Advertisements
Advertisements
प्रश्न
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 \[x = 0 \text{ to } x - d\] .
Advertisements
उत्तर
Given,
\[\nu = a\sqrt{x} \left( \text{ uniformly accelerated motion } \right)\]
\[\text{ Displacement, s = d - 0 = d }\]
\[\text{ Putting x = 0, we get } \nu_1 = 0\]
\[\text{ Putting x = d, we get } \nu_2 = a\sqrt{d}\]
\[\alpha = \frac{\nu_2^2 - \nu_1^2}{2s} = \frac{a^2 d}{2d} = \frac{a^2}{2}\]
\[\text{ Force, F = m} \alpha = \frac{m a^2}{2}\]
\[\text{ Work done, W = Fs } \cos \theta\]
\[ = \frac{m a^2}{2} \times d = \frac{m a^2 d}{2}\]
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.
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 60 kg man pushes a 40 kg man by a force of 60 N. The 40 kg man has pushed the other man with a force of
In tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. List which of the following works are positive, which are negative and which are zero?
(a) work by the winning team on the losing team
(b) work by the losing team on the winning team
(c) work by the ground on the winning team
(d) work by the ground on the losing team
(e) total external work on the two teams.
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?
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 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.
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.
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. Show that the work done by the applied force does not exceed 40 J.
A uniform chain of length L and mass M overhangs a horizontal table with its two third part on the table. The friction coefficient between the table and the chain is μ . Find the work done by friction during the period the chain slips off the table.
A lawn roller is pulled along a horizontal surface through a distance of 20 m by a rope with a force of 200 N. If the rope makes an angle of 60° with the vertical while pulling, the amount of work done by the pulling force is:
A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is ______.
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 ______.
Work done by gas in cyclic process is ______ J.
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:
What does 'dW' represent in the variable force work calculation?
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 ______.
