   Chapter 5, Problem 31P

Chapter
Section
Textbook Problem

A horizontal spring attached to a wall has a force constant of 850 N/m. A block of mass 1.00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in Figure 5.22. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c) Find the energy stored in the spring when the mass is stretched 6.00 cm from equilibrium and again when the mass passes through equilibrium after being released from rest. (d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. Substitute to obtain a numerical value. (e) What is the speed at the halfway point? Why isn’t it half the speed at equilibrium?

(a)

To determine
The objects that constitute the system and through what force they interact.

Explanation

The objects that constitute the system are the mass, the spring and the Earth. The spring and the mass will interact with the spring force. The mass and the Earth will be having an interaction force named the gravitational force due to the weight of the object. The system will be having another force named as normal force.

Thus, the objects that constitute the system are the mass, the spring and the Earth...

(b)

To determine
The points of interest.

(c)

To determine
The energy stored in the spring when the mass is stretched and when the mass is passed through equilibrium after being released from the rest.

(d)

To determine
The expression for the conservation of energy equation and the expression and numerical value of speed of the mass as it passes the equilibrium.

(e)

To determine
The speed of the mass at half way point and why is not half the speed at equilibrium.

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