A fisherman\'s scale stretches 4.2 cm when a 2.7 kg fish hangs from it. (a) What

Question

A fisherman's scale stretches 4.2 cm when a 2.7 kg fish hangs from it.

(a) What is the spring stiffness constant?_________ N/m

(b) What will be the amplitude and frequency of vibration if the fish is pulled down 3.0 cm more and released so that it vibrates up and down? amplitude___________ cm frequency ________Hz

--A small fly of mass 0.12 g is caught in a spider's web. The web vibrates predominately with a frequency of 7.0 Hz.

(a) What is the value of the effective spring stiffness constant k for the web?
N/m
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.58 g were trapped?
Hz

Explanation / Answer

a) mg= kx

2.7 (9.8) =K (4.2 x 10^-2)

K = 630 n/m

b) Amplitude = 3cm. T = 2pi sqroot (m/K) = 2x 3.14 sqroot ( 2.7/ 630 ) = 0.4.11 sec apprx

f = 1/T =1/ 0.411= 2.432 hz

c) T =  2pi sqroot (m/K)

1/7 = 2x 3.14 sqroot ( 0.12 x 10^-3 /K)

1/7 = 6.28 sqroot (0.12 x 10^-3 / K)

1/43.96 = sqroot (0.12 x 10^-3 / K)

squaring on both sides,

1/1932.4816 = ( 0.12 x 10^-3 / K)

K = 0.232 N/m apprx

d) f = 1/ 2pi sqroot ( K/m)

f= 0.159 sqroot ( 0.232/ 0.58 x 10^-3)

f = 3.18 hz apprx

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.