Moderate -0.5 This is a straightforward dimensional analysis question requiring students to rearrange E = kx²/2 to find [k] = [E]/[x²] = ML²T⁻²/L² = MT⁻². It's routine application of a standard technique with clear steps, making it slightly easier than average, though the mechanics context and need to recall energy dimensions prevents it from being trivial.
A formula for the elastic potential energy, \(E\), stored in a stretched spring is given by
$$E = \frac{kx^2}{2}$$
where \(x\) is the extension of the spring and \(k\) is a constant.
Use dimensional analysis to find the dimensions of \(k\).
[3 marks]
Question 3:
3 | Recalls the correct dimensions for
energy | 1.2 | B1 | [ E ]= ML2T−2
[ k ] (L)2 = ML2T−2
[ k ]= MT−2
Forms an equation to find the
dimensions of k using their
expression for energy and L for the
extension of the spring – the L
does not need to be squared
Their expression must contain M,
L and T
Condone use of units for this mark
only | 1.1a | M1
Completes a rigorous argument
using correct dimensions for
energy, the extension of the spring
and the dimensionless constant to
MT−2for
obtain the dimensions of
k | 2.1 | R1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
A formula for the elastic potential energy, $E$, stored in a stretched spring is given by
$$E = \frac{kx^2}{2}$$
where $x$ is the extension of the spring and $k$ is a constant.
Use dimensional analysis to find the dimensions of $k$.
[3 marks]
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2019 Q3 [3]}}