Question 7
A rubber band is
stretched and then relaxed to its original length. The diagram shows the force-extension
graph for this process.
As the force is
increased, the curve follows the path OPQ to extension e.
As the force is reduced, the curve follows the path QRO to return to zero
extension.
The area labelled X is
between the curves OPQ and QRO. The area labelled Y is bounded by the curve QRO
and the horizontal axis.
Which statement about
the process is correct?
A Area
X is the energy which heats the band as it is stretched to extension e.
B (Area
X + area Y) is the minimum energy required to stretch the band to extension e.
C Area
X is the elastic potential energy stored in the band when it is stretched to
extension e.
D (Area Y – area X) is the net work done on the
band during the process.
Reference: Past Exam Paper – November 2011 Paper 11 Q24 & P13 Q22 &
June 2017 Paper 12 Q21
Solution:
Answer:
B.
The work done in
stretching the rubber band along the path OPQ is the area under the curve OPQ
for loading. This corresponds to (area X + area Y). [B is correct]
Area X between the
stretching (OPQ) the contraction (QRO) curves represents the amount of thermal
energy (heat) dissipated (lost) in the rubber.
Area Y represents the recoverable elastic potential energy stored at maximum extension.
if X is thermal energy then why is option A incorrect?
ReplyDeleteA tells us that X is the total energy while X is actually the thermal energy lost
DeleteBut option A says that X heats the band, isn't that referring to the thermal energy that is lost to the rubber, instead of the total energy?
DeleteAs the rubber is stretched, energy is stored as elastic PE. It is ONLY when the rubber is allow to contract (the force is reduced), that heat is dissipated. So, during stretching, the energy is in the form of elastic PE.
Delete