Blocks on Spring without Friction

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SUMMARY

The discussion centers on the mechanics of a spring-block system, specifically analyzing potential energy and mechanical energy when a spring is stretched and then released. The potential energy calculation using PE=(mgh) was incorrectly applied; the correct formula for potential energy in a spring is PE = (1/2)kx², where k is the spring constant. The total mechanical energy remains constant throughout the motion, and the speed of the block can be determined using energy conservation principles. Key calculations include determining the spring constant and applying it to find the speed of the block at various positions.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of potential energy and kinetic energy equations
  • Familiarity with conservation of mechanical energy principles
  • Basic physics concepts related to mass, force, and acceleration
NEXT STEPS
  • Learn how to calculate spring constant (k) using Hooke's Law
  • Study the derivation of potential energy in springs (PE = (1/2)kx²)
  • Explore the conservation of mechanical energy in dynamic systems
  • Investigate the relationship between speed and energy in oscillatory motion
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of spring systems and energy conservation principles.

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A spring is stretched a distance of Dx = 40 cm beyond its relaxed length of xo by a force, F = 20 N. Attached to the end of the spring is an block of mass m = 12 kg, which rests on a horizontal frictionless surface.
After a moment, the force is removed.

a) What is the potential energy of the block due to the spring when it is held in the stretched position?

For this question, I did PE=(mgh). So, PE= (12)(9.8)(0.4m) and got 47.04 J, but that's not the right answer.

b) What is the total mechanical energy of the block when it is held in the stretched position?

c) What is the total mechanical energy of the block when it returns to its unstretched position?

d) When the spring again returns to its unstretched length, what is the speed of the block?

e) What is the total mechanical energy of the block when it has returned only halfway (20 cm) to its unstretched position?

f) When the spring has returned only halfway (20 cm), what is the speed of the block?
 
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