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Chapter 15: Q29P (page 437)

Find the mechanical energy of a block鈥搒pring 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脳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脳10-2J

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

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Most popular questions from this chapter

Question: A physical pendulum consists of two-meter-long sticks joined together as shown in Figure. What is the pendulum鈥檚 period of oscillation about a pin inserted through point at the center of the horizontal stick?

In Figure 15-37, two blocks(m=1.8kgandM=10kg)(and) and a spring (k=200 N/m) are arranged on a horizontal, frictionless surface. The coefficient of static friction between the two blocks is 0.40.What amplitude of simple harmonic motion of the spring鈥揵locks system puts the smaller block on the verge of slipping over the larger block?

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 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.

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