Home
Class 11
PHYSICS
A block of mass m welded with a light sp...

A block of mass m welded with a light spring of stiffness k is in equilibrium on an smooth inclined plane with angle of inclination `theta`. If a variable external force is applied slowly till the spring comes to its relaxed position, find the work done by spring force.

Text Solution

Verified by Experts

Referring to the FBD as shown in figure, we have four forces (N, mg, `F_(spring)` and `F_(ext)` acting on the particle.

Initially, the block is at equilibrium.
`kx_i=mg sin thetaimpliesx_i=(mgsintheta)/(k)`
When the block is pulled by an external force to bring the spring to relaxed length `x_f=0`
Hence, work done by spring force,
`W_(sp)=-1/2k(x_f^2-x_i^2)`

`=-1/2[0-((mgsintheta)/(k))^2]`
`=1/2((mgsintheta)^2)/(2k)`
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 block of mass m is released from the top of fixed inclined smooth plane. if theta is the angle of inclination then vertical accelertion of block is

A block of mass m fitted with a light spring of stiffness k and natural length l_(0) kept on a smooth radial groove made on a disc rotaing with a constant angular axis . If the block is released slowly . Find the maximum elongation of the spring

A block of mass m attached with a an ideal spring of force constant k is placed on a rough inclined plane having inclination theta with the horizontal and coefficient of friction mu=1//2 tan theta , Initially the block is held stationary with the spring in its relaxed state, find the maximum extension in the spring if the block is released.

A block of mass 5 kg is at rest on a rough inclined surface. If angle of inclination of plane is 60^(@) , then force applied by it on block is

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:

A block of mass m is moving down with constant velocity along an inclined plane of inclination theta . What is the work done by external force in pulling the block along the inclined plane through a height h with constant velocity?

A block of mass m is placed on a smooth inclined plane of inclination theta with the horizontal. The force exerted by the plane on the block has a magnitude

Two blocks of masses m_(1) and m_(2) being connected with a light spring of stiffness k are driven with forces F_(1) and F_(2) on a smooth horizontal plane.

A block of mass m is connected rigidly with a smooth wedge (plank) by a light spring of stiffness k. If the wedge is moved with constant velocity v_0 , find the work done by the external agent till the maximum compression of the spring.

A block of mass m connected to a spring of stiffness k is placed on horizontal smooth surface. When block is at x=0 , spring is in natural length. The block is also subjected to a force F=(k|x|)/(@) then