Work, Energy, and Power

Work done is a product of force and displacement. In the context of the work-energy theorem, if work is done against a frictional force, the kinetic energy:

A constant force $F$ is applied to a body of mass $m$ initially at rest. The plot of kinetic energy versus displacement $x$ is a:

A particle of mass $m$ is accelerated from rest to speed $v$ by a force $F$ over distance $d$. If the same force $F$ acts on mass $2m$ over the same distance $d$, the final kinetic energy of the second mass will be:

When we apply the Work-Energy Theorem to a system, the work done by internal forces:

A block of mass $m$ is pulled along a smooth horizontal surface by a constant force $F$ inclined at an angle $\theta$ to the horizontal. The work done by the normal reaction force after a displacement $s$ is:

A particle of mass $m$ is moving in a potential field $U = 0.5 kx^2$. If its total energy is $E$, then its kinetic energy at position $x$ is:

A car of mass $1000\text{ kg}$ is moving at $20\text{ m/s}$. When brakes are applied, it stops in $10\text{ m}$. The work done by the braking force is:

The potential energy of a $1 \text{ kg}$ particle free to move along the x-axis is given by $V(x) = (x^4/4 - x^2/2) \text{ J}$. If the total mechanical energy of the particle is $2 \text{ J}$, then the maximum speed (in $\text{m/s}$) it can attain is:

A particle of mass $m$ is projected with velocity $v_0$ from the origin along the x-axis. A resistive force $f = -mv^2$ acts on it. The distance at which its kinetic energy reduces to $1/e$ of its initial value is:

A block of mass $m$ is attached to a spring of constant $k$ and is resting on a smooth horizontal table. The block is pushed by a constant force $F$. The maximum kinetic energy of the block will be:

What is the relation between kinetic energy ($K$) and linear momentum ($p$) for a body of mass $m$?

The work done by the restoring force when a spring is stretched is:

If the kinetic energy of an object is zero, its linear momentum is:

Which form of energy is possessed by water stored in a dam?

Two bodies of masses $m_1$ and $m_2$ have equal momentum. The ratio of their kinetic energies is:

A motor-boat is moving at a constant velocity of $20 \text{ m/s}$. If the resistance of water to the motion of the boat is $600 \text{ N}$, the power of the engine is:

A body of mass $m$ is falling freely under gravity. The rate of change of its kinetic energy is proportional to:

A machine delivers power to a body which is proportional to velocity $v$. If $P = kv$, what is the relationship between displacement $s$ and time $t$ starting from rest?

A force $\vec{F} = (2 + x) \hat{i}$ acts on a particle. Find the change in kinetic energy as it moves from $x = 2 \text{ m}$ to $x = 4 \text{ m}$.

A water drop of radius $1 \text{ mm}$ falls from a height of $500 \text{ m}$ above the ground. It hits the ground with a speed of $10 \text{ m/s}$. Which of the following is the work done by the resistive force of air? ($g = 10 \text{ m/s}^2$)

Which of the following is true for a body performing vertical circular motion at the top-most point?

When a compressed spring is released, its potential energy is converted into:

The law of conservation of mechanical energy is a specific case of:

A ball is thrown upwards with a kinetic energy $E$. At the highest point, its potential energy is:

A small block of mass $m$ slides without friction along a track. The block is released from rest at point A, which is at a height of $5R$. It then slides down to ground level at point B (height $0$) and continues up to point C, which is at a height of $2R$. What is the ratio of the block's speed at point B to its speed at point C?

The relationship between the conservative force $F(x)$ and the potential energy $U(x)$ is given by which of the following expressions?

A girl of mass $40 \text{ kg}$ climbs a staircase of 20 steps, each $15 \text{ cm}$ high, in $10 \text{ s}$. The work done by her against gravity is (Take $g = 10 \text{ m/s}^2$):

A unit mass particle moves along the x-axis under a force such that its potential energy $U(x) = (x^4/4 - x^2/2)$. The minimum total energy required for the particle to escape to infinity from the origin is:

A block of mass $M$ is hanging from a vertical spring. The spring is stretched by $y_0$ in equilibrium. If the block is pulled down by $y$ and released, the maximum kinetic energy is:

A particle of mass $m$ is attached to a string of length $L$ and given a horizontal velocity $v_0 = \sqrt{3gL}$ at the bottom. The tension in the string when the string is horizontal is:

Which of the following remains constant in an isolated system during an inelastic collision?

If the kinetic energy of a system increases after a collision (like an explosion), it is sometimes called a ____________ collision.

During a collision, the internal forces are usually ____________ the external forces.

