Patterns of problems

## Work, Energy And Power

- It is always better to be prepared. Practice the kind of problems asked in various exams
1
Pattern: Work done by a object
Description: When a force acts on an object over a distance, it is said to have done work on the object. When a force acts to cause an object to be displaced, three quantities must be known in order to calculate the work. Those three quantities are force, displacement and the angle between the force and the displacement. The work is subsequently calculated as where is the angle between the force and the displacement vectors. There are cases when the work done is zero, (i) when displacement is zero, (ii) when force is zero and (iii) when force and displacement are mutually perpendicular to each other.
• To find the angle between force and displacement
• To find the work done by the frictional force, gravitational force, tension or force due to weight
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2
Pattern: Work Done by a Variable force
Description: In case the force acting on the body is not constant, then the total work done cannot be directly calculated. In cases, the force may be constant for short intervals throughout the trajectory. In that case, the total work done is calculated as the sum of all the individual work done by the force during each interval where it stays constant. Otherwise, an equation of a constantly varying force may also be given in which case first the infinitesimal work done needs to be calculated . In particular questions, these two formats may be mashed together, asking you to calculate the total work done when the force varies continuously for short time spans and the nature of variation changes between intervals.
• Calculate the work done from a graph representing motion
• Calculate the work done when the equation of either the Force or the trajectory is given.
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3
Pattern: Problems involving Springs
Description: Due to the variety of problems that can be created using the simple spring force formula and due to the variable nature of the force exerted, problems involving springs are very common. When drawing the FBD, remember to that the spring force acts proportional to and opposite to the displacement vector and the potential energy stored in the spring is   where is the displacement about mean position of spring. Problems involving one spring attached to one body are most common. Combinations of masses attached to springs in different arrangements may also come so it is best to prepare for those as well.
• Find work done to extend/compress a spring
• Find Potential energy stored in a spring
• Find Kinetic energy of masses after spring is released
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4
Pattern: Collisions
Description: Important thing to remember in problems involving collisions is that momentum is always conserved. The Kinetic energy of the bodies may or may not be conserved depending on whether the collision is elastic or inelastic. In an elastic collision , the bodies bounce off of each other with their velocities determined by the coefficient of restitution. In a perfectly inelastic collision , the bodies stick together after the collision and move as a single body. Often, the collision will be inelastic .
• Find the kinetic energies of bodies after collision
• Count number of collisions
• Find coefficient of restitution
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5
Pattern: Work Energy Theorem
Description: By far the most important topic of this chapter, the work energy theorem establishes a relationship between the work done on a body with its change in kinetic and potential energies. The simple formula is very versatile and can be used extensively. Either one of these quantities can be asked to be calculated when some information about the other two are given.