Work by a Constant Force

A particle moves from position $3\hat{i} + 2\hat{j} - 6\hat{k}$ to $14\hat{i} + 13\hat{j} + 9\hat{k}$ due to uniform force of $(4\hat{i} + \hat{j} + 3\hat{k})$ N. If displacement is in metre then work done will be

A 1 kg block subjected to two simultaneous forces $(2\hat{i} + 3\hat{j} + 4\hat{k})\text{ N}$ and $(3\hat{i} - \hat{j} - 2\hat{k})\text{ N}$ is moved a distance of 25 m along $(3\hat{i} - 4\hat{j})$ direction. The work done in this process is ______ J.

A mass of 1 kg is kept on an inclined plane with $30^\circ$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of $4\text{ m/s}$. The work done by the frictional force in time 2 s is ______ J. (Take $g = 10\text{ m/s}^2$)

A particle is displaced from point $P(3\text{ m}, 4\text{ m}, 5\text{ m})$ to a point $Q(2\text{ m}, 3\text{ m}, 4\text{ m})$ under a constant force $\vec{F} = (3\hat{i} + 4\hat{j} + 5\hat{k})\text{ N}$. The work done by the force in this process is

A force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i} - 2\hat{j} - \hat{k}$. What will be the value of $b$, if work done on the particle is zero.

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle $45^\circ$ with the horizontal. The friction coefficient between the block and the surface is 0.25. The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is:

A force $(3x^2 + 2x - 5)\text{ N}$ displaces a body from $x = 2\text{ m}$ to $x = 4\text{ m}$. Work done by this force is ________ J.

A body of mass $50\text{ kg}$ is lifted to a height of $20\text{ m}$ from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be:

A block of mass $100\text{ kg}$ slides over a distance of $10\text{ m}$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction $(\text{in } J$) is:

A block of mass $1\text{ kg}$ is pushed up a surface inclined to horizontal at an angle of $60^\circ$ by a force of $10\text{ N}$ parallel to the inclined surface as shown in figure. When the block is pushed up by $10\text{ m}$ along inclined surface, the work done against frictional force is:

$\left[g = 10\text{ m/s}^2\right]$

A small particle moves to position $5\hat{i} - 2\hat{j} + \hat{k}$ from its initial position $2\hat{i} + 3\hat{j} - 4\hat{k}$ under the action of force $5\hat{i} + 2\hat{j} + 7\hat{k}\text{ N}$. The value of work done will be __________ J.

Identify the correct statements from the following:

A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.

B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.

C. Work done by friction on a body sliding down an inclined plane is positive.

D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.

E. Work done by the air resistance on an oscillating pendulum is negative.

Choose the correct answer from the options given below:

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____________ kJ. [The coefficient of friction between tyre of bus and road is 0.04.]

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45${}^\circ$ and 60${}^\circ$ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $\frac{1}{\sqrt{x}}$. The value of x is .....................

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g = 9.8 ms${}^{-2}$)

A force $(F) = -5\hat{\mathbf{i}} - 7\hat{\mathbf{j}} + 3\hat{\mathbf{k}}$ acting on a particle causes a displacement $(s) = 3\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + a\hat{\mathbf{k}}$ in its own direction. If the work done is 14 J, then the value of ' $a$ ' is

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time t is -

A particle moves from a point $\left(-2\hat{i} + 5\hat{j}\right)$ to $\left(4\hat{j} + 3\hat{k}\right)$ when a force of $\left(4\hat{i} + 3\hat{j}\right)$ N is applied. How much work has been done by the force?

A uniform force of $\left(3\hat{i} + \hat{j}\right)$ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position $\left(2\hat{i} + \hat{k}\right)$ metre to position $\left(4\hat{i} + 3\hat{j} - \hat{k}\right)$ metre. The work done by the force on the particle is

A particle of mass $100\text{ g}$ is thrown vertically upwards with a speed of $5\text{ m/s}$. The work done by the force of gravity during the time the particle goes up is

300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Work done against friction is (Take g = 10 m/s2)

A force $\vec{F} = \left(5\vec{i} + 3\vec{j} + 2\vec{k}\right)\text{ N}$ is applied over a particle which displaces it from its origin to the point $\vec{r} = \left(2\vec{i} - \vec{j}\right)\text{ m}$ The work done on the particle in joules is

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that

A body moves a distance of $10\text{ m}$ along a straight line under the action of a $5\text{ N}$ force. If the work done is $25\text{ J}$, then angle between the force and direction of motion of the body is

When a body moves with a constant speed along a circle