A common technique used to measure the force constant of a spring is demonstrated by the setup as shown. The spring is hung vertically (7.12a), and anobject of mass m is attached to its lower end. Under the action of the "load" mg, the spring stretches a distance d from its equilibrium position (7.12b). (A)If a spring is stretched 2.0 cm by a suspended object having a mass of 0.55 kg, what is the force constant of the spring? (B) How much work is done by thespring on the object as it stretches through this distance?F,The elongation discaused by the weight mgthe attached object.mgFigure 7.12 (Example 7.5)Determining the force constant kof a spring.

The stretch in the string x=2.0 cm=0.02 m The mass of the object m=0.55 kg The weight of the spring…

Answered: A common technique used to measure the…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 20P

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A particle of mass m is at rest at the end of a spring (force constant = k) hanging from a fixed support. At t = 0, a constant downward force F is applied to the mass and acts for a time t0. Show that, after the force is removed, the displacement of the mass from its equilibrium position (x = x0, where x is down) is where
Use the data in Table P16.59 for a block of mass m = 0.250 kg and assume friction is negligible. a. Write an expression for the force FH exerted by the spring on the block. b. Sketch FH versus t.
A block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown in Figure P7.15. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is k = 0.350. Figure P7.15
A spring 1.50 m long with force constant 475 N/m is hung from the ceiling of an elevator, and a block of mass 10.0 kg is attached to the bottom of the spring. (a) By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (b) If the elevator subsequently accelerates upward at 2.00 m/s2, what is the position of the block, taking the equilibrium position found in part (a) as y = 0 and upwards as the positive y-direction. (c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?
A block of mass 0.250 kg is placed on top of a light, vertical spring of force constant 5 000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?
A vibration sensor, used in testing a washing machine, consists of a cube of aluminum 1.50 cm on edge mounted on one end of a strip of spring steel (like a hacksaw blade) that lies in a vertical plane. The strips mass is small compared with that of the cube, but the strips length is large compared with the size of the cube. The other end of the strip is clamped to the frame of the washing machine that is not operating. A horizontal force of 1.43 N applied to the cube is required to hold it 2.75 cm away from its equilibrium position. If it is released, what is its frequency of vibration?
Refer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?
A 69.5 kg bungee jumper is standing on a tall platform (h0 = 53 m), as seen in the photo. The bungee cord has an untrained length of L0 = 10 m, and when stretched, behaves like an ideal spring with a spring constant of k = 64.0 N/m. The jumper falls from rest, and the only forces acting on him are his weight and, for the latter part of the descent, the elastic force of the bungee cord (Assume the cord is attached at the center of mass and the center of mass drops from rest from the height of the platform.) What is his maximum speed during the fall? _______ m/s How high above the water is he when he reaches this speed? _______ m How high above the water is he when he reaches the lowest point in the fall? _______ m
A wire of original length L and cross sectional area A is stretched within its elastic limit by a stress S.Show that the density of stored elastic energy in the stretched wire is S2/2Y.
A block of mass m = 2.00 kg is attached to a spring of force constant k = 5.70 ✕ 102 N/m that lies on a horizontal frictionless surface as shown in the figure below. The block is pulled to a position xi = 5.55 cm to the right of equilibrium and released from rest. The left end of a horizontal spring of force constant k is attached to a vertical wall. The right end is attached to a block of mass m, which rests on a horizontal floor. The equilibrium position of the spring is labeled x = 0. The block has been moved to the right to a position labeled x = xi, so that the spring is stretched. (a) Find the the work required to stretch the spring. J(b) Find the speed the block has as it passes through equilibrium.
An m=20.0g object is held against the free end of a spring of constant k=25.0N/m that is compressed a distance x=10.0cm from its equilibrium length. Once released, the object slides d1=1.15m across the tabletop and eventually lands d2=1.44m from the edge of the table on the floor, as shown in the figure. Calculate the coefficient of friction μ between the table and the object. The sliding distance includes the compression of the spring, and the tabletop is h=1.00m above the floor level. μ=?
A scene in a movie has a stuntman falling through a floor onto a bed in the room below. The plan is to have the actor fall on his back, but a researcher has been hired to investigate the safety of this stunt. When the researcher examines the mattress, she sees that it effectively has a spring constant 65144 N/m for the area likely to be impacted by the stuntman, but it cannot depress more than 13.55 cm without injuring him. To approach this problem, consider a simplified version of the situation. A mass falls through a height of 3.32 m before landing on a spring of force constant 65144 N/m. Calculate the maximum mass that can fall on the mattress without exceeding the maximum compression distance.

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