Nonlinear springs are classified as hard or soft, depending upon the curvature of their force-deflection curve (see figure). If a delicate instrument having a mass of 5 kg is placed on a spring of length / so that its base is just touching the undeformed spring and then is inadvertently released from that position, determine the maximum deflection xm of the spring and the maximum force Fm exerted by the spring, assuming (a) a linear spring of constant
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Vector Mechanics For Engineers
- Block A has a mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B, having a mass mB, is pressed against A so that the spring deforms a distance d, show that for separation to occur it is necessary that d > 2µkg(mA + mB )/k, where µkis the coefficient of kinetic friction between the blocks and the ground. Also, what is the distance the blocks slide on the surface before they separate?arrow_forwardSHOW COMPLETE SOLUTION A spring is used to stop 50kg block moving down a 20 degrees inclined plane. The spring has a constant K= 30KN/M and is held by the cables so that it is initially compressed 50mm. Knowing that the velocity of the package is 2m/s when it is 8m from the spring and assuming the kinetic coefficient of friction between the package and the incline is 0.20. Determine: D. Final total potential energy E. Initial kinetic energy F. Initial total potential energyarrow_forward13. An object (at earth) at rest with a mass of 3kg is being dropped 3m above the spring whose constant is 10N/mm. If the spring has to stopped the falling object, determine the magnitude of deflection of the spring right after the stoppage. Assume no energy loss during operation. draw a figure.arrow_forward
- Activity 3. A body that weighs W Newtons falls from rest from a height of 600mm and strikes a spring whose scale is 7.00 N/mm. If the maximum compression of the spring is 150 mm, what is the value of W? Disregard the mass of the spring.arrow_forwardA 5-kg bag is gently pushed off the top of a wall and swings in a vertical plane at the end of a 2.4m rope which can withstand a maximum tension of 100 N. Determine (a) the elevation h betweenpoint A and point B where the rope will break, (b) the distance d from the vertical wall to thepoint where the bag will strike the floor.arrow_forwardA 200-lb bungee jumper jumps from a bridge 130 ft above a river. The bungee cord has an unstretched length of 60 ft and has a spring constant k = 14 lb/ft. (a) How far above the river is the jumper when the cord brings him to a stop? (b) What maximum force does the cord exert on him? (c) What is the maximum velocity does the jumper reach?arrow_forward
- 3 - In the figure, the 200-lb crate is being pulled up the slope by the motor M. If the velocity of the point P is 2s³ ft/s (where s is the displacement of the crate), and the coefficient of kinetic friction between the crate and the slope is u = 0.2, what will the towing force applied by M be when the box has moved 10 ft up the slope?arrow_forwardTo apply Newton’s second law and the theorem of conservation of energy to solve kinetic problems. A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has lengthL when unstretched, will first straighten and then stretch as the jumper falls.Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant k. The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle. Use g for the magnitude of the acceleration due to gravity. How far below the bridge, d, will the jumper eventually be hanging, once the jumper stops oscillating and comes finally to rest? Assume that the jumper does not touch the water. Express your answer in…arrow_forwardAn elastic cable is to be designed for bungee jumping from a tower 130 ft high. The specifications call for the cable to be 85 ft long when unstretched, and to stretch to a total length of 100 ft when a 600-lb weight is attached to it and dropped from the tower. Determine (a) the required spring constant k of the cable, (b) how close to the ground a 186-lb man will come if he uses this cable to jump from the tower.arrow_forward
- URGENT Collar A slides over the smooth vertical bar shown in the figure. The masses Wa = 10lbs and WB = 5lbs. When h = 0.12192m, the spring is unextended. When the system is in equilibrium, h = 0m. Determine the constant k of the spring. Note: The normal of the collar is 100 times its mass (that of the collar), remember that g = 32.16 ft/s2.arrow_forwardA block of mass m= 2.0 kg is released from rest on an inclined plane at a height of h = 1.5 m. It moves down the rough incline with slope theta= 30.0°and continues on the horizontal frictionless surface. As shown in the figure, there is a spring with negligible mass and force constant k = 300 N/m. The coefficient of kinetic friction between the block and the incline is 0.250 What is the speed of the block when it gets down on the horizontal surface before it touches the spring? The box continues to move on the horizontal surface and compresses the spring. What will be the maximum compression of the spring?arrow_forwardA catapult is used to throw large projectiles by the ancient civilization. If a catapult swung from rest position and shot a 10-kg projectile at a velocity of 50 meters per second. Determine the force in Newtons exerted by the catapult on the projectile.arrow_forward
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