  Problem solving tips

Work, Energy And Power

- Want to score better marks in exams? Have a look at some problem solving tips.
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Tip 1: Work done by a variable force
We write the expression of force in terms of the displacement.

Then work done for small displacement is given as
The limits are applied and the work done is integrated from initial limit to the the final limit.
Sample problems:
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Tip 2: Problems on motion in a vertical circle  All these conditions are a result of applying newton's second law and conservation of mechanical energy. We can use a similar approach when a circular path is involved in the question.  Sample problems:
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Tip 3: Problems on finding maximum extension/ compression in a spring
Such problems can be solved by keeping in mind these points:
• Draw the free body diagram of the block.
• Applying work theorem on block for which the work done is by these forces: spring force, the external force
• At maximum extension,
Note that at maximum extension, net force is NOT zero, but the velocity is zero.  Sample problems:
In the adjoining figure block A is of mass and block B is of mass . The spring has force constant . All the surfaces are smooth and the system is released from the rest with spring unstretched. Then:
This question has multiple correct options
A
The maximum extension of the spring is
B
Tension in the thread for extension of in spring is
C
Net acceleration of block B when the extension in the spring is maximum, is
D
None of these
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Tip 4: Problems on collisions in 1-D
At first, we determine the system under observation.
For any collision, the net momentum of the system (consisting of colliding particles) is always conserved if the net external forces are zero.
For elastic collisions, the coefficient of restitution
So we apply:
• Momentum conservation before and after the collision
• Kinetic Energy conservation before and after the collision.
For completely inelastic collisions, the coefficient of restitution
• Momentum conservation before and after the collision is still valid
• The final velocity of both the colliding masses is same.  Sample questions:
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Tip 5: Problems on collisions in 2-D
In oblique collisions, we have to simply find the line of impact(L.O.I.), i.e. the common normal.
Then we resolve the velocities along the common normal and perpendicular to it.
By momentum conservation in x and y direction,

The velocities perpendicular to the line of impact remain unaffected.  We can apply the equations of coefficient of restitution along the line of impact.  Sample problems: