MCAT Physics > Energy

Background

Energy (E) is the capacity of a physical substance to do work (scalar value)

MCAT Energy - Potential and Kinetic Energy

Potential Energy

Potential Energy (PE/U) is the energy that has the potential to do something

PE (U) = mgh

Kinetic Energy

Kinetic Energy (KE) is the energy of motion

KE = ½mv2

Mechanical Energy

Total Mechanical Energy is the sum of kinetic and potential energy

ΔEtotal = ΔPE (U) + ΔKE

Conservation of Mechanical Energy states in the absence of non-conservative forces, the sum of the KE and PE will be constant. If work done to move a particle is zero, or the net forces is the same, then force is conservative. When non-conservative forces are present (friction/air resistance) energy is not fully conserved and some is lost to heat, sound or other factors. To increase available kinetic energy, increase potential energy

½mv2 = mgh = 0

Work

Work (W) is the process by which energy is transferred between systems

MCAT Energy - Work Done

W = Fd = Fdcosθ = KE = ½mv2 = PE = mgh

Work/Energy Theorem describes a direct relationship between the work done by all forces acting on an object and the change in the objects kinetic energy.

Wnet = ΔKE

Power

Power (P) is the rate at which energy (work) is transferred between systems

P = ΔW/Δt

Momentum

Momentum (p) is a vector quantity of objects in motion (magnitude/direction of force). Momentum is conserved with constant net forces or in the absence of external forces

MCAT Energy - Momentum BeforeMCAT Energy - Momentum After

Σp = Σmv

Impulse

Impulse (J) occurs when net forces act on an object causing it to change motion

J = Ft = Δp

Efficiency

Efficiency is a comparison of the work put in and the work put out

Efficiency = AMA/TMA = Wout/Win = ((load)(load distance))/(load)(load distance) x 100

Collisions

Ideal Collisions occur when two objects instantaneously collide in a specific location and total momentum is conserved as long as no net forces act on the objects

1) Completely Elastic Collisions occur when 2+ objects collide such that the total momentum and KE are conserved. No energy has transformed into light, sound, etc.

mvai + mvbi = mvaf + mvbf

KEa1 + KEb1 = KEa2 + KEb2

MCAT Energy - Completely Elastic Collision

2) Inelastic Collisions occur when objects do not stick together and KE is converted to heat, light, sound, and object deformation. Doesn't result in a decrease of kinetic energy unless external forces are present (conservation)

MCAT Energy - Inelastic Collision

mvai + mvbi = mvaf + mvbf

3) Completely Inelastic Collisions occur 2+ objects stick together and the kinetic energy is not conserved but momentum is

MCAT Energy - Completely Inelastic Collision

mvai + mvbi = (ma + mb)vf

Simple Machines

See Simple Machines

Center of Mass

Center of Mass is a point within any 2D/3D object at which the entire objects mass could be represented by a single particle

Center of Mass (x,y,z…) = (m1 x1 + m2 x2 + m3 x3)/(m1 + m2 + m3)

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