Fundamental Concepts in Introductory Physics: Mechanics, Forces, and Motion

Study Guide - Smart Notes

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Projectile Motion

Optimal Launch Angle and Range

Projectile motion describes the path of an object launched into the air, subject only to gravity (ignoring air resistance). The range is maximized when the launch angle is 45°.

Key Point: The optimal angle for maximum range on level ground is 45°.
Equation: The range of a projectile is given by:
Example: A ball launched at 45° will travel farther than one launched at 30° or 60° (assuming equal initial speeds).

Friction and Circular Motion

Static and Kinetic Friction

Friction is the force that resists motion between two surfaces. Static friction prevents motion, while kinetic friction acts during motion.

Key Point: The coefficient of static friction determines the maximum force before sliding occurs.
Equation:
Example: A car driving around a curve relies on static friction to avoid skidding.

Circular Motion and Centripetal Force

Objects moving in a circle experience a centripetal force directed toward the center of the circle.

Key Point: Centripetal force is required for circular motion.
Equation:
Example: A car turning on a curved road must overcome friction to maintain its path.

Forces and Newton's Laws

Newton's Second Law

Newton's Second Law relates force, mass, and acceleration.

Key Point:
Example: If a net force of 15 N acts on a 5 kg object, its acceleration is m/s2.

Normal Force on Inclined Planes

The normal force is the perpendicular contact force exerted by a surface.

Key Point: On an incline,
Example: A sled on a 20° slope with mass 25 kg has

Work, Energy, and Power

Kinetic Energy and Work

Kinetic energy is the energy of motion. Work is done when a force moves an object.

Key Point:
Equation:
Example: Pushing a block across a table does work against friction.

Collisions and Conservation Laws

Conservation of Momentum

In the absence of external forces, the total momentum of a system remains constant.

Key Point:
Example: Two ice skaters push off each other and move in opposite directions.

Gravity and Free Fall

Acceleration Due to Gravity

Objects in free fall near Earth's surface accelerate downward at m/s2.

Key Point: The time to fall from height is
Example: Dropping a rock from 15 meters takes seconds.

Vectors and Vector Addition

Magnitude and Direction

Vectors have both magnitude and direction. The sum of two vectors depends on their relative orientation.

Key Point: For perpendicular vectors,
Example: Adding a 3-unit east vector and a 4-unit north vector yields a 5-unit northeast vector.

Physics of Ropes and Tension

Tension in a Rope

Tension is the force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends.

Key Point: In a tug-of-war, the tension equals the force applied by each team if the rope is stationary.
Example: Two people pull with 100 N each; the tension is 100 N.

Physics of Scales and Apparent Weight

Apparent Weight in Accelerating Elevators

Apparent weight changes when an elevator accelerates.

Key Point: if accelerating upward, if downward.
Example: A 60 kg person in an elevator accelerating upward at 2 m/s2 feels N.

Physics of Inclined Planes

Critical Angle for Sliding

The angle at which an object begins to slide is determined by the coefficient of static friction.

Key Point:
Example: If , then

Terminal Velocity and Air Resistance

Terminal Velocity

Terminal velocity is the constant speed reached by an object when the force of gravity is balanced by air resistance.

Key Point: For large Reynolds number, air resistance is proportional to the square of velocity.
Equation:
Example: A falling sphere reaches terminal velocity when .

Tables: Comparison and Classification

Sample Table: Forces on Stacked Blocks

The following table summarizes the forces exerted by a table on stacked blocks:

Block	Mass (kg)	Force from Table (N)
Top	3	29.4
Middle	7	78.4
Bottom	5	98.0

Additional info: Forces calculated using for each block and summing masses above each block.

Additional Info

Vector Addition: For vectors at arbitrary angles, use the law of cosines:
Terminal Velocity Ratio: For spheres of different radii and densities,