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On a frictionless, horizontal air track, a glider
Chapter 14, Problem 17E(choose chapter or problem)
On a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.50 N/cm. The graph in ?Fig. E14.19 shows the acceleration of the glider as a function of time. Find (a) the mass of the glider; (b) the maximum displacement of the glider from the equilibrium point; (c) the maximum force the spring exerts on the glider.
Questions & Answers
QUESTION:
On a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.50 N/cm. The graph in ?Fig. E14.19 shows the acceleration of the glider as a function of time. Find (a) the mass of the glider; (b) the maximum displacement of the glider from the equilibrium point; (c) the maximum force the spring exerts on the glider.
ANSWER:Step 1 of 3
The time period of oscillation of \(\mathrm{SHM}\) is given by \(T=2 \pi \sqrt{\frac{m}{k}} \ldots .(1)\), where \(m\) is the mass of the object and \(k\) is spring constant.
Now, if we have a look at the given figure, the time period of one complete oscillation is \(T=0.30 s-0.10 s=0.20 s\)
We are given, \(k=2.50 \mathrm{~N} / \mathrm{cm}=250 \mathrm{~N} / \mathrm{m}\)