This ain't textbook:

All the rods in figure are hinged smoothly as shown. The vertical red line is infact a spring of force const 'k'...

In terms of the angle A, k, m find the period of small oscillations (along x) of the blocks.

Textbook:

This is a standard textbook question:
The spring-block shown falls from a height of 1m. Assuming the spring to be sufficiently long answer these two questions:

1)What is the maxm. speed of the block?
2)What is the amplitude of oscillation?

Anyone who answers both correctly???

SHM..finally.

The block (mass 5kg) is released from rest when all springs are relaxed...

It undergoes SHM...Find the amplitude of oscillation of the point P.

Tis simple:

The grey blocks are of mass 1kg and the red one 2kg... the force F is 35N...all surfaces have coeff. of friction .5.

Angle A=37*.

Obviously, find the accn. of the grey block.

WARNING : THIS IS TOUGH:

If someone does'nt have a liking towards really tough ones, plz. take a walkover...

The dual-wedge shown in the figure is MASSLESS. All surfaces are smooth.
Find the min ratio m1/m2 so that the ball m2 'starts climbing up the wedge'..ie. it starts moving up the incline in the direction shown.

Seems trivial, but ain't:

The answer to this problem should act as an eye opener to the simplicity of many things;

Assume: m1 moves downwards. Find the accn. of m1.
Bet you had to frame some (2) equations...i don't...
Try to observe something in the result. Report anything unusual;

Running out...

Try this:

The rigid body is so selected from a collection of spheres, rings, discs etc. such that when released from rest in the position shown, it leaves contact with the horizontal plane at exactly 60*...as shown.

This would assist in a smooth 'transition' from the horizontal to the inclined surface;

So, whats the nature of the rigid body???

The simpler, the merrier.

I' scrapping this question...you would never solve it as it seemingly can't be solved...i tried some graph plotting software but could make nothing...some people more skilled in trigo. would have done it maybe...

And, as you can see, i'm really out of cool problems. I'll try to make some oer the weekend.
See you on monday.

The length of both the rods in the figure is 1m. The rods are smoothly hinged.
Find the velocity of the plunger in the cylinder.

Who stole my L???

A cubical block is given an initial velocity V on a rough horizontal floor...After some time, it is found to stop.
The angular momentum of the block about any point on the ground is non-zero initially but zero finally. Which force is single-handedly responsible for this loss:

A)Normal reaction.
B)Friction
C)Weight of the Block
D)Coriolis force.

Just for kicks:

A ball of mass 4kg is projected and the range is found to be 10 meters..
The same ball is again projected with the same velocity and angle, except that this time, at the highest point of its trajectory, it explodes into 2 fragments of mass 1kg and 3kg...the instantaneous velocities of both masses just after the explosion is horizontal..

Finally, the mass 1kg is found at a distance of 3m from the point of projection...(assume that the fragments stick to the ground on contact)
Specify the location of the 3kg fragment...

Plz. note:

In the first diagram, note that though v1CosA=v2, same constraint does not hold for accn.

In the second diagram, v1(1-CosA)+v2=0 but not a1(1-CosA)+a2=0...




I wanted you to observe that you can relate the velocities by taking the tensions..



Try it: in each question, observe the tension (in the dirn. of motion) and the coefficients in the velocity constraints...

Blue...

Somebody made a giant spherical cavity in the earth such that the earth's center and a point in the surface are diametrically opposite.

The someone drops a small ball from a small opening at the surface into the cavity. In how many minutes does the ball reach the center of earth???

Let Tension lead the way..

Relate the accns. of the masses in the diagrams.

In the 1st diagram, the thread goes through a very small ring, free to slide on a fixed beam..You have to relate the accn. when the angle (specified in dig.) is A.

Some of you were confused abt. velocity constraints..so, for a few days, lets restrict ourselves to rigid body constraints..

for practice and initiation, lets solve the following problems:

Given the velocity of one body, find that of the other. (don't blame me if you find these trivial)..

Calculate 'e':

In the given figure, all surfaces have equal coeff. of restitution. The ball collides with the vertical wall at the highest point in its path. The path of the ball is shown.

Calculate 'e'.