PAG 10.3 Comparison of Methods of Determining Spring Stiffness

Question 1

What equation can be used to determine a spring constant using a static method?

Answer 1

F = kx

Question 2

what equation can be used to determine a spring constant using a dynamic method?

Answer 2

T = 2π√(m/k)

Question 3

How will the timer period of a mass-spring oscillator change if the spring constant is quartered?

Answer 3

Time period will double
T is inversely proportional to the square root of k

Question 4

How can the force applied to a spring by hanging mass be calculated?

Answer 4

F = mg

Question 5

How can the spring constant be determined from a graph of force against extension

Answer 5

Spring constant is given by the gradient of a force-extension graph

Question 6

What should a graph of force against extension look like?

Answer 6

Straight line through the origin

Question 7

How will your results be affected if the load applied exceeds the limit of proportionality?

Answer 7

Hooke’s law only applied up to the limit of proportionality, so beyond this point the gradient will no longer be constant, k cannot be determined

Question 8

Describe how the time period of a simple mass-spring oscillator varies with the length of the spring

Answer 8

Time period of a mass-spring oscillator does not depend on the length of the spring.
It only depends on the mass and the spring constant

Question 9

What should your graph of t squared against mass look like?

Answer 9

Straight line through the origin

Question 10

How could spring constant be calculated from a graph of T squared against m?

Answer 10

‘k’ is given by 4πr^2/ gradient

Question 11

How can the time period of a mass-spring oscillator be measured?

Answer 11

Time for 10 oscillations, Divide by 10

Question 12

What can be added to your apparatus to make measuring time period easier?

Answer 12

Fiducial marker to see when complete oscillation done properly

Question 13

Why may your measured value for the time period not be equal to the true value?

Answer 13

Human react time will cause your stop-clock reading to differ slightly from the true value.
Uncertainty determining exactly when a fully oscillation has been completed

Question 14

How could the uncertainty due to human-reaction time be eliminated?

Answer 14

Electronic timing, manual stop-clock
Light gate or motion sensor

Question 15

Suggest an advantage for using the static method over dynamic?

Answer 15

More accurate measurements due to less uncertainties due to human reaction time

Question 16

What safety precautions should be taken when applying a load to a spring?

Answer 16

Always wear safety goggles in case the spring snaps, the applied load should not exceed the maximum capacity of the spring.
If the spring begins to deform plastically, do not add further load

Question 17

What safety precaution should be taken when hanging a load from a clamp stand?

Answer 17

A counterweight or G clamp should be attached to the base of the clamp stand to provide a counter moment and prevent the stand from toppling.