A box of mass M is at rest on a horizontal surface. A boy of mass `m (lt M)` wants to push the box by applying a horizontal force on it. The boy knows that he will not be able to push the box as the coefficient of friction `mu` between his shoes and ground is almost equal to that between the box and the ground. He decides to run, acquire a speed u and then bang into the box. After hitting the box, the boy keeps pushing as hard as possible. What is the maximum distance through which the box can be displaced this way ?

A box of mass M is at rest on a horizontal surface. A boy of mass `m (

1.	A box of mass M is at rest on a horizontal surface. A boy of mass `m (lt M)` wants to push the box by applying a horizontal force on it. The boy knows that he will not be able to push the box as the coefficient of friction `mu` between his shoes and ground is almost equal to that between the box and the ground. He decides to run, acquire a speed u and then bang into the box. After hitting the box, the boy keeps pushing as hard as possible. What is the maximum distance through which the box can be displaced this way ?
Answer» Correct Answer - `(m^(2)u^(2))/(2mug(M^(2)-m^(2)))`

Discussion

No Comment Found

Related InterviewSolutions

Ball A is about to hit a wall at an angle of incidence of `theta = 30^(@)`. But before hitting the wall it made a head on collision with another identical ball B. The ball B then collides with the wall. The coefficient of restitution for collision between two balls is `e_(1) = 0.8` and that between a ball and the wall is `e_(1) = 0.6`. Find the final velocity of ball B. Initial velocity of A was `u = 5 ms^(-1)`. Neglect friction. `[tan^(-1)((2.25)/(2.34))=44^(@)]`
A ball moving with velocity `V_(0)`, makes a head on collision with another identical ball at rest. The velocity of incident ball and the other ball after collision is `V_(1)` and `V_(2)` respectively. (a) Using momentum conservation write an equation having `V_(1) and V_(2)` as unknowns. Plot a graph of `V_(1)` vs `V_(2)` using this equation. (b) Assuming the collision to be elastic write an equation for kinetic energy. Plot a graph of `V_(1)` vs `V_(2)` using this equation. (c) The intersection point of the above two graphs gives solution. Find `V_(1) and V_(2)` . (d) In a particular collision, the plot of graphs mentioned above is as shown in figure Find `V_(1) and V_(2)` for this collision. Also write the percentage loss in kinetic energy during the collision.
Two identical thin rods are welded as shown in the fig. B is midpoint of rod CD. Now the system is cut into two parts through its center of mass M. The part AM weights 4 kg. Find the mass of the other part.
Three identical particles are placed on a horizontal smooth table, connected with strings as shown. The particle B is imparted a velocity `V_(0) = 9 m//s` in horizontal direction perpendicular to the line ABC. Find speed of particle A when it is about to collide with C.
Two small motors are kept on a smooth table at a separation `L`. The motors have mass `M and 2M` and are connected by a light thread. The motors begin to wrap the thread and thereby move closer to each other. The tension in the thread is maintained constant at F. Find the time after which the two motors will collide. Neglect the dimensions of the motors and their stands.
A heavy ball of radius R is travelling on a smooth horizontal surface with a velocity of u0 towards left. A horizontally moving small ball of mass m strikes it at a height `(R)/(2)` above the centre while travelling with velocity u towards right. (a) After collision the small ball moves in vertically upwards direction with velocity u. Prove that this can happen only if `u gt sqrt(3)u_(0)` (b) Find the velocity of small ball after collision if the collision is elastic and the balls are smooth.
A ball of mass m approaches a heavy wall of mass M with speed 4 m/s along the normal to the wall. The speed of wall before collision is 1m/s towards the ball. The ball collides elastically with the wall. What can you say about the speed of the ball after collision? Will it be slightly less than or slightly higher than 6 m/s ?
A smooth rope of mas `m` and length `L` lies in a heap on a smooth horizontal floor, with one end attached to a block of mass `M`. The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude `V_(0)` as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance `x` from point `P` as shown in figure `-2( P` is a point on the rope which has just started to move at the given instant `)`, choose correct options for next three question. The speed of block of mass `M` is
A particle of mass m is flying horizontally at velocity u. It strikes a smooth inclined surface and its velocity becomes vertical. (a) Find the loss in kinetic energy of the particle due to impact if the inclination of the incline is `60^(@)` to the horizontal. (b) Can the particle go vertically up after collision if inclination of the incline is `30^(@)` ?
In the shown figure, pulleys and strings are ideal and horizontal surface is smooth. The block C (mass 2m) is given a horizontal velocity of `V_(0) = 3 m//s` towards right and the entire system is let go. Find the velocity of three blocks, just after the strings regain tension. Mass of A and B are `2m and m` respectively and take `g = 10 m//s^(2)`.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment