Question

Ron weighs a bottle with a mass of 0.5 kilograms on a spring scale. The spring stretches by 1 centimeter. He then weighs a second bottle on the same spring scale. What is the mass of the second bottle, in kg, if the spring stretches by 2 cm

Answer 1

1 kg

Step-by-step explanation:

Applying,

Hook's law,

F = ke................. Equation 1

Where F = force, k = force constant of the spring, e = extension.

But from the question,

The weight of the bottle is the force acting on the spring scale

therefore,

mg = ke............ Equation 2

Where m = mass of the bottle, g = acceleration due to gravity.

make k the subject of the equation

k = mg/e............ Equation 3

Given: m = 0.5 kg, e = 1 cm = 0.01 m

Constant: g = 9.8 m/s²

k = (0.5×9.8)/0.01

k = 490 N/m

If the mass of the second bottle is weighed,

given: e = 2 cm = 0.02 m

subtitute into equation 1

m×9.8 = 490×0.02

9.8m = 9.8

m = 9.8/9.8

m = 1 kg.

Hence the mass of the second bottle is 1 kg