Question

Question 13

a) The fan blades on a jet engine make one thousand revolutions in a time of 36.6 ms. What is the angular frequency of the blades?

b) Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 155 N/m. The motion of the object on spring 1 has twice the amplitude as the motion of the object on spring 2. The magnitude of the maximum velocity is the same in each case. Find the spring constant of spring 2.

Answer 1

here,

a)

number of revolutions , N = 1000 rev

the time taken , t = 36.6 s = 0.0366 s

the angular frequency of the blades , w = 2 * pi * f

w = 2*pi * ( N/t)

w = 2*pi*(1000 /0.0366) rad/s

w = 1.72 * 10^5 rad/s

the angular frequency of the blades is 1.72 * 10^5 rad/s

b)

the spring constant of 1 , K1 = 155 N/m

A1 = 2 * A2

as they same magnitude of maimum velocity

vm1 = vm2

A1 * w1 = A2 * w2

A1 * sqrt(K1 /m) = A2 * sqrt(K2 /m)

2 * A2 * sqrt(155) = A2 * sqrt(K2)

2 * sqrt(155) = sqrt(K2)

K2 = 620 N/m

the spring constant of 2 is 620 N/m