Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by
`F = -hati+2hatj+3hatkN`
Where `hati,hatj,hatk` are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?
A lawyer alleges in court that the police had forced his client to issue a statement of confession. What kind of force is this ?
A neutron exerts a force on a proton which is
(a) gravitational
(b) electromagnetic
(c) nuclear
(d) weak
Calculate the force with which you attract the earth.
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.
The force with which the earth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation G = 6.67 × 11−11 N−m2/kg2, mass of the moon = 7.36 × 1022 kg, mass of the earth = 6 × 1024 kg and the distance between the earth and the moon = 3.8 × 105 km.
The magnetic force on a charged particle is always perpendicular to its velocity. Can the magnetic force change the velocity of the particles? Speed of the particle?
The work done by all the forces (external and internal) on a system equals the change in ______.
A block of mass m slides down a smooth vertical circular track. During the motion, the block is in
A block of mass 5.0 kg slides down an incline of inclination 30° and length 10 m. Find the work done by the force of gravity.
A block of mass m is kept over another block of mass M and the system rests on a horizontal surface (In the following figure). A constant horizontal force F acting on the lower block produces an acceleration \[\frac{F}{2 \left( m + M \right)}\] in the system, and the two blocks always move together. (a) Find the coefficient of kinetic friction between the bigger block and the horizontal surface. (b) Find the frictional force acting on the smaller block. (c) Find the work done by the force of friction on the smaller block by the bigger block during a displacement d of the system.
A particle of mass m moves on a straight line with its velocity varying with the distance travelled, according to the equation \[\nu = a\sqrt{x}\] , where a is a constant. Find the total work done by all the forces during a displacement from \[x = 0 \text{ to } x - d\] .
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 work done by the force of gravity in that one second if the work done by the applied force is 40 J.
In a children's park, there is a slide which has a total length of 10 m and a height of 8⋅0 m . A vertical ladder is provided to reach the top. A boy weighing 200 N climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the slide is three tenth of his weight. Find (a) the work done by the ladder on the boy as he goes up; (b) the work done by the slide on the boy as he comes down. Neglect any work done by forces inside the body of the boy
A body of mass 0.5 kg travels in a straight line with velocity v = a x3/2 where a = 5 m–1/2s–1. The work done by the net force during its displacement from x = 0 to x = 2 m is ______.
A body is being raised to a height h from the surface of earth. What is the sign of work done by applied force?
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 ______.
If a force varies linearly with displacement, the area under the F-s graph forms:
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 ______.
