Question #68089

The scale of a spring balance reading from 0 to 50 lb is 4 inch long.A pakage suspended from the balance is found to oacillate vertically eith a frequency of 2.0 Hz.how much does the pakage weigh?

Expert's answer

Newton's second law:

mg= kx (1), where k is the coefficient of elasticity, m=50lb=22.68 kg, g=9.8 N/kg, x=4inch=0.1016 m

Of (1) k= mg/x (2)

Of (2) k=2187.64 N/m

The oscillation frequency:

1/f= 2π sqrt(m/k) (3)

Of (3) m= k/4π2f2 (4), where k=2187.64 N/m, f=2 Hz

Of (4) m=13.87 kg

Answer:

13.87 kg or 30.58 lb

mg= kx (1), where k is the coefficient of elasticity, m=50lb=22.68 kg, g=9.8 N/kg, x=4inch=0.1016 m

Of (1) k= mg/x (2)

Of (2) k=2187.64 N/m

The oscillation frequency:

1/f= 2π sqrt(m/k) (3)

Of (3) m= k/4π2f2 (4), where k=2187.64 N/m, f=2 Hz

Of (4) m=13.87 kg

Answer:

13.87 kg or 30.58 lb

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