PHY101 Exam-1 Study Guide: Physics with Calculus Fundamentals

About Science

Scientific Hypothesis

A scientific hypothesis is a proposed explanation for a phenomenon that can be tested and potentially proven wrong. This is a fundamental aspect of the scientific method.

• Testable: Must be able to design experiments or observations to check validity.

• Falsifiable: There must be a possibility to prove it incorrect.

• Example: "Objects fall toward the Earth because of gravity" is testable and falsifiable.

Linear Motion and Forces

Scalars vs Vectors

Physical quantities are classified as scalars or vectors based on whether they have direction.

• Scalars: Have magnitude only (e.g., speed, mass).

• Vectors: Have both magnitude and direction (e.g., force, velocity, acceleration).

• Example: Velocity is a vector; speed is a scalar.

Forces as Vectors

All forces are vector quantities, meaning they have both magnitude and direction.

• Examples: Friction, weight, air resistance, and normal force.

Vector Addition

Forces combine according to vector rules, depending on their directions.

• Same direction: Add magnitudes.

• Opposite direction: Subtract magnitudes.

• Angled forces: Use vector addition methods (e.g., parallelogram rule).

• Resultant Force Range: Two equal forces can produce a resultant between 0 and twice their magnitude.

Newton's First Law of Motion - Inertia

Newton's First Law states that an object remains at rest or moves with constant velocity unless acted upon by a net external force.

• Inertia: The tendency of an object to resist changes in motion.

• Balanced Forces: Produce zero net force and zero acceleration.

• Example: A book on a table remains at rest unless pushed.

Net Force and Motion

If the net force on an object is zero, its velocity remains constant (no acceleration).

• Friction and Constant Velocity: When an object moves at constant velocity, the applied force equals the friction force.

• Balanced Forces: Forces that cancel each other so the net force equals zero.

Acceleration

Acceleration is the rate of change of velocity.

• Formula: $a = \Delta v / \Delta t$

• Turning Motion: Changing direction changes velocity, so acceleration occurs even if speed is constant.

• Example: A car turning a corner accelerates because its velocity direction changes.

Gravity and Free Fall

Free Fall

Free fall occurs when gravity is the only force acting on an object.

• Acceleration due to gravity: Near Earth's surface, $g \approx 9.8\ \text{m/s}^2$ downward.

• Free Fall Distance: $d = (1/2)gt^2$

• Highest Point Motion: Velocity is zero at the highest point, but acceleration is still downward.

Mass and Weight

Mass

Mass is the amount of matter in an object and does not change with location.

• Example: An astronaut's mass is the same on Earth and the Moon.

Weight

Weight is the gravitational force acting on an object.

• Formula: $W = mg$

• Mass vs Weight on Planets: Mass stays constant; weight changes depending on planetary gravity.

Newton's Second Law of Motion

Force and Acceleration

Newton's Second Law states that force causes acceleration.

• Formula: $F = ma$

• Constant Force: Produces constant acceleration.

• Mass and Acceleration: Greater mass means smaller acceleration for the same force.

Work and Energy

Work

Work occurs when a force moves an object over a distance.

• Formula: $W = Fd$

• Unit: Joule (J), where $1\ \text{J} = 1\ \text{N} \cdot 1\ \text{m}$

• Work on Inclines: Gravity can do work along a slope.

• Normal Force Work: Normal force does no work because it is perpendicular to motion.

Kinetic Energy

Kinetic energy is the energy an object has due to motion.

• Formula: $KE = (1/2)mv^2$

• Energy Conversion: Lost mechanical energy often becomes thermal energy due to friction.

Solar Energy Sources

Many energy sources on Earth, such as wind, hydroelectric, and fossil fuels, ultimately originate from solar energy.

Gravity and Planetary Motion

Newton's Law of Gravitation

Newton's Law of Universal Gravitation describes the force between two masses.

• Formula: $F = \frac{GMm}{r^2}$

• Surface Gravity: $g = \frac{GM}{R^2}$

• Planet Discovery: Planets have been discovered through gravitational effects on other planets' orbits.

Elasticity

Hooke's Law

Elastic materials follow Hooke's Law, where extension is proportional to the applied force.

• Formula: $F = kx$

• k: Spring constant (measure of stiffness).

Force and Motion

Force vs Motion

Force determines acceleration, not velocity direction.

• Example: A force applied to a stationary object causes it to accelerate.

Important Formulas Table

Concept	Formula
Acceleration	$a = \Delta v / \Delta t$
Free fall distance	$d = (1/2)gt^2$
Weight	$W = mg$
Work	$W = Fd$
Kinetic Energy	$KE = (1/2)mv^2$
Gravitational Force	$F = \frac{GMm}{r^2}$
Surface gravity	$g = \frac{GM}{R^2}$