Physics Momentum and Energy Concepts

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Questions and Answers

What is the definition of momentum in physics?

The rate of change of position

The product of mass and velocity (correct)

The force applied over time

The energy transferred during a collision

Which law explains the conservation of momentum in a system of interacting bodies?

Newton's second law

Newton's third law (correct)

Newton's first law

Law of universal gravitation

In what type of system is total momentum conserved?

A system with friction

A system in equilibrium

An open system with external forces

An isolated system (correct)

How is Newton's second law expressed in terms of momentum?

Force equals the change in momentum over time Signup and view all the answers

What must be true about the total momentum of two colliding bodies before and after their interaction?

It must remain constant Signup and view all the answers

What is the SI unit of kinetic energy?

Joule Signup and view all the answers

Which statement about kinetic energy is true?

It is zero when the particle is at rest. Signup and view all the answers

Which equation correctly defines impulse?

Impulse = Force × Change in Time Signup and view all the answers

What does power measure?

The rate at which work is done Signup and view all the answers

What happens to gravitational potential energy as a basketball descends?

It converts to kinetic energy. Signup and view all the answers

Which unit is equivalent to 1 watt?

1 J/s Signup and view all the answers

Which of the following statements is false regarding kinetic energy?

Its value may be negative during motion. Signup and view all the answers

In the context of Newton's Law, impulse primarily involves which aspect of force?

Instantaneous force over time Signup and view all the answers

What type of friction acts on an object before it starts to slide?

Static friction Signup and view all the answers

What happens when an object experiences positive work?

The object speeds up Signup and view all the answers

Which of the following is the SI unit of work?

Joule Signup and view all the answers

What occurs when the net work on an object is zero?

The object's speed remains constant Signup and view all the answers

When does a force do no work on an object?

When the force is perpendicular to the displacement Signup and view all the answers

Which formula represents work done by a force at an angle?

W = Fd cos(θ) Signup and view all the answers

If an object lifts a weight of 1 N a distance of 1 m at constant speed, how much work is done?

1 J Signup and view all the answers

What is the formula for the radial acceleration component in nonuniform circular motion?

ar = v^2/R Signup and view all the answers

Which of the following is NOT a type of force classified in the content?

Centrifugal force Signup and view all the answers

Which unit is used to measure the magnitude of force?

Newton Signup and view all the answers

In order for a body to be in equilibrium, what must be true about the net force acting on it?

The net force must be zero. Signup and view all the answers

Which of the following forces is classified as a long-range force?

Weight Signup and view all the answers

What is a characteristic of tangential acceleration in nonuniform circular motion?

It is parallel to the instantaneous velocity. Signup and view all the answers

What is the weight of a medium apple as stated in common force magnitudes?

1 N Signup and view all the answers

Which of the following statements about forces is true?

Tension is a form of contact force. Signup and view all the answers

What is the acceleration of a freely falling object in the absence of air resistance?

9.8 m/s² Signup and view all the answers

What type of motion describes the horizontal component of a projectile's trajectory when air resistance is neglected?

Constant velocity motion Signup and view all the answers

What does instantaneous velocity represent in motion?

The velocity at a specific instant of time Signup and view all the answers

Which component of a projectile's motion is affected by constant acceleration due to gravity?

Vertical motion Signup and view all the answers

Which of the following correctly describes average acceleration?

The rate of change of velocity with respect to time Signup and view all the answers

Which equation is used to describe motion with constant acceleration?

v = u + at Signup and view all the answers

In projectile motion, if the initial angle is increased while keeping the initial speed constant, what happens to the vertical component of the motion?

Increases and decreases over time Signup and view all the answers

How does average speed differ from average velocity?

Average speed is not the magnitude of average velocity Signup and view all the answers

What is the formula used to calculate the magnitude of centripetal acceleration in uniform circular motion?

arad = v²/R Signup and view all the answers

What does free fall refer to?

Motion of an object under the influence of gravity alone Signup and view all the answers

When a projectile is launched diagonally, which of the following initial velocity components remains constant throughout its flight?

Horizontal component Signup and view all the answers

What is the formula for average x-velocity?

vx = (xf - xi)/(tf - ti) Signup and view all the answers

What happens to the path of a projectile if air resistance is taken into account?

It follows a parabolic trajectory Signup and view all the answers

What is the relationship between period T, radius R, and centripetal acceleration in uniform circular motion?

arad = 4π²R/T² Signup and view all the answers

What does constant acceleration imply in straight-line motion?

The rate of change of velocity is uniform Signup and view all the answers

What describes the relationship between displacement, time, and average velocity?

