Question

A spring scale hung from the ceiling stretches by 5.5cm when a 1.6kg mass is hung from it. The 1.6kg mass is removed and replaced with a 1.9kg mass.

Part A

What is the stretch of the spring?

Answer 1

x2 = x1*m2/m1

= 0.055*1.9/1.6 = 0.0653 m = 6.53 cm

Answer 2

(a) for a spring:

F = kx

F = mg = (1.6)(9.81) = 15.696 N

k = F/x = 15.696/0.05 = 313.92 N/meter
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(b)

delta x = F/k = mg/k = (1.9)(9.81)/313.92 = 0.09 meters

Length of spring = 0.09 + 0.55 = 0.61 meters

Answer 3

by hooke's law, we know that force is directly proportional to the stretch. F= kx

=> the new strech is: 5.5 * (1.9/1.6) cm

=> 6.53125 cm