The force constant of this spring is 16.03N/m; the length of time block is in contact with the spring before it comes to rest is 1.14s; If the force constant of the spring is increased, the time required to stop the block will decrease.
What happens if a block slides on a frictionless horizontal surface?
When a block slides over a horizontal surface without friction, it has kinetic energy. Before coming to rest, it runs into an untensioned spring and compresses it.
The energy is purely kinetic when the mass first comes into contact with the spring. Energy is transformed into spring potential energy as the spring is squeezed. To find the spring force constant, equate the energies. One-fourth of a period is represented by the motion. A stiffer spring will result in a smaller stopping distance for the mass, which will result in a faster stopping time.
(a)Equations: Conservation of energy using a spring.
Ei=Ef
1/2mvo2 = 1/2kA2
A= vo√m/k
K is force constant
k is 16.03N/m
(b) Time
T = 2∏√m/k
T = 1.14s
(c) The time to stop reduces as the force constant rises. A stronger spring and a greater stopping force result from a higher force constant, and a shorter stopping time follows. The compressed spring contains all of the energy left behind after the spring has stopped the block. The block will be accelerated back the way it came when the spring pushes back on it. The block will leave the spring moving in the opposite direction from where it first came into contact with it, but at the same speed. Equal to the stopping time is the accelerating time.
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