   Chapter 13, Problem 21P

Chapter
Section
Textbook Problem

A horizontal spring attached to a wall has a force constant of k = 8.50 × 102 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P13.21. (a) The block is pulled to a position xi = 6.00 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.00 cm from equilibrium. (b) Find the speed of the block as it passes through the equilibrium position. (c) What is the speed of the block when it is at a position xi/2 = 3.00 cm? Figure P13.21

a)

To determine
The potential energy stored in the spring when the block is 6.00cm from the equilibrium position.

Explanation

Given info: The force constant of the spring is 8.50×102Nm-1 . The mass of the block is 1.00kg . The block is pulled xi=6.00cm from the equilibrium position and released.

Explanation:

The elastic potential energy stored in a system in simple harmonic motion is given by,

PE=12kx2

Here,

PE is the potential energy

k is the force constant of the spring

x is the displacement from the equilibrium

Substituting 8.50×102Nm-1 for k , 6.00cm for x to find the potential energy is,

PE=12(8

b)

To determine
The speed of the block when it passes through the equilibrium position.

c)

To determine
The speed of the block when x=xi2 .

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