Work Energy Theorem

A satellite of mass $m$, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is

A $3 kg$ object has initial velocity $\left(6\widehat{\mathrm{i}}-2\widehat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ The total work done $\left(\mathrm{in} \mathrm{J}\right)$ on the object if its velocity changes to $(8\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$ is

An ideal massless spring $\mathrm{S}$ can be compressed $1.0 \mathrm{m}$ in equilibrium by a force of $100 \mathrm{N}$. This same spring is placed at the bottom of a friction less inclined plane which makes an angle $\mathrm{\theta } = 30°$ with the horizontal. A $10 \mathrm{kg}$ mass $\mathrm{m}$ is released from the rest at the top of the inclined plane and is brought to rest momentarily after compressing the spring by $2.0 \mathrm{m}$. What will be the distance through which the mass moved before coming to rest ?

A variable force acts on body of mass $1 \mathrm{kg}$ and it changes the velocity of the body from $2 \mathrm{m}/\mathrm{s}$ to $6 \mathrm{m}/\mathrm{s}$. Find the work done (in $\mathrm{joule}$) on the body by the variable force.

What is work-energy theorem?

Work energy theorem is applicable for conservative forces only.

A body of mass $0.5 \mathrm{kg}$ travels in a straight line with velocity $v=x^{1/2}$. What is the work done by the net force during its displacement from $x=0$ to $x=2 \mathrm{m}$?

Three identical solid spheres move down through three inclined planes $A, B and C$ all same dimensions, $A$ is without friction, $B$ is undergoing pure rolling and $C$ is rolling with slipping. Compare the kinetic energies $E_A, E_B and E_C$ at the bottom.

A body of mass $2 \mathrm{kg}$ thrown vertically upward from the ground with a velocity of $8 \mathrm{m} {\mathrm{s}}^{-1}$ reaches a maximum height of $3 \mathrm{m}$. Magnitude of work done by the air resistance is (Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A car of mass $2000 \mathrm{kg}$ is moving at a speed of $20 {\mathrm{ms}}^{-1}$ up an inclined plane making an angle $30°$ with the horizontal. At some point, the motor stops, and the car continues to move along the plane due to its initial velocity. If it is just able to reach the destination which is at a height of $10 \mathrm{m}$ above the point, calculate the work done against friction acting between the tyres of the car and the plane. (Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

An object of mass $8 \mathrm{kg}$ moves along positive $X-$axis. When it passes through $X=0,$ a constant force directed along the negative $X-$axis begins to act on it. The kinetic energy of the object is found to be $0$ and $30 \mathrm{J}$ for $X=5 \mathrm{m}$ and $X=0 \mathrm{m}$ respectively. If the force continues to act further, then the object moves back along negative $X-$axis. The speed of the object when it reaches $X=-3 \mathrm{m}$

An ideal massless spring $\mathrm{S}$ can be compressed $1.0 \mathrm{m}$ in equilibrium by a force of $100 \mathrm{N}$. This same spring is placed at the bottom of a friction less inclined plane which makes an angle $\mathrm{\theta } = 30°$ with the horizontal. A $10 \mathrm{kg}$ mass $\mathrm{m}$ is released from the rest at the top of the inclined plane and is brought to rest momentarily after compressing the spring by $2.0 \mathrm{m}$. What will be the distance through which the mass moved before coming to rest ?

What minimum horizontal velocity has to be imparted the ball suspended from a thread of length $l$ for it to reach the height of the suspension?

What is the critical speed of block of mass $m$tied to one end of a string which is whirled round in a vertical circle of a radius $R$ at the top of the circle?

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because

A body of mass $3 \mathrm{kg}$ is put under a forces which in turn causes a displacement in it is given by $S=\frac{t^3}{3}$ $\left(\mathrm{in} \mathrm{m}\right).$What will be the work done by the force in first $2 \mathrm{s}$ ?

A particle of mass$m = 1 \mathrm{kg}$ lying on$x$-axis experiences a force given by law, $F=x(3x-2) \mathrm{N}$. Where, $x$ is the coordinate of the particle in $\mathrm{meters}$.

A two-dimensional force field $\overrightarrow{\mathrm{F}}=(3x^2 \hat{\mathrm{i}}+4\mathrm{ }\hat{\mathrm{j}})$ acts on a particle where force is in newton and $x$ is in meter. The particle moves from the coordinates $\left(\mathrm{2,} 3\right)$to $(3, 0)$. Calculate the kinetic energy change during this process. (The coordinates are in meter.)

The system have initial configuration as given in the figure



Now, The bob is released and the string starts wrapping around the pulley. (The pulley is held in place by a force applied at the centre.Given that, string and the pulley are light.)



What is the tension in the string as a function of $\theta$ ?

If a solid cylinder of mass $3\mathit{ }\mathrm{kg}$ is rolling on a horizontal surface with a velocity of $4\mathit{ }\mathrm{m} {\mathrm{s}}^{-1}$. It collides with a horizontal spring of spring constant $200\mathit{ }\mathrm{N} {\mathrm{m}}^{-1}$. What will be the maximum compression produced in the spring?