Potential Energy

Differentiate between stable, unstable and neutral equilibrium.

A satellite is moving in a circular orbit around the earth. The total energy of the satellite is$E=-2\times {10}^5 \mathrm{J}$. The amount of energy to be imparted to the satellite to transfer it to a circular orbit where its potential energy is $U=-1\times {10}^5 \mathrm{J}$ is equal to _____$\times {10}^6 \mathrm{J}$

What is potential energy?

A ball of mass $0.1 \mathrm{kg}$ is thrown vertically upwards with a velocity of $20 \mathrm{m}/\mathrm{s}$. What is the potential energy at the maximum height? What is the potential energy of the ball when it reaches three-quarters of the maximum height while moving upwards?

The potential energy of a particle as function of position $x$ is given by$U=(x²-4x+2) \mathrm{J}$, where$x$ is in metre. The equilibrium position of the particle will be

A body of mass $1 \mathrm{kg}$ is suspended from massless spring of natural length $1 \mathrm{m}$. If mass is released from rest, spring can stretch up to a vertical distance of $40 \mathrm{cm}$, the potential energy stored in the spring at this extension is ($g= 10 \mathrm{m}/{\mathrm{s}}^2$)

Potential energy is defined for a system whose elements interact via conservative force. A hypothetical system has potential energy corresponding to a conservative force given as $U= 7x^{2}y-2x$. Find the force on the system corresponding to the above energy function.

When a spring is stretched by $2 \mathrm{cm}$, the energy stored is $100 \mathrm{J}$. If it is stretched further by $2 \mathrm{cm}$, its energy increases by _____.

A uniform body of length $6 \mathrm{m}$ is carried by a father and a son by keeping the ends on their shoulders. If the son carries only one fourth the load carried by the father, find the position of the centre of gravity.

A uniform meter scale has a mass of $100 \mathrm{gm}$. Masses of $250 \mathrm{gm}$ and $300 \mathrm{gm}$ are suspended from its end. At what points must the rod be supported so that it may remain horizontally in equilibrium.

Chemical, gravitational and nuclear energies are nothing but potential energies for different types of forces in nature. Explain this statement clearly with examples.

A mass of $200 \mathrm{gm}$ is placed at one end of a uniform metre scale. The scale balances in a knife edge at a point $15 \mathrm{cm}$ from the end. Find the weight of the metre scale.

A uniform plank $2 \mathrm{m}$ long weighing $1 \mathrm{kg}$ rests symmetrically as two knife edges one metre apart from each other. If a mass of $2 \mathrm{kg}$ be hung at one end of the plank and a mass of $3 \mathrm{kg}$ at the other end, find the reactions on the knife edges.

What is the potential energy of a body in space?

What is the potential energy of a mass kept at the centre of the earth?

Define potential energy. Give examples.

Write down the relation connecting potential energy and force.

A particle of mass $40 \mathrm{gm}$ slides along a track with elevated ends and a flat horizontal bottom. At the bottom where the horizontal portion begins a spring is kept. When the particle falls from the height slides and reaches it gets compressed by $19.6 \mathrm{cm}$. What is the spring constant of the spring? Assume that the track and the flat horizontal portion are frictionless.

A metre scale weighing $90 \mathrm{gm}$ is fixed at one end is hung in the vertical plane. If the free end is displaced by $30°$ from the vertical, calculate the work done.

A $4 \mathrm{kg}$ mass falls from a height of $6 \mathrm{m}$ and rebound, to a height a $4 \mathrm{m}$. Calculate the loss of energy due to impact.