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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 damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10.0N/m), and a damping force (F=-bv). Initially, it oscillates with amplitude of25.0cm; because of the damping, the amplitude falls to three-fourths of this initial value at the completion of four oscillations. (a) What is the value of b? (b) How much energy has been “lost” during these four oscillations?

A particle executes linear SHM with frequency 0.25Hz about the point x=0. Att=0, it has displacement x=0.37cm and zero velocity. For the motion, determine the (a) period, (b) angular frequency, (c) amplitude, (d) displacement x(t), (e) velocity v(t), (f) maximum speed, (g) magnitude of the maximum acceleration, (h) displacement at t=3.0s, and (i) speed att=30s.

The balance wheel of an old-fashioned watch oscillates with angular amplitudeπradand periodrole="math" localid="1655102340305" 0.500s.

  1. Find the maximum angular speed of the wheel.
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A uniform spring with k = 8600 N.mis cut into pieces 1and 2of unstretched lengthsL1=7.0cm andL2=10cm. What are (a)k1and (b)k2? A block attached to the original spring as in Fig.15-7oscillates at 200 Hz. What is the oscillation frequency of the block attached to (c) piece 1and (d) piece 2?

A 2.00 kgblock hangs from a spring. A 300 kgbody hung below the block stretches the spring 2.00 cmfarther.

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