A metallic bob X of mass m is released from position A. It collides elastically with another identical bob Y placed at rest at position B on a horizontal frictionless table. The angle AOB is 30°. How high does the bob X rise immediately after the
Given:
A metallic bob X of mass m is released from position A. It collides
elastically with another identical bob Y placed at rest at position B. The
angle AOB is 30°.
Concept Used:
In an elastic collision between two identical masses, the moving mass
comes to rest, and the mass at rest starts moving with the velocity of the
first mass.
Formula Used:
Conservation of energy and conservation of momentum principles are
used. The height reached by the bob after the initial potential energy can
determine the collision.
Calculation
⇒ Initial potential energy of bob X at A:
⇒ PEA = mgh
⇒ h = L(1 - cos(θ)),
Where L is the length of the pendulum and θ is the angle.
⇒ h = L(1 - cos(30°))
⇒ h = L(1 - √3/2)
Since the collision is elastic and bobs are identical, bob Y will rise to the
same height on the other side. Hence,
The height reached by bob Y (initially bob X) = h = L(1 - √3/2)
∴ Bob X rises immediately after the collision to the same height as that of position A on the other side in the same trajectory.
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