Procedure
a G-clamp the metre rule securely to the bench using the wooden blocks to protect the rule and bench.
b Sellotape one or more slotted masses near the end of the rule.
c Twang and time several oscillations.
d Adjust the vibrating length (or mass attached) and repeat.
Teaching notes
1 You could use this experiment as a follow-up to the standard "g from a pendulum". There are more variables to play with so you can easily set up differentiated tasks for your students.
2 In this case we can find E for wood because for this cantilever we have ...
ω2 = Exy3 / 4ML3 where
x = width of ruler
y = thickness of ruler (scale to undersurface)
M = mass Sellotaped on
L = vibrating length
E = Young modulus of wood
ω = 2π/T
So T2 v M (or L3) gives you E from the gradient.
3 With a wide range of abilities you can have one group simply verifying it's S.H.M. (by proving T is independent of amplitude), another determining E, and another using log graphs to discover thatT is proportional to L3/2. It's also a good one for error analysis; which term contributes the largest error in E (answers on a postcard)?
The vibrations are quite fast (especially at short lengths). To obtain an accurate result for T, time many oscillations and find the average time for a single oscillation.
4 If you have the materials you can try things other than metre rules.
c Twang and time several oscillations.
d Adjust the vibrating length (or mass attached) and repeat.
Teaching notes
1 You could use this experiment as a follow-up to the standard "g from a pendulum". There are more variables to play with so you can easily set up differentiated tasks for your students.
2 In this case we can find E for wood because for this cantilever we have ...
ω2 = Exy3 / 4ML3 where
x = width of ruler
y = thickness of ruler (scale to undersurface)
M = mass Sellotaped on
L = vibrating length
E = Young modulus of wood
ω = 2π/T
So T2 v M (or L3) gives you E from the gradient.
3 With a wide range of abilities you can have one group simply verifying it's S.H.M. (by proving T is independent of amplitude), another determining E, and another using log graphs to discover thatT is proportional to L3/2. It's also a good one for error analysis; which term contributes the largest error in E (answers on a postcard)?
The vibrations are quite fast (especially at short lengths). To obtain an accurate result for T, time many oscillations and find the average time for a single oscillation.
4 If you have the materials you can try things other than metre rules.
