PHYS 0110 — Introduction to Physics 1

PHYS 0110 Study Guide

Introduction to Physics 1

PHYS 0110 is Pitt's algebra-based introductory physics course. Its catalog description includes mechanics, heat and thermodynamics, and waves. Published sections can differ in emphasis; a Fall 2022 syllabus includes motion, forces, energy, momentum, rotation, fluids, and waves. Scope: Pitt catalog and example syllabus.

These original notes and examples emphasize algebra, units, and physical interpretation. Match thermal topics to your instructor's assigned material. Here Δ means final minus initial; subscripts distinguish initial and final quantities or label a variable.

Core topics

Motion and graphs

Position describes location relative to an origin. Velocity describes how position changes, and acceleration describes how velocity changes. The slope of a position–time graph is velocity; the slope of a velocity–time graph is acceleration. The signed area under a velocity–time graph gives displacement. An object can move left while accelerating right if it is slowing down.

Forces and equilibrium

Draw one free-body diagram per object. Weight, normal force, tension, and friction are interactions, not labels for motion. A body at rest or moving at constant velocity has zero net force. In circular motion, the net force has an inward component even if speed is constant. For extended bodies, equilibrium also requires balanced torques.

Energy and momentum

Energy is useful when position and speed matter more than elapsed time. Momentum is useful for collisions and brief interactions. A collision can conserve total momentum while converting kinetic energy into deformation, heat, or sound. Do not conserve kinetic energy in a sticking collision.

Fluids

Pressure is force per area, not total force. Static fluid pressure increases with depth. Buoyancy comes from pressure differences and equals the weight of displaced fluid. In an ideal steady flow, narrowing a pipe increases speed; the corresponding pressure change requires a model such as Bernoulli's equation.

Thermal physics and waves

Temperature, heat, and internal energy are related but different. Heating can raise temperature or change phase. A wave transports a disturbance and energy while material particles often oscillate near equilibrium positions. Frequency is set by the source; wave speed depends on the medium and wave type.

Important vocabulary

Distance: Total path length traveled.
Displacement: Final position minus initial position.
Speed: Magnitude of velocity.
Acceleration: Change in velocity per time.
Free fall: Motion under gravity alone.
Projectile: Object following motion with gravity and negligible other forces in the ideal model.
Inertia: Tendency to maintain velocity when net force is zero.
Weight: Gravitational force on an object.
Normal force: Contact force perpendicular to a surface.
Tension: Pull transmitted by a stretched rope or similar connector.
Work: Energy transfer due to force through displacement.
Power: Energy transfer or work per time.
Impulse: Force acting over time, producing momentum change.
Elastic collision: Collision conserving total kinetic energy as well as momentum in an isolated system.
Inelastic collision: Collision in which total kinetic energy is not conserved.
Torque: Turning effect of a force about a pivot.
Pressure: Normal force per area.
Density: Mass per volume.
Buoyancy: Net upward fluid force from pressure differences.
Specific heat capacity: Heat needed per unit mass per temperature change.
Latent heat: Energy per mass associated with a phase change.
Thermal equilibrium: Condition with no net heat transfer between bodies in thermal contact.
Period: Time for one cycle.
Frequency: Cycles per second.
Amplitude: Maximum displacement from equilibrium for an oscillation.
Standing wave: Pattern with stationary nodes and antinodes from wave interference.

Formula reference

Mechanics

vaverage = Δx/Δt; aaverage = Δv/Δt.
Constant acceleration: v = v_{0} + at; Δx = v_{0}t + (1/2)at^{2}; v^{2} = v_{0}^{2} + 2aΔx.
Projectile components: v_{0}x = v_{0}cosθ; v_{0}y = v_{0}sinθ. Neglecting drag, ax = 0 and ay = −g when up is positive.
Level-ground projectile range R = v_{0}^{2}sin(2θ)/g, only when launch and landing heights match and drag is negligible.
ΣF = ma; weight magnitude mg; g ≈ 9.81 m/s^{2}.
Static friction |fs| ≤ μsN; kinetic friction |fk| = μkN in the elementary model.
Circular acceleration ac = v^{2}/r.
Constant-force work W = Fd cosθ; K = (1/2)mv^{2}; Wnet = ΔK.
Near-surface gravitational U = mgh; spring U = (1/2)kx^{2}.
Average power P = W/Δt.
Momentum p = mv; impulse J = FaverageΔt = Δp.
Isolated collision: m_{1}v_{1}i + m_{2}v_{2}i = m_{1}v_{1}f + m_{2}v_{2}f in one dimension.
Torque magnitude τ = rF sinθ; static equilibrium requires ΣFx = 0, ΣFy = 0, and Στ = 0.
Rotational kinetic energy Krot = (1/2)Iω^{2}; rolling without slipping has vCM = Rω.

