25 Apr, 2012
In a ball
PRESENTATION: A heavy ball is suspended from two identical strings. If the lower string is pulled slowly the upper string eventually breaks, but if it is pulled suddenly it is the lower string that is broken.
- Moment of Inertia of a Ping-Pong Ball, Xian-Sheng CaoPhys. Teach. 50, 292 (2012)
- Inertia in Action, Diane Riendeau, Phys. Teach. 49, 186 (2011)
- The inertia ball, Karen Bouffard, Phys. Teach. 39, 46 (2001)
INTRODUCTION: Inertia is defined in Physics as the opposition of any body to the variation of its state of movement. It is the case in particular of the resistance of a standing body to move, or the resistance of any moving body to change the speed or direction of its movement.
Inertia is common to all matter. The first observations were done by Descartes and Galileo, and Newton denoted it within its book “Philosophiae Naturalist Principia Matematica” as the First law of Movement, the Inertia law.
OBJECTIVE: To demonstrate the first Newton Law, or Inertia law.
MATERIALS: a wooden sphere with hooks fixed on two diametrically opposed points, string, a stand, a bar to pull the string (optional), soft tissue (towels).
SETUP: Suspend the mass from the stand using a string tied to one of the hooks, and tie two other strings to the lower hook. If we pull with a fast movement, one of them this lower string will break due to the inertia of the ball. If we pull slowly the second string tied to the lower hook the upper string will break now, due to the effect of the ball weight.
EXPLANATION: The constant of proportionality between mass and force is denoted as mass, which corresponds to the numerical value of inertia. The higher the inertia of a body the lower will be the acceleration it acquires under the effect of a certain force. As the mass of the ball is much larger than those of the strings, and as for the upper string to be broken the mass has to move, if we pull suddenly the lower string the inertia of the ball will cause it not to move and the lower string will be broken. If we apply the same force but now gradually the ball will move, now transmitting the lower string tension to the upper one, which added to the ball weight will produce the upper string to break first.
Newton’s second law can be used to formalize the phenomenon. If the upper and lower string tensions are denoted as Tupper and Tlower respectively, and as Tlower has the same direction that the weight:
-Tupper+Tlower+m.g=m.a; -Tupper+Tlower=m.a- m.g
If the force is applied slowly, the acceleration ‘a‘ is lower than ‘g’, so Tupper>Tlower and the upper string is broken first. If the force is applied very fast ‘a‘ is bigger than ‘g‘ so Tlower>Tupper and the lower string is broken.
CONCEPTS: Newton’s first law, mass, weight, inertia.
- Tipler P.A. Física. Barcelona: Reverté, 2010.
- De Juana J.M., Física General, Pearson, 2009.
- Serway R.A y J.W.Jewett. Física, Thomson-Paraninfo, 2010.
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