Average velocity is the displacement divided by time Signup and view all the answers

Study Notes

Chapter 2: Motion Along a Straight Line

Kinematics is the study of motion
Velocity and acceleration are important physical quantities
A typical runner speeds up, then slows down during a race

Learning Goals for Chapter 2

Understanding displacement and average velocity in straight-line motion
Definition and difference between instantaneous velocity and speed
Using average and instantaneous acceleration to describe changes in velocity
Solving problems involving freely falling objects under gravity
Analyzing straight-line motion with non-constant acceleration

Displacement, Time, and Average Velocity

A particle moving on the x-axis has a coordinate x
Change in coordinate: Δx = x₂ - x₁
Average x-velocity: v_av-x = Δx/Δt

Rules for the Sign of x-Velocity

Positive & Increasing (more positive): Positive x-velocity; particle moves in the +x direction
Positive & Decreasing (less positive): Negative x-velocity; particle moves in the -x direction
Negative & Increasing (less negative): Positive x-velocity; particle moves in the +x direction
Negative & Decreasing (more negative): Negative x-velocity; particle moves in the -x direction

Instantaneous Velocity

Instantaneous velocity at a specific time/point: v_x = dx/dt
Average speed is not the magnitude of the average velocity

Average Acceleration

Acceleration describes the rate of change of velocity with time
Average x-acceleration: a_av-x = Δv_x/Δt

Instantaneous Acceleration

Instantaneous acceleration: a_x = dv_x/dt

2.1 - Example problem (Cheetah and Antelope)

The problem involves analyzing the motion of a cheetah and an antelope with given initial and final positions and times.
Includes finding average velocity, displacement.
Initial calculations involve position of cheetah and antelope at specific intervals of time, to calculate displacement and average x-velocity

Motion with Constant Acceleration

Constant x-acceleration: a_x-t graph is a horizontal line (slope = 0)
The area under a_x-t graph equals the change in x-velocity from time 0 to time t

Equations of Motion with Constant Acceleration

Four equations applicable to straight-line motion with constant acceleration a_x. These equations relate quantities such as position (x), velocity (v), acceleration (a), and time (t). The equations are:
v_x = v_0x + a_xt
x = x₀ + v_0xt + 1/2 a_xt²
v_x² = v_0x² + 2a_x(x - x₀)
x - x₀ = 1/2(v_0x + v_x)t

Exp. 2.4 (Example problem)

The example involves a motorcycle with known acceleration and initial velocity.
The solution finds the unknown final velocity and position in a given time

Exp. 2.5 (Example problem)

The problem involves a police officer and motorist on an x-axis

Freely Falling Bodies

Free fall is motion under only gravity's influence
Strobe light flashes at equal time intervals, showing constant acceleration
Velocity change is the same in each interval

A Freely Falling Coin (Exp. 2.6)

Acceleration due to gravity (g) is constant (approximately 9.8 m/s²)

Exp. 2.7 (Example problem)

The example analyzes a ball moving vertically with an initial velocity.
It examines various aspects like maximum height, total time in the air, velocity at different points in the trajectory,etc.

Chapter 3: Motion in Two or Three Dimensions

Projectile motion: Describes the path of an object launched into the air, under the influence of only gravity. This is modeled as two independent motions in the x and y axes.
Projectile motion is the combination of horizontal motion with constant velocity and vertical motion with constant acceleration due to gravity

Projectile Motion - Initial Velocity

Initial velocity components of a projectile (like a kicked soccer ball) relate to the initial speed and launch angle

The Equations for Projectile Motion

Derivation and use of equations for x (horizontal) and y (vertical) components of a projectile's motion, when initial position is zero. These describe speed/direction as a function of time.

3.7 - Example problem

This section details data and problems related to projectile motion

Acceleration for Uniform Circular Motion

For uniform circular motion, acceleration is constant but always towards the center of the circle. The magnitude is related to the speed and radius.

Uniform Circular Motion

Acceleration has a constant magnitude but a changing direction.
Velocity and acceleration are perpendicular.

Projectile Motion - Summary

The x-motion and y-motion are independent when air resistance is negligible.

Nonuniform Circular Motion

The motion is not uniform if speed varies during circular motion. The radial component is still v²/R, but there's also a tangential component.

Chapter 4: Newton's Laws of Motion

Defining forces as pushes or pulls that act on objects
Identifying forces as interactions between objects or between an object and its environment.
Forces are vector quantities

Properties of a Force

Push or Pull
Interaction between two objects, or between an object and its environment
Magnitude and direction

There are Four Common Types of Forces

Normal Force: When an object rests/pushes on a surface, the surface pushes perpendicularly. It's a contact force.
Friction Force: A surface exerts a friction force parallel to the surface. It's another contact force,
Tension Force: A pulling force exerted by a rope/cord. It's a contact force.
Weight: The pull of gravity on an object. It's a long-range force

Magnitudes of Common Forces

Forces are measured in newtons (N)
Examples of force magnitudes (values) and what they measure (weight of a large whale, locomotive, linebacker, etc.)

