A slinky has a mass of 0.28 kg and negligible length. When it is stretched 1.2 m
ID: 2299016 • Letter: A
Question
A slinky has a mass of 0.28 kg and negligible length. When it is stretched 1.2 m, it is found that transverse waves travel the length of the slinky in 0.68 s. (The Slinky stretches like an ideal spring, and propagates transverse waves like a rope with variable tension.)
(a) What is the force constant, k, of the slinky?
N/m
(b) If the slinky is stretched less, will the time required for a wave to travel the length of the slinky increase, decrease, or stay the same?
(c) If the slinky is stretched 0.6 m, how much time does it take a wave to travel the length of the Slinky?
Explanation / Answer
a)v=sqrt(TL/m)
v=1.2/0.68=1.765m/s
T=v^2*m/L=0.727N
k=T/L=0.6055N/m
b)Let the extension decrease by a factor of a.
The tension will decrease by a factor say a.
the velocity decreases by a factor of sqrt(a)*sqrt(a)=a.
time taken = L*a/v*a=L/v
Clearly the time taken remains the same
c)time=0.68s