Advertisements
Advertisements
प्रश्न
A force \[F = \alpha + bx\] acts on a particle in the x-direction, where a and b are constants. Find the work done by this force during a displacement from x = 0 to x = d.
Advertisements
उत्तर
Given that force is a function of displacement, i.e.
So, work done by this force during the displacement x = 0 to x = d,
\[W = \int\limits_0^d \left( a + bx \right) dx\]
\[W = \left[ ax + \frac{b x^2}{2} \right]_0^d \]
\[W = ad + \frac{b d^2}{2}\]
\[ \Rightarrow W = \left( a + \frac{bd}{2} \right)d\]
APPEARS IN
संबंधित प्रश्न
State if the following statement is true or false. Give a reason for your answer.
Work done in the motion of a body over a closed loop is zero for every force in nature.
Is it true that the reaction of a gravitational force is always gravitational, of an electromagnetic force is always electromagnetic and so on?
When Neils Bohr shook hand with Werner Heisenberg, what kind of force they exerted ?
Mark the correct statements :
(a) The nuclear force between two protons is always greater than the electromagnetic force between them.
(b) The electromagnetic force between two protons is always greater than the gravitational force between them.
(c) The gravitational force between two protons may be greater than the nuclear force between them.
(d) Electromagnetic force between two protons may be greater than the nuclear force acting between them.
If all matters were made of electrically neutral particles such as neutrons,
(a) there would be no force of friction
(b) there would be no tension in the string
(c) it would not be possible to sit on a chair
(d) the earth could not move around the sun.
A monkey is sitting on a tree limb. The limb exerts a normal force of 48 N and a frictional force of 20 N. Find the magnitude of the total force exerted by the limb on the monkey.
A body builder exerts a force of 150 N against a bullworker and compresses it by 20 cm. Calculate the spring constant of the spring in the bullworker.
Find the ratio of the magnitude of the electric force to the gravitational force acting between two protons.
The work done by all the forces (external and internal) on a system equals the change in ______.
A constant force of 2⋅5 N accelerates a stationary particle of mass 15 g through a displacement of 2⋅5 m. Find the work done and the average power delivered.
A particle moves from a point \[\overrightarrow{r}_1 = \left( 2 m \right) \overrightarrow{ i } + \left( 3 m \right) \overrightarrow{ j } \] to another point
\[\overrightarrow{r}_2 = \left( 3 m \right) \overrightarrow{ i } + \left( 2 m \right) \overrightarrow{ j } \] acts on it. Find the work done by the force on the particle during the displacement.
A man moves on a straight horizontal road with a block of mass 2 kg in his hand. If he covers a distance of 40 m with an acceleration of 0⋅5 m/s2, find the work done by the man on the block during the motion.
A box weighing 2000 N is to be slowly slid through 20 m on a straight track with friction coefficient 0⋅2 with the box. (a) Find the work done by the person pulling the box with a chain at an angle θ with the horizontal. (b) Find the work when the person has chosen a value of θ, which ensures him the minimum magnitude of the force.
A block of weight 100 N is slowly moved up a smooth incline of inclination 37° by a person. Calculate the work done by the person in moving the block through a distance of 2 m, if the driving force is (a) parallel to the incline and (b) in the horizontal direction.
A uniform chain of mass m and length l overhangs a table with its two third part on the table. Find the work to be done by a person to put the hanging part back on the table.
A block of mass m is taken from A to B slowly under the action of a constant force R Work done by this force is ______.
A particle of mass 'm' and charge 'q' is placed at rest in uniform electric field E and then released. The momentum gained by the particle after moving a distance 'y' is \[\sqrt{2x}.\] Then x is equal to ______.
