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Potential Energy

A sphere of m...

Question

A sphere of mass m and radius R rolls without sliding on a horizontal surface. It collides with a light spring of stiffness K with a kinetic energy E. If the surface (AB) under the spring is smooth and E 7J and K 10 N/m, mot find the maximum compression of the spring.

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Solution

$\begin{matrix} s p r i n g p o t e n t i a l E_{s} e n e r g y i s d e f i e n d a s, E_{s} = \frac{1}{2} k x^{2} h e r e k i s t h e s p r i n g c o n s tan t o r s t i f f n e s s c o n s tan t a n d x i s t h e c o m p r e s s i o n o r e l o n g a t i o n . I n e q i l i b r i u m, E_{k} = E_{s} = \frac{1}{2} k x^{2} S o, c o m p r e s s i o n, x = v (2 E_{k} / k) w e g e t, x = v (2 E_{k} / k) = v [2 (7 J) / 10 N / m] = 1.18 m R o u n d i n g u p t o o n e sin g n i f i c a n t f i g u r e, t h e max i m u m c o m p r e s s i o n o f t h e s p r i n g w i l l b e 1 m . \end{matrix}$

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