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& EST Willis Tower vibration The mass of the Willis (formerly Sears) Tower in Chicago is about
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- You have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in Figure P7.41. When a car moves to the right in the figure and strikes the springs, they exert a force to the left on the car to slow it down. Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2 = 3 400 N/m. After the first spring compresses by a distance of d = 30.0 cm, the second spring acts with the first to increase the force to the left on the car in Figure P7.41. When the spring with spring constant k2 compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can no longer compress. A typical car on the siding has a mass of 6 000 kg. When you present your design to your supervisor, he asks you for the maximum speed that a car can have and be stopped by your device. Figure P7.41arrow_forwardA spring has a length of 0.200 m when a 0.300kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it. (a) What is the force constant of the spring? (b) What is The unloaded length of the spring?arrow_forwardIn a control system, an accelerometer consists of a 4.70-g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of 0.800g, the object should be at a location 0.500 cm away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct.arrow_forward
- One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. (a) Calculate the force constant of its plunger’s spring if you must compress it 0.150 m to drive the 0.0500kg plunger to a top speed of 20.0m/s. (b) What force must be exerted to compress the spring?arrow_forwardConsidering the spring shown below with spring coefficient = 2000 N/mm, mass = 400 kg and original length = 300 mm. Calculate the actual length of this spring after effecting the load. = 2000 N/mm Hibbeler, 2006 Select one: O i. 302 mm ii. 298 mm iii. 200 mm iv. 300 mm wwwarrow_forwardThe continuity equation is an expressiom of a.Conservation of mass b.Conservation of energy c.Conservation of angular momentum d.Conservation of momentum Which of the ff. statements is NOT true about acceleration?a.Acceleration is uniform for straight line motion. b.For circular motion, acceleration is constant in magnitude and direction c.Acceleration is uniform if the velocity changes by equal amount in equal time d.The average acceleration cannot be used in precise calculations unless the acceleration is uniform Tensile and compressive stress are caused by forces ________ to the area on which they act a.Perpendicular b.Angled c.Parallel d.Skewarrow_forward
- 5m 4m B The unstretched length of spring AB is 5 m. If the block is held in the equilibrium position shown, www www 4m the spring constant for spring AB is 40N/m and for spring AC is 30 N/m. 'A determine the mass of the block at D. Note that Darrow_forwardA very light spring with spring constant K = 700 N/m is hung (s) by a fixed ceiling. Two forces F, = F2 = 20 N act at the lower end of the spring as shown in the figure below. The extension (increase in length) of the spring due to these two forces is: A. 0.040 m B. 0.012 m C. 0.021 m D. 0.082 m E. Zero F2 O A O B O C O D O Earrow_forwardA crate with mass m is placed above a ramp with an angle 0, and a distance L from a spring with a spring constant k. Suppose that the ramp and crate experience a coefficient of kinetic friction u, solve for the following: a. speed of crate before it compresses the spring b. maximum compression of the spring C. How far does the crate get to its initial distance when it rebounds? Wwwwwarrow_forward
- Part A If the block is acted upon by a vertical force F= (7 sin8t) N, where t is in seconds, select the equation which describes the motion of the block when it is pulled down 100 mm from the equilibrium position and released from rest at t = 0. Displacement y is measured in II. Assume that positive displacement is downward. Express your answer in terms of the variablet. Express the coefficients to three siginificant figures so the displacement is measured in millimeters. ▾ View Available Hint(s) ▾ Hint 1. How to approach the problem Apply the general solution for the displacement of the block. It should include a complementary solution that defines free vibration, and a particular solution that describes forced vibration of the block caused by the applied force. Calculate the natural frequency and determine the constants of integration using the position and velocity of the block at t = 0, and substitute the found values into the general solution. y = ΔΙΑΣΦ OF ? mmarrow_forwardHelioseismology in an Alternate Universe 0 points possible (ungraded) Stars, like planets, can vibrate. On Earth, we call these vibrations earthquakes, and their study is called seismology. The study of the vibrations of the sun is called helioseismology. Earth's crust is made up of solid, rigid rock, so elastic forces are largely responsible for the propagation of earthquake vibrations. Stars, however, are made of hot plasma, so elastic forces are negligible. Instead, the relevant force in an oscillating star is gravity. In our universe, the force of gravity between two objects is Fg (r): Gm1m2 p2 where G is the Newton's gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between the objects. Imagine that we are in an alternate universe in which the force of gravity is instead given by Fg (r) Zm1m2 p3 Mass, distance, and force all have the same units in this alternate universe, i.e. kilograms, meters, and Newtons (kg - m/s²), respectively, and Z…arrow_forwardA 0.82 kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstrained length quadruples. What is the mass of the second block? kgarrow_forward
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