The 10 -kg sphere C is released from rest when θ=0^∘ and the tension in the spring is 100 N. Det

step 1 So here in this question the potential energy of the system is given by u and that is equals to

The 10 -kg sphere C is released from rest when θ=0^∘ and the...

The 10 -kg sphere $C$ is released from rest when $\theta=0^{\circ}$ and the tension in the spring is 100 N. Determine the speed of the sphere at the instant $\theta=90^{\circ} .$ Neglect the mass of rod $A B$ and the size of the sphere.

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Key Concepts

Work-Energy Principle

The work-energy principle connects the work done by forces on an object with the change in its kinetic energy. It is a central idea in dynamics that allows one to compute the speed of an object by equating the work done by various forces (including gravitational and elastic forces) to the kinetic energy gained.

Elastic Potential Energy

Associated with the deformation of elastic materials such as springs, elastic potential energy is the energy stored when an object is stretched or compressed. It is typically governed by Hooke's Law, which relates the force exerted by a spring to the displacement from its equilibrium position.

Conservation of Mechanical Energy

This principle states that if no non-conservative forces (like friction) perform work, the total mechanical energy (the sum of kinetic and potential energies) of a system remains constant. It is used to relate the initial energy states of a system to the final kinetic energy after energy transformations have occurred.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. In mechanical problems, changes in height result in changes in gravitational potential energy, which are converted to or from kinetic energy as the object moves.

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