Standard +0.3 This is a standard elastic energy problem requiring finding equilibrium extension, then applying energy conservation between two positions. It involves routine application of Hooke's law, equilibrium conditions, and energy principles with straightforward algebra—slightly above average due to the multi-step nature but no novel insight required.
One end of a light elastic string of natural length \(1.6\) m and modulus of elasticity \(28\) N is attached to a fixed point \(O\). The other end of the string is attached to a particle \(P\) of mass \(0.35\) kg which hangs in equilibrium vertically below \(O\). The particle \(P\) is projected vertically upwards from the equilibrium position with speed \(1.8\) m s\(^{-1}\). Calculate the speed of \(P\) at the instant the string first becomes slack. [5]
Question 3:
3 | 28e
= 0.35g
1.6
e = 0.2
0.35v2 0.22 1.82
=28× ×1.6+0.35× −0.35g×0.2
2 2 2
–1
v = 1.11 m s | M1
A1
M1
A1
A1
[5] | Equates λext/l and weight
OP = 1.8 m
EE/KE/PE balance
All correct terms with candidate’s
value of e
One end of a light elastic string of natural length $1.6$ m and modulus of elasticity $28$ N is attached to a fixed point $O$. The other end of the string is attached to a particle $P$ of mass $0.35$ kg which hangs in equilibrium vertically below $O$. The particle $P$ is projected vertically upwards from the equilibrium position with speed $1.8$ m s$^{-1}$. Calculate the speed of $P$ at the instant the string first becomes slack. [5]
\hfill \mbox{\textit{CAIE M2 2014 Q3 [5]}}