Fluids and thermal physics

Density ρ = m/V; pressure p = F/A.
Static liquid pressure p = psurface + ρgh, with h measured downward and approximately constant density.
Buoyancy FB = ρfluidgVdisplaced.
Incompressible continuity A_{1}v_{1} = A_{2}v_{2}.
Bernoulli p + (1/2)ρv^{2} + ρgy = constant along a streamline under steady, incompressible, negligible-viscosity assumptions.
Sensible heat Q = mcΔT; phase-change heat Q = mL.
Ideal gas PV = nRT using absolute temperature and absolute pressure.
First law ΔU = Q − Wby: heat entering the system is positive, and Wby is work done by the system. Some texts instead define work done on the system; check the sign convention.
Efficiency η = useful work output/heat input for a heat engine; multiply by 100 for percent.

Oscillations and sound

f = 1/T; wave speed vwave = fλ.
Ideal spring period T = 2π√(m/k).
Small-angle pendulum period T = 2π√(L/g).
String-wave speed vwave = √(Ftension/μ), μ = mass/length.
Both-ends-fixed string or ideal open–open pipe: fn = n vwave/(2L).
Ideal open–closed pipe: fn = n vwave/(4L), n = 1, 3, 5, … . End corrections are neglected.
Sound level β = 10log_{10}(I/I_{0}) dB, conventionally I_{0} = 10^{-12} W/m^{2}.

Worked examples

Example 1 Braking distance

A car moves at 20 m/s and brakes with constant acceleration −5.0 m/s^{2}. Using 0 = 20^{2} + 2(−5.0)Δx gives Δx = 40 m. Time is (0 − 20)/(−5.0) = 4.0 s. This excludes driver reaction time and assumes constant braking acceleration.

Example 2 A floating block

A uniform block has density 600 kg/m^{3} and floats in water of density 1000 kg/m^{3}. Balance weight and buoyancy: ρblockVtotalg = ρwaterVsubmergedg. Thus Vsubmerged/Vtotal = 0.60. Sixty percent of the volume is submerged, assuming no additional forces.

Example 3 Heating water

How much energy warms 0.200 kg water by 15°C without a phase change? With c = 4184 J/(kg·°C), Q = 0.200 × 4184 × 15 = 12,552 J ≈ 12.6 kJ. If energy is delivered at 100 W entirely to the water, time is Q/P ≈ 126 s. Real equipment loses some energy to surroundings.

Practice questions and answers

A 60 kg person stands still on a level floor. Normal force? About 589 N upward.
A 2 kg object rises 3 m at constant speed. Change in gravitational energy? 58.9 J.
Momentum of a 0.50 kg ball at 8 m/s? 4 kg·m/s in the velocity direction.
A 250 Hz wave travels at 340 m/s. Wavelength? 1.36 m.
Water depth increases by 2.0 m. Pressure increase? About 19.6 kPa.
Frequency doubles in the same nondispersive medium. What happens to wavelength? It halves.

Mistakes to catch

Calling a negative acceleration “slowing down” without comparing velocity direction.
Putting a Newton's-third-law force pair on the same object's diagram.
Using radius where a torque problem requires perpendicular lever arm.
Using gauge pressure in PV = nRT instead of absolute pressure.
Confusing temperature change with a phase change.

Review routine

Before substituting numbers, explain the physical relationship in a sentence. Estimate whether the answer should grow or shrink when a variable doubles. After solving, check units, direction, and plausibility. Practice drawing diagrams from text descriptions without immediately reaching for a formula.