A particle moves along x-axis from \(x=0\) to \(x=4\) under the action of force given by \(F=\left(5-7x+4x^{2}\right)N\). What will be the work done in this process?
Ans: \(W=49.3J\).
A body moves from point A and point B under the action of a force. Force F is in Newton and distance x is in metre. Calculate: the work done?
Ans: \(W_{AB}=23J\).
A force \(F=p+qx\) acts on a particle in the x-axis, where p and q are constants. What will be the work done by this force during the displacement from \(x=0\) to \(x=d\).
Ans: \(W=\left[p+\frac{qd}{2}\right]d\).
The variation of force acting on a body with the displacement of body is shown in below diagram; Calculate: the work done by the force in the interval (i) \(0\le x \le 2m\) and (ii) \(2m\le x \le 4m\).
Ans:(i) \(2J\) and (ii) \(-4J\).
Calculate: the work done in moving the object from \(x=2m\) to \(x=3m\) from following graph.
Ans: \(25J\).
A women pushes a trunk on a railway platform which has rough surface. She applies a force of \(100N\) over a distance \(10m\). Then after she get progressively tired and her applied force reduces linearly with distance to \(50N\). The total distance through which trunk has moved is \(20m\). Plot the force applied by the women and the frictional force is \(50N\).Calculate: the work done by the two forces over the distance of \(2m\) .
Ans: \(W_{1}=1750J\) and \(W_{2}=-1000J\).
A force \(\vec{F}=2x\hat{j} N\) acts in a region where a particle moves anticlockwise in square loop of \(2m\) in X-Y plane. Calculate: the total amount of work done?
Ans: \(8J\).
The force-displacement graph is as shown below; Here: the force F is in Newton and distance x is in metre. Calculate: the work done by the force.
Ans: \(W=-20J\).
The relation between the displacement x and the time t for a body of mass \(2kg\) moving under the action of force is given by \(x=\frac{t^{3}}{3}\). Where; x is in metre and t is in seconds. Calculate: the work done by the body in first \(3sec\).
Ans: \(W=81J\).
A body moves from point A to point B under the action of force, varying in magnitude as shown in below figure. Obtain the work done. Force is expressed in newtons and displacement in metre.
Ans: \(W=22.5J\).
The displacement x of a particle, moving in one dimension under the action of a constant force is related to the time by the equation \(t=\sqrt{x}+3\), where x is in metre and t is in seconds. Then Calculate: (i) Displacement of Particle when its velocity is Zero.? and (ii) Work done in first Six Seconds?
