- #1
John McAndrew
- 6
- 0
I have a question that appears elementary, but bizarre in its conclusion:
A mass ##M## is accelerated by a spring of length ##L##, wave-speed ##v_p##, spring-constant ##K## and a constant force ##F## at the other end. As ##K## increases, the extension of the spring ##dx## decreases as does the energy stored ## \frac{1}{2} k{dx}^2 ##. The max rate at which work can be done by the spring on the mass is of the order:
##P## = (energy stored in spring)/(propagation time over spring's ##L##)
= ## \frac{1}{2} k{dx}^2v_p/L ##
Hence as ##K\rightarrow \infty, P \rightarrow 0##: the mass can't accelerate!
Is this correct?
The physics seems to say yes, but I don't quite believe it and may have gone wrong somewhere.
A mass ##M## is accelerated by a spring of length ##L##, wave-speed ##v_p##, spring-constant ##K## and a constant force ##F## at the other end. As ##K## increases, the extension of the spring ##dx## decreases as does the energy stored ## \frac{1}{2} k{dx}^2 ##. The max rate at which work can be done by the spring on the mass is of the order:
##P## = (energy stored in spring)/(propagation time over spring's ##L##)
= ## \frac{1}{2} k{dx}^2v_p/L ##
Hence as ##K\rightarrow \infty, P \rightarrow 0##: the mass can't accelerate!
Is this correct?
The physics seems to say yes, but I don't quite believe it and may have gone wrong somewhere.
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