Physics midterm

Significant Figures

Rules for counting significant figures in measurements.

Speed

Example of a scalar: 1.5 m/s.

Vectors

Have magnitude and direction.

Vector Properties

Magnitude and direction of a vector remain unchanged if moved parallel to its original position.

Adding vectors

Use the Pythagorean theorem.

Distance

A measure of how far an object has traveled.

Scalar quantity

Only magnitude, no direction.

Total distance

Example: A person walks 2 m right, then 4 m left. Total distance = 2+4=6.

Displacement

Overall change in position from the starting point (origin).

Vector quantity

Includes magnitude and direction.

Pythagorean Theorem for Displacement

Used when movement occurs in multiple directions; Formula: c^2 = a^2 + b^2.

Average speed

Formula: Average speed = total Distance / Total Time.

Velocity

Rate of change of displacement with time.

Instantaneous velocity

The velocity of an object at a specific point in time.

Constant velocity

Velocity that remains unchanged.

Slope of Position-Time Graphs

Indicates velocity.

Acceleration

The rate of change of velocity over time (m/s²).

Formula for Acceleration

a = (final velocity - initial velocity) / time.

Positive Acceleration

Object speeds up.

Negative Acceleration

Object slows down.

Kinematics

The study of the motion of objects, including displacement, velocity, acceleration, and time.

Final Velocity Equation

vf=vi+at

Displacement Equation (Average Velocity)

d=1/2 (vi+vf)t

Displacement Equation (Initial Velocity)

d=vit+1/2 at2

Final Velocity Squared Equation

vf2=vi2+2ad

Freefall

An object in motion under the influence of only the force of gravity.

Rate of Freefall

All objects regardless of mass fall under the same rate.

Relative Velocity

The velocity of an object as observed from a particular frame of reference.

Frame of Reference

A viewpoint from which motion is observed (can be stationary or moving).

Relative Velocity Calculation (Same Direction)

Adding the velocities.

Relative Velocity Calculation (Opposite Direction)

Subtracting the velocities.

1D Motion

Movement along a single line (e.g., vertical or horizontal).

2D Motion

Movement along two dimensions (e.g., horizontal and vertical) but without thickness.

Projectile Motion

A projectile is any object moving through the air under the influence of gravity.

Independence of Motion

Horizontal and vertical motions are independent of each other.

Horizontal Motion

Velocity: vx = dx ÷ t; Acceleration: ax = 0.

Vertical Motion Final Velocity

Final Velocity: vf = vi + (a × t).

Vertical Motion Final Velocity Squared

Final Velocity Squared: vf² = vi² + (2 × a × d).

Vertical Motion Displacement

Displacement: d=vit+1/2 at2.

Horizontal Projectile Problem

Two baseballs: one thrown horizontally, one dropped from the same height. Both hit the ground at the same time.

Newton's Laws of Motion

Forces: A force is a push or pull that can cause an object to move.

Forces

A force is a push or pull that can cause an object to move. Forces are vector quantities (have both magnitude and direction).

Balanced Forces

When forces acting on an object are equal in size and opposite in direction, there is no movement (net force = 0).

Unbalanced Forces

When forces acting on an object are not equal, causing the object to accelerate in the direction of the greater force.

Net force

The difference between the greater and weaker force.

Newton's First Law (Law of Inertia)

An object at rest will remain at rest unless there is an external unbalanced force acting upon that object, an object in motion will remain in motion and move in a straight line unless there is an external unbalanced force acting upon that object.

Inertia

The resistance of an object to any change in its state of motion (whether at rest or moving). More mass = more inertia.

Newton's Second Law

F = ma (Net force equals mass times acceleration).

Force and Acceleration

If the force applied to an object increases, the acceleration increases. If the mass of an object increases, acceleration decreases for the same applied force.

Example of Newton's Second Law

A heavier truck accelerates slower than a lighter one when the same force is applied.

Newton's Third Law (Action and Reaction)

Every force has an equal and opposite force.

Example of Action-Reaction Pairs

When walking, your foot pushes on the ground, and the ground pushes back on your foot with an equal force.

Gravity

Pulls objects toward the center of Earth (always acts downward).

Normal Force

The force exerted by a surface to support the weight of an object resting on it (acts perpendicular to the surface).

Tension

The force transmitted through a rope, string, or cable when it is pulled tight (acts along the direction of the rope).

Applied Force

A force applied to an object (e.g., pushing a box).

Friction

The force opposing motion between two surfaces in contact. Can be kinetic (when objects move) or static (when objects are at rest).

Kinetic Friction

Opposes motion when two objects are moving relative to each other. Example: Box sliding on the floor.

Static Friction

Resists the start of motion between two objects at rest.

Field Forces

Pushes or pulls that occur between two objects without the objects touching one another (e.g., gravity).

Contact Forces

Require direct interaction (e.g., friction, tension).

Gravitational Force

A force of attraction between objects with mass. The gravitational force depends on mass and the distance between objects.

Gravitational Inverse Square Law

The farther away you are from an object, the weaker the gravitational force.

Formula for Gravitational Force

fg = Gm1m2/r2.

Gravitational Force

The force between you and the object decreases by the square of the distance between you.

Gravitational Constant

A constant used in the formula for gravitational force.

Masses of the Two Objects

The quantities of matter in the two objects that exert gravitational force on each other.

Distance Between Them

The space separating the two objects, which affects the gravitational force.

Acceleration due to Gravity

Near Earth's surface, gravity causes an object to accelerate at 9.8 m/s².

Weight

The force exerted by gravity on an object.

Formula for Weight

W = mg, where W is weight, m is mass, and g is gravitational acceleration.

Tension Force

The force exerted by a rope or string when pulled.

Friction

Resistance between surfaces that are in contact.

Static Friction

Occurs when objects are at rest relative to each other.

Kinetic Friction

Occurs when objects are moving relative to each other.

Spring Force

The force exerted by a spring when compressed or stretched.

Newton's Second Law of Motion

States that unbalanced forces cause an object to accelerate in the direction of the net force.

Newton's Third Law of Motion

States that for every action, there is an equal and opposite reaction.

Skydiver and Earth's Gravity

Gravity is the force that pulls objects toward Earth, equal and opposite between Earth and the skydiver.

Action-Reaction Pairs

For example, when walking, you push on the ground, and the ground pushes back on you.

Newton's Universal Law of Gravitation

States that all objects with mass exert a gravitational pull on each other.

Gravitational Force Formula

Fg = Gm1m2/r², where Fg is gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers.

Free Fall Acceleration

All objects fall at the same rate in the absence of air resistance (9.8 m/s² on Earth).

Terminal Velocity

The maximum velocity an object reaches when falling, when the force of gravity is balanced by air resistance (drag).

Air Resistance

Opposes the motion of objects falling through the atmosphere.

Effect of Surface Area on Drag Force

The greater the surface area, the greater the drag force.