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“ … Assume the string is inextensible and elastic…”

Published online by Cambridge University Press:  22 September 2016

Tom Roper  and
Ron Hartley
Tom Roper
Affiliation:
Centre for Studies in Science and Mathematics Education, The University, Leeds LS2 9JT and Heckmondwike Grammar School, High Street, Heckmondwike, W. Yorks WF16 0AH
Ron Hartley
Affiliation:
Centre for Studies in Science and Mathematics Education, The University, Leeds LS2 9JT and Heckmondwike Grammar School, High Street, Heckmondwike, W. Yorks WF16 0AH
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Extract

If the above phrase appeared in an A-level paper the Board responsible would receive many protests: “a contradiction in terms”, “impossible”. But is it? Our attention was drawn to this via this A-level problem from the J.M.B.

Three smooth spheres A, B and C, of equal radii and masses m, 2m and am, respectively, lie at rest in a straight line on a smooth horizontal table, with B between A and C. The sphere is connected to A and C by light inelastic strings, which are initially slack. The sphere A is then projected directly away from B with speed u. Find, in terms of a and u, the common velocity of the three spheres when C has been jerked into motion.

Find also in terms of a, m and u, the impulse in each string at the instant when C starts to move. Verify that the ratio of these impulses is independent of a.

(Further Maths, Paper II, 1988)

Type
Research Article
Information
The Mathematical Gazette , Volume 75 , Issue 471 , March 1991 , pp. 15 - 23
Copyright
Copyright © The Mathematical Association 1991

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References

1. Thompson, E.E., “Can an inextensible string be elastic?” Math. Gaz. 70, No. 454 (Dec. 1986).Google Scholar
2. Symge, J.L. and Griffith, B.A., “Principles of Mechanics”, 3rd Edition. McGraw-Hill (1959).Google Scholar
3. Love, A.E.H., “Theoretical Mechanics—An introductory treatise on the principles of Dynamics”. C.U.P. (1897).Google Scholar
4. Humphrey, D., “Intermediate Mechanics-Dynamics”. Longmans (1930).Google Scholar
5. Francis, A.J., Advanced Level Mechanics. G. Bell & Sons Ltd. (1977).Google Scholar