Home
Class 11
PHYSICS
A body of mass m hangs by an inextensibl...

A body of mass m hangs by an inextensible string that passes over a smooth mass less pulley that is fitted with a light spring of stiffness k as shown in figure. If the body is released from rest and the spring is released, calculate the maximum elongation of the spring.

Text Solution

Verified by Experts

Let the spring be elongated by x. That means the pulley falls through a distance x.
Consequently the string of the pulley is slackened to the same extent x. Therefore, the total distance moved by the body is `2x`. Since the spring is elongated by x,
`DeltaPE_(spri ng)=1/2kx^2`
As the body falls through a distance `2x`,
`(DeltaPE)_(gr)=-mg(2x)`
Since the body is initially at rest and comes to rest just at the instant of maximum elongation of the spring, `DeltaPE=0`
Applying the principle of conservation of energy, we get
`(DeltaPE)+(DeltaKE)=0`
`impliesDeltaPE_(Spri ng)+DeltaPE_(gr)+DeltaKE=0`
`1/2kx^2-mg(2x)+0=0impliesx=(4mg)/(k)`
Promotional Banner

Topper's Solved these Questions

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Solved Examples|15 Videos

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Exercise 8.1|25 Videos

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise Multiple Correct|5 Videos

Similar Questions

Explore conceptually related problems

A disc of mass m is connected with an ideal spring of stiffness k . If it is released from rest, it rolls without sliding on an inclination plane. The maximum elongation of the spring is:

In an ideal pulley particle system, mass m_2 is connected with a vertical spring of stiffness k . If mass m_2 is released from rest, when the spring is underformed, find the maximum compression of the spring.

A rod mass (M) hinged at (O) is kept in equilibrium with a spring of stiffness (k) as shown in figure. The potential energy stored in the spring is .

A block of mass 2 m hangs by an inextensible light string that passes over a smooth pulley. Another mass m hangs from the other end of the string and is connected to a vertical massless spring. The system is stationary. Just after the string is cut, the accelerations of m and 2m, respectively, are -

Two block of masses m_(1) and m_(2) are in equilibrium. The block m_(2) hangs from a fixed smooth pulley by an inextensible string that is fitted with a light spring of stiffness k as shown in fig. Neglecting friction and mass of the string, find the acceleration of the bodies just after the string S is cut.

The block of mass m is released when the spring was in its natrual length. Spring constant is k. Find the maximum elongation of the spring.

A block of mass m held touching the upper end of a light spring of force constant K as shown in figure. Find the maximum potential energy stored in the spring if the block is released suddenly on the spring.

A system of wedge and block as shown in figure, is released with the spring in its natural length. All surfaces are frictionless. Maximum elongation in the spring will be .