Question

The scale of a spring balance that reads from 0 to 42.1 kg is 10.0 cm long. A package suspended from the balance is found to oscillate vertically with a frequency of 2.87 Hz. (a) What is the spring constant? (b) How much does the package weigh?

Answer 1

a )

given m = 42.1 kg ,

x = 10 cm = 0.1 m

the weight is " W "

W = m g

W = 42.1 X 9.8

W = 412.58 N = F

the spring constant i s" K "

K = F / x

K = 412.58 / 0.1

K = 4125.8 N/m

the spring constant is K = 4125.8 N/m

b )

f = 2.87 Hz

the frequency f = ( 1/2 ) ( K/m )^1/2  

then rewriting for m is

m = K / 4 ² f²

m = 4125.8 / 4 X 3.14² X 2.87²

m = 12.7 kg

then the the package weight is W = m g

W = 12.7 X 9.8

W = 124.466 N

the package weight is W = 124.466 N