. What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator that is accelerating upward at 4.30 m/s*2? Give answer in seconds. 1. What is its 4.30 m/s^2? 2. What is the notion for this pendulum if it is placed in a truck that is accelerating horizontally at 4.30 m/s^2? Question 6: Find the period of oscillation (in seconds) of the system below. The mass is 43.8 kg and the two springs have springs constants of 755 N/m and 230. N/m respectively. Question 7: A 40.0 kg block at rest on a horizontal frictionless table is connected to the wall via a spring with a spring constant k = 12.0 N/m. A 2.80 x 10 2kg bullet travelling with a speed of 5.60 x 102 m/s embeds itself in the block. What is the amplitude in meters of the resulting simple harmonic motion? Recall that the amplitude is the m mum displacement from equilibrium. - - -00000 Question 8: A large block P executes horizontal simple harmonic motion with a frequency of f = 1.77 Hz as it slides across a frictionless surface. Block B rests on it, as shown in the figure below, and the coefficient of static friction between the two blocks is /, = 0.530 B P 8 What maximum amplitude of oscillation can the system sustain if block B is not to slip? Give your answer in centimeters (not meters). Question 9: The figure shows a simple pendulum of length L = 89.0 cm and mass m = 1.60 kg. Its bob is observed to have a speed of vo = 3.40 m/s when the cord makes an angle 00 = 40.0. 9a What is the speed (in m/s) of the bob when it is in its lowest position? 9b What is the least value (in m/s) that vo must have if the cord is to swing up to a horizontal position? Question 10: A mass, my = 8.74 kg, is in equilibrium while connected to a light spring of constant k = 120. N/m that is fastened to a wall, as shown in the figure (part a) below. mi [a) -A- m1 m2 (9) m1 m 2 10a A second mass, my = 6.15 kg, is slowly pushed up against mass my. compressing the spring by the amount A = 0.241 m (see figure, part b). The system is then released, and both masses start moving to the right on the frictionless surface. When m, reaches the equilibrium point, my loses contact with my (see figure, part c) and moves to the right with speed v. Determine the value of u in mis. 10b How far apart are the masses when the spring is fully stretched for the first time? Give your answer in meters. Question 11: The residents of a small planet have bored a hole straight through its centre as part of a communications system. The hole has been filled with a tube and the air has been p ssed back and forth by dropping packets through the tube. The planet has a uniform density of 4420 kg/m*3, and it has a radius of R=6.07x10*6 m. What is the speed in m/s of the message packet as it passes a point a distance of 0.440R from the ce sume that this 'oscillator' will have a period equal to that of a satellite in orbit at the surface of the planet. 2. How does it take (in sec ssage to pass from one side of the planet to the other