← All printables Chapter 05 · Mechanics · 2 sheets · read the chapter →

Vedatom Physics

FORMULA CARD · PHYSICS.VEDATOM.COM

Chapter 05 · Part I · Mechanics
Revised on ____________________

Chapter 05 · Work, Energy and Power

Forces you can integrate away

sheets
diagrams
results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

Work

A DOT PRODUCT, WITH A SIGN

I.Constant force W = F·d = F d cos θ

II.Variable force W = ∫ F·dr area under an F–x graph

III.Gravity W = − m g Δh path-independent

IV.Spring W = 12 k x_i² − 12 k x_f²

V.Kinetic friction W = − f_k s s is the path length, not displacement

VI.Normal force W = 0 whenever it is ⊥ to the motion

VII.Zero-work forces tension on a fixed pulley, centripetal force, static friction on a rolling wheel

VIII.Sign θ < 90° adds energy, θ > 90° removes it

Friction is the one force here whose work depends on the route. Everything else on this sheet can be replaced by a difference of potential energies.

The work–energy theorem and power

TRUE FOR ANY FORCE, ANY PATH

I.Kinetic energy K = 12 m v² = p²2m

II.The theorem W_net = ΔK = K_f − K_i

III.Average power ⟨P⟩ = Wt

IV.Instantaneous power P = F·v = F v cos θ

V.Constant-power motion v = √( 2 P tm ) from rest; x ∝ t^3/2

VI.Efficiency η = P_outP_in

III

Potential energy

ONLY CONSERVATIVE FORCES HAVE ONE

I.Definition ΔU = − W_cons the reference is yours to choose

II.Near-Earth gravity U = m g h

III.Spring U = 12 k x² x from the natural length

IV.General gravity U = − G M mr zero at infinity

V.Force from U F_x = − dUdx the slope of the landscape

VI.Conservative test W around any closed loop is zero

VII.Equilibrium dUdx = 0 stable if U″ > 0

Conservation of energy

WHERE THE ACCOUNTING IS DONE

I.No friction K + U = constant

II.With friction ΔK + ΔU = − f_k s the deficit is heat

III.General W_ext = ΔK + ΔU + ΔE_int

IV.Speed at the bottom v = √(2 g h) any smooth track, any shape

V.Vertical circle, lowest point v ≥ √(5 g L) for a string to complete the loop

Joule

1 J = 1 N m

Electron-volt

1 eV = 1.6×10⁻¹⁹ J

Calorie

1 cal = 4.186 J

Kilowatt-hour

1 kWh = 3.6×10⁶ J

Horsepower

1 hp = 746 W

g h per metre

9.8 J kg⁻¹

The energy landscape

READ THE GRAPH, SKIP THE ALGEBRA

Turning points Where E = U(x). The particle stops and reverses; K = E − U is never negative, so regions with U > E are forbidden.

Bound and free A well with E below the barrier top traps the particle between two turning points. Raise E above the barrier and the motion becomes unbounded.

Where marks are lost in this chapter

1W = F d cos θ uses the displacement of the point of application — friction's work uses the path length.

2“The normal force never does work.” Only while the surface is still: a moving wedge or a lift floor does.

3Setting the work of one force equal to ΔK. The theorem sums the work of every force.

4Using energy to find a time. Energy relates speeds to positions; time enters only through kinematics.