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Chapter 15: Q29P (page 437)

Find the mechanical energy of a block–spring system having a spring constant 1.3 N/ cmofand oscillation amplitude of 2.4cm.

Short Answer

Expert verified

The mechanical energy of the block-spring system is3.74×10-2J

Step by step solution

01

The given data

  1. The amplitude of motion,xm=2.4cmor0.024m
  2. The spring constant of the system,k=1.3N/cmor130N/m.
02

Understanding the concept of mechanical energy

We can find the mechanical energy of the block-spring system using the law of conservation of energy.

Formula:

The elastic P.E energy of the system PE=12kx2....(1)

The law of conservation of energy gives E= constant (2)

03

Calculation of mechanical energy of the spring-block system

From equation (ii), we can say that the mechanical energy of the system = the maximum elastic P.E energy of the system. Hence, we get the total energy of the system as:

E=12kxm2=12130(0.024)2 =3.74×10-2J

Therefore, the mechanical energy of the block-spring system is3.74×10-2J.

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Most popular questions from this chapter

A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through the stick a distanced from the50cmmark. The period of oscillation is2.5s. Findd.

A block weighing 20 Noscillates at one end of a vertical spring for which k=100 N/m; the other end of the spring is attached to a ceiling. At a certain instant the spring is stretched 0.30 mbeyond its relaxed length (the length when no object is attached) and the block has zero velocity. (a) What is the net force on the block at this instant? What are the (b) amplitude and (c) period of the resulting simple harmonic motion? (d) What is the maximum kinetic energy of the block as it oscillates?

A 3.0kg particle is in simple harmonic motion in one dimension and moves according to the equation x=(5.0 m)cos [(ττ/3rad/s)t-ττ/4rad],with t in seconds. (a) At what value of x is the potential energy of the particle equal to half the total energy? (b) How long does the particle take to move to this position x from the equilibrium position?

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