# [NSCI 1501] - Midterm Exam Guide - Ultimate 16 pages long Study Guide!

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NSCI 1501

MIDTERM EXAM

STUDY GUIDE

Energy Equation

The fundamental law of mechanics is the force equation F = ma that yields at each

moment the acceleration of a body.

we derive two reduced versions of the force (force-acceleration) equation:

o the energy (or work-energy) equation and

o the momentum (or impulse-momentum) equation, which do not involve the

acceleration but relate the initial and final speeds or velocities and the

cumulative effect of the acting forces.

The eeg euatio − also alled wok-energy or energy conservation euatio −

relates the initial (v0) and final (v) speeds of a body to the work (W) produced by the

acting forces.

The eeg euatio is less detailed tha F = a − it does ot otai tie t,

aeleatio a, ad dietio of otio − ut it is siple and in many important

cases much more convenient.

The physical quantities of work, kinetic energy, and potential energy are of

fundamental importance and usefulness in describing physical, chemical and

biological phenomena such as heat, electricity, atoms, chemical bonds, metabolism,

etc.

The work-energy or energy conservation or just energy equation is obtained by

sala ultiplig the foe-acceleration equation by the displacement (x).

The energy equation relates the final speed (v) to the initial speed (v0) and the work

(W) done on the body.

All details of the motion between the initial and the final points are contained in the

work sum.

This may not seem that great since we have transferred all complexities to the

calculation of the work done

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For the most important kind of forces that we call conservative gravitational, elastic,

eleti foes − the su of the wok doe depeds ol o the iitial ad fial

positions, i.e. on initial and final heights.

Work and Kinetic Energy

Work: When we push a body we realize that the physical quantities of interest are

the force we apply and also the distance we keep applying it. The product of force

and displacement we call work (W).

Only the component of force along the displacement of the body does work.

For example, if you push a book across a level tabletop you do work, but the force of

gravity that acts perpendicular to the displacement of the book does not do any

work at all.

The work (W) done by a force on a body is the scalar product of force (F) times the

displacement (x) of the body

W = F⋅ → W = F osθ

Theta is the angle between force and displacement, meaning that only the force

component parallel to the displacement does work.

The work of a force is positive, zero or negative when the force has a component in

the direction of the displacement, zero (perpendicular to the displacement) or

negative (opposite to the displacement)

Kinetic Energy: A body that moves has Kinetic Energy; it is able to push, pull or

deform some other body.

The greater the mass (m) and speed (v) of the moving body the more it can affect

others.

Work and (kinetic) energy are measured in J (joules)

Work can be converted to kinetic energy and vice versa. When a net force acts in the

direction of motion of a body, the speed and kinetic energy of the body increase.

The work of the force is converted to kinetic energy.

For example, a car is pushed forward and moves faster.

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