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A measure of inelasticity in a head-on collision of two
Chapter 1, Problem 37P(choose chapter or problem)
(II) A measure of inelasticity in a head-on collision of two objects is the coefficient of restitution, e, defined as
\(e=\frac{v_{\mathrm{A}}^{\prime}-v_{\mathrm{B}}^{\prime}}{v_{\mathrm{B}}-v_{\mathrm{A}}}\),
where \(v_{\mathrm{A}}^{\prime}-v_{\mathrm{B}}^{\prime}\) is the relative velocity of the two objects after the collision and \(v_{\mathrm{B}}-v_{\mathrm{A}}\) is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7-36. Determine a formula for e in terms of the original height h and the maximum height \(h^{\prime}\) reached after one collision.
Questions & Answers
QUESTION:
(II) A measure of inelasticity in a head-on collision of two objects is the coefficient of restitution, e, defined as
\(e=\frac{v_{\mathrm{A}}^{\prime}-v_{\mathrm{B}}^{\prime}}{v_{\mathrm{B}}-v_{\mathrm{A}}}\),
where \(v_{\mathrm{A}}^{\prime}-v_{\mathrm{B}}^{\prime}\) is the relative velocity of the two objects after the collision and \(v_{\mathrm{B}}-v_{\mathrm{A}}\) is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7-36. Determine a formula for e in terms of the original height h and the maximum height \(h^{\prime}\) reached after one collision.
ANSWER:
Step 1 of 7
Given,
A measure of inelasticity in a head-on collision of two objects is the coefficient of restitution, 
where 
Let 
