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
Suppose the magnitude of Nuclear force between two protons varies with the distance between them as shown in figure. Estimate the ratio "Nuclear force/Coulomb force" for
(a) x = 8 fm
(b) x = 4 fm
(c) x = 2 fm
(d) x = 1 fm (1 fm = 10 −15m).
A neutron exerts a force on a proton which is
(a) gravitational
(b) electromagnetic
(c) nuclear
(d) weak
Which of the following systems may be adequately described by classical physics ?
(a) motion of a cricket ball
(b) motion of a dust particle
(c) a hydrogen atom
(d) a neutron changing to a proton.
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.
Two charged particles placed at a separation of 20 cm exert 20 N of Coulomb force on each other. What will be the force of the separation is increased to 25 cm?
The work done by the external forces on a system equals the change in
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the plane. The motion of the particle takes place in a plane. It follows that
(a) its velocity is constant
(b) its acceleration is constant
(c) its kinetic energy is constant
(d) it moves in a circular path.
A box is pushed through 4.0 m across a floor offering 100 N resistance. How much work is done by the resisting force?
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.
Find the average frictional force needed to stop a car weighing 500 kg at a distance of 25 m if the initial speed is 72 km/h.
Find the average force needed to accelerate a car weighing 500 kg from rest to 72 km/h through a distance of 25 m.
A block of mass 2 kg kept at rest on an inclined plane of inclination 37° is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for one second. Find the kinetic energy of the block at the instant the force ceases to act. Take g = 10 m/s2.
A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shows the displacement-time curve for its motion?
A body is being raised to a height h from the surface of earth. What is the sign of work done by gravitational force?
A body is displaced from (0, 0) to (1 m, 1 m) along the path x = y by a force F = (x2`hat"J"` + y`hat"i"`)N. The work done by this force will be:
If a force varies linearly with displacement, the area under the F-s graph forms:
When force varies non-linearly with displacement, what method must be used to find work?
