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A sphere of mass m and radius R rolls without sliding on a horizontal surface.It collides with a light spring attached to a wall of stiffness k=10N/m with a kinetic enery E=7J.If the surface AB under spring is smooth,prove that maximum compression of spring is 1m.

A sphere of mass m and radius R rolls without sliding on a horizontal surface.It collides with a light spring attached to a wall of stiffness k=10N/m with a kinetic enery E=7J.If the surface AB under spring is smooth,prove that maximum compression of spring is 1m.

Grade:12

1 Answers

rake
askIITians Faculty 73 Points
7 years ago

Spring potential Es energy is defined as,

Es = ½ kx2

Here k is the spring constant or stiffness constant and x is the compression or elongation.

In equilibrium, EK = Es

kx2

So, compression, x = v[2 EK/k]

Substitute, 7 J for EK and 10 N/m for stiffness constant k in the equation x = v[2 EK/k], we get,

x = v[2 EK/k]

=v[2(7J)/(10 N/m)]

= 1.18 m

Rounding up to one significant figure, the maximum compression of the spring will be 1 m.

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