anonymous
  • anonymous
Initially sliding with a speed of 2.2 , a 9.15 block collides with a spring and compresses it 27.5 cm before coming to rest.What is the force constant of the spring?
Physics
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SOLVED
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chestercat
  • chestercat
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Mani_Jha
  • Mani_Jha
Use the conservation of energy. The block initially has only kinetic energy. When it collides with the spring, it tries to displace the spring too, but at the cost of its own kinetic energy. If x is the spring's compression, \[mv ^{2}/2=kx ^{2}/2\]
anonymous
  • anonymous
where did u get these two equations from
Mani_Jha
  • Mani_Jha
The initial kinetic energy of the block was mv^2/2 When a spring is compressed/extended by a distance x, the work that has to be done on it is: kx^2/2 It can be proved by integration.

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anonymous
  • anonymous
i dont understand how w= 1/2 mv^2
anonymous
  • anonymous
i thought k=1/2mv^2
Mani_Jha
  • Mani_Jha
The kinetic energy of a body moving with speed v is mv^2/2. Do you want me to derive it? Since energy can't be destroyed or created(it is conserved), the total energy before is equal to the total energy after. Initially, only the block was moving, and the spring is at rest. so the energy is only mv^2/2. In the final case, the body comes to rest, and the spring is compressed. So the total energy is kx^2/2. By the conservation of energy, these two should be equal. Ok?
anonymous
  • anonymous
so u got it from w=kf-ki
Mani_Jha
  • Mani_Jha
Somewhat. The work done in bringing the block to rest is mv^2/2-0=mv^2/2. This work is done by the spring, which extracts kx^2/2 amount of energy from the block.
Mani_Jha
  • Mani_Jha
Got it?
anonymous
  • anonymous
yah
anonymous
  • anonymous
is the answer 586

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