MULUNGUSHI UNIVERSITY
PHY 102 Tutorial sheet 1
1. (a) A spring that obeys Hook’s law has a spring constant k. Show that the energy stored E stored
in the spring when it has been extended elastically by an amount x is given by
1
W = kx2
2
(b) A light spring of unextended length of 14.2 cm is suspended vertically from a fixed point as
illustrated below. A mass of weight 3.8 N is hung from the of the spring as shown above. The
length of the spring is now 16.3 cm.
An additional force F then extends the spring so that its length becomes 17.8cm.
i. Show that the spring constant of the spring is 1.8 Nm−1 .
ii. For the extension of the spring from a length of 16.3cm to a length of 17.8 cm,
* Calculate the change in the gravitation Potential energy of the mass on the spring.
* Show that the change in elastic Potential Energy of the spring is 0.077 J.
* Determine the work done by the force F.
2. (a) The variation with extension x of the force F for a spring A is shown in fig 9.10. The point L on
the graph is the elastic limit of the spring.
iii. Describe the meaning of elastic limit
iv. Calculate the spring constant kA for the spring A.
v. Calculate the work done in extending the spring with a force of 6.4 N
(b) A second spring B of spring constant 2kA is now joined to spring A as shown on fig 9.11. A force
of 6.4 N extends the combination of the springs for the combination of the springs, calculate,
i the total extension
ii the spring constant
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3. A wire of length 1.70 m hungs vertically from a fixed point, as shown in fig 9.9. The wire has
a cross section area 5.74 × 10−8 m2 and is made of a material that has a young modulus of 1.60
×1011 Pa. A load of 25 N is hung from the wire,
i Calculate the extension of the wire
ii The same load is hung from a second wire of the same material. This wire is twice the length
but the same volume as the first wire. State and explain how the extension of the second wire
compares with that of the first.
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