Drawing Force Vectors

Vectors represent forces. The length shows magnitude (longer = larger force)

Newton's First Law

Equilibrium: When a body is at rest or moving at a constant velocity in a straight line
Net force condition for equilibrium; The sum of all forces on a body must be zero

Net force causes acceleration

Acceleration occurs in the direction of net force, when the net force is not zero

Newton's First Law (revisited)

Pucks on a frictionless surface, acted on by zero net force remain in equilibrium/constant velocity.

When is Newton's First Law Valid?

Inertial frame of reference: When Newton's first law is valid.

Crash Test Dummies

The apparent force pushing dummies forward when a car stops is a result of their inertia tending to keep moving forward.

Newton's Second Law of Motion

Object's acceleration is proportional to the net force, and inversely proportional to the object's mass

Systems of Units:

The SI, cgs, and British systems for forces, masses and accelerations. The SI system of units is almost universally used in physics

4.5 - Example problem (Bottle Motion)

A problem involving the motion of a bottle with initial velocity and acceleration. The problem examines and uses Newton's 2nd law of motion to solve for the unknown forces on the bottle

Mass and Weight

Weight is the force of gravity on an object
Weight w = mass m × acceleration due to gravity (g)
g's value varies based on location

Relating Mass and Weight of a Body

Weight = mass × acceleration due to gravity (w = mg) applies when a body is stationary or accelerating.

Newton's Third Law

For every action force, there's an equal and opposite reaction force. These forces act on different objects

Free-Body Diagrams

Drawing a free-body diagram isolates forces on an object to analyze motions

5.3 & 5.6 & 5.7 - Examples (Engine, Chains, Ring, Iceboat, etc.)

Calculations involving forces on different objects

Frictional Forces

Friction arises from interactions between molecules on surfaces

Kinetic and Static Friction

Kinetic friction acts when a body slides; fk = μ_kn
Static friction acts when there's no relative motion between bodies

Static Friction vs Kinetic Friction (Example Problems)

Examples illustrating how static friction acts before motion and kinetic friction acts after

Some Approximate Coefficients of Friction

Values of the coefficients of friction for various materials (steel on steel, rubber on concrete, etc.).

5.13 - Example problem (Pulling a Crate)

The example involves pulling a crate, showing different free-body diagrams at different stages of the crate's motion (before it moves, after it moves at constant velocity).

Gravitational potential energy

An object in the gravitational field of Earth has associated gravitational potential energy U_grav = mg*y (related to vertical position y and acceleration g due to gravity)

7.6 - Example problem (Crate on a Ramp)

A problem involving a crate sliding up and down a ramp. The problem involves finding speed at different positions on the surface of the inclined plane and its relationship with potential and kinetic energy.

Chapter 6: Work and Kinetic Energy

Force required to create movement (in a straight line)
Work done by a force = force × displacement × cos (angle between force and displacement)

Units of work/energy

The SI unit of work/energy is the Joule (J)

Work Done by a Constant Force

The work done by a constant force is expressed mathematically with a vector dot product

Types of Work

Positive work: When force component is in direction of displacement
Negative work: When force component is opposite to displacement
Zero work: When force component is perpendicular to displacement

Total Work

This is the net work done by all forces acting on an object. A change in kinetic energy corresponds to work being done on an object

Kinetic Energy

Kinetic energy of an object = 1/2 × mass × velocity² = (1/2)*mv²

Chapter 8: Momentum, Impulse, and Collisions

Momentum and Newton's Second Law

Momentum p = mass × velocity
Newton's 2nd law ΣF = dp/dt (which relates net force and rate of change of momentum.)

Conservation of Momentum

The total momentum of an isolated system (where no external forces are acting) is conserved.

8.2 & 8.5 - Example problems (Momentum/Collisions/etc.)

Problems illustrating momentum and its conservation

Power

Power is the rate at which work is done (P = W/t)
The SI unit for power is the watt (W).

Power (Lifting Box)

Examples illustrating power, including scenarios where work is done and time for doing the work, and calculating power output.

Gravitational Potential Energy (revisited)

The potential energy is related to the vertical position in a gravitational field.

7.6 - Example problem (Details about energy transformations using kinetic and potential energy)

Illustrates details related to energy transformations when an object is sliding up and down a inclined surface.

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Description

Test your understanding of key concepts in physics related to momentum, kinetic energy, and work. This quiz covers definitions, laws, and properties that govern these fundamental ideas. Perfect for students wanting to review essential physics principles.