When a ball hits the ground and does not bounce back at all, it is called:

If two bodies of masses $m_1$ and $m_2$ have the same kinetic energy, the ratio of their momenta $p_1/p_2$ is:

An object of mass $m$ strikes a stationary object of mass $2m$ elastically. The fraction of kinetic energy retained by the striking object is:

A ball of mass $M$ moving with velocity $v$ collides with a stationary ball of mass $M$. If the collision is inelastic with $e = 0.5$, the ratio of final velocities is:

A ball is dropped from a height $h$ on a floor. The time it takes to reach the floor is $t_0$. What is the total time before it stops bouncing if $e$ is the coefficient of restitution?

The coefficient of restitution $e$ for a collision is the ratio of:

A shell of mass $200$ g is fired with a velocity of $80$ m/s from a gun of mass $100$ kg. What is the recoil velocity of the gun?

A force $F$ is applied to a spring. If the $F-x$ graph is a straight line through the origin, the work done in stretching the spring is equal to the area of the:

In the expression $W = \int_{x_i}^{x_f} F(x) dx$, $x_i$ and $x_f$ are called:

What is the work done by a force $F = 2$ N in moving an object from $x=0$ to $x=3$ m if the force is constant?

The relation between work $W$ and force $F$ for a small displacement $dx$ is:

A particle moves along the x-axis from $x = 0$ to $x = 4$ m. The force acting on it is $F = (3x^2 + 1)$ N for the interval $0 \le x \le 2$ m, and the force remains constant at $13$ N for the interval $2 \le x \le 4$ m. Calculate the total work done by this force during the entire displacement from $x = 0$ to $x = 4$ m.

If a force $F = 2x + 1$ acts on a body, what is the work done in the displacement from $x=1$ to $x=3$ m?

Work done by a force $F = x^3$ for displacement from $x=0$ to $x=2$ is:

A force $F = k/x^2$ (for $x>0$) acts on a particle. If the work done in moving the particle from $x=10$ to $x=20$ is $W$, then the work done from $x=20$ to $x=40$ is:

A force $\vec{F} = (y \hat{i} - x \hat{j})$ is non-conservative. Find the work done along the square path $(0,0) \to (a,0) \to (a,a) \to (0,a) \to (0,0)$.

A particle moves along $x$-axis from $x=0$ to $x=2$ under $F = 6x$. The work done is:

Potential energy of a spring is a type of _______ energy.

If a force of $10 N$ stretches a spring by $0.1 m$, what is the spring constant $k$?

The potential energy of a spring is zero when the spring is in its:

The spring constant for a parallel combination of two identical springs (each of constant $k$) is:

Three identical springs, each of force constant $k$, are connected in series to form System 1 and in parallel to form System 2. If both systems are stretched by the same total extension $x$ from their respective equilibrium positions, what is the ratio of the elastic potential energy stored in System 1 to that stored in System 2?

When a mass attached to a spring oscillates, at which point is the potential energy maximum?

A spring is stretched by $x$. If the potential energy is $U$, what is the force $F$ at that point?

Two springs with constants $k$ and $2k$ are connected in series. The potential energy stored in the first spring is $U$. The total potential energy of the system is:

A spring of length $L$ and constant $k$ is stretched to length $1.1L$. The work done is $W$. If it is then stretched to $1.2L$, the total work done from $L$ is:

A spring with constant $k$ is cut into $3$ pieces with lengths in ratio $1:1:2$. The $k$ of the longest piece is:

A particle moves with a velocity $v = 5\ m/s$ under a force $F = 20\ N$. If they are in the same direction, power is:

If work is done at a constant rate, the graph of Work vs Time is a:

The power of a machine is $2\ kW$. This means it can do:

Power can be calculated as the product of force and:

A block of mass $m$ is being pulled by a constant power $P$ on a frictionless surface. If it starts from rest, its acceleration $a$ at time $t$ is:

A constant power $P$ is applied to a car of mass $m$. The velocity of the car increases from $u$ to $v$. The time taken is:

The power of a pump which can pump $200 \text{ kg}$ of water to a height of $50 \text{ m}$ in $10 \text{ seconds}$ is ($g = 10 \text{ m/s}^2$):

A $1\text{ HP}$ motor can lift a certain weight to a certain height in $20\text{ minutes}$. To lift the same weight to the same height in $5\text{ minutes}$, the required power of the motor should be:

An object of mass $m$ is being pushed up an incline of angle $\phi$ with a constant velocity $v$. The coefficient of friction is $\mu$. The power required is:

The instantaneous power $P$ of a body is given by $P = 3t^2 - 2t + 1$. The change in kinetic energy of the body between $t = 2\text{ s}$ and $t = 4\text{ s}$ is: