Physical Quantities and Forces in Mechanics

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Questions and Answers

What type of variables have only magnitude and no direction?

Concurrent forces

Resultant forces

Scalar variables (correct)

Vector variables

Which law can be used to determine the resultant of concurrent forces?

Friction law

Newton's second law

Bernoulli's principle

Parallelogram law (correct)

What are forces that require physical contact between objects called?

Resultant forces

Concurrent forces

Action-at-a-distance forces

Surface forces (correct)

Which of the following is an example of a vector variable?

Speed Signup and view all the answers

What occurs to forces between two objects when their interaction ceases?

The forces cease to exist Signup and view all the answers

What characterizes action-at-a-distance forces?

They can exert a push or pull without physical contact. Signup and view all the answers

Which of the following is an example of an action-at-a-distance force?

Gravitational force Signup and view all the answers

According to Newton's First Law, what will happen to an object with zero net force acting on it?

It will remain in its state of motion. Signup and view all the answers

Which equation correctly represents Newton's Second Law of Motion in terms of acceleration?

F = m * a Signup and view all the answers

In the context of forces, what do the components of a force represent?

The individual forces that sum to the net force. Signup and view all the answers

What does the third law of motion state about the forces exerted by two objects on each other?

They exist in equal magnitude and opposite direction. Signup and view all the answers

How is centrifugal force defined in a rotating frame of reference?

An inertial force directed radially outwards from the axis of rotation. Signup and view all the answers

What is the purpose of the normal force acting on an object in contact with a surface?

To prevent the object from penetrating the surface. Signup and view all the answers

In what situation does the friction force typically act?

In the opposite direction to the object's motion. Signup and view all the answers

What is the equation for calculating the centrifugal force experienced by an object in a rotating frame?

$F = m imes oldsymbol{ heta} imes r$ Signup and view all the answers

Study Notes

Physical Quantities in Machine Construction

Physical quantities are categorized as scalar or vector.
Scalar quantities have magnitude only (e.g., length, mass, temperature, time).
Vector quantities have both magnitude and direction (e.g., speed, force, torque).
Vector variables are represented using bold symbols with arrows on top.

Resultant Forces

Several forces acting on a body can be combined to find the resultant force.
Resultant force of concurrent forces can be found using parallelogram law, triangle rule or polygon rule.
Concurrent forces are those whose lines of action intersect at a common point.
The resultant force is the vector sum of the components.

Forces: Contact and Action-at-a-Distance

Forces are interactions between objects.
Contact forces arise from physical contact (e.g., frictional, tensional, normal forces).
Action-at-a-distance forces act without physical contact (e.g., gravitational, electric, magnetic forces).

Forces and Resultants or Components

Force is a push or pull.
Force, often represented by a vector F, can be resolved into components along different axes using trigonometric functions.
F_x = F cos α
F_y = F sin α
|F|= √(F_x² + F_y²)
α = tan^-1 (F_y/F_x)

Newton's Laws of Motion

First Law: An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Second Law: The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. (F = ma)
Third Law: For every action, there is an equal and opposite reaction.

Centrifugal Force

An apparent outward force experienced by an object moving in a circular path.
Directed away from the axis of rotation.
F = mω²r

Normal Force

A contact force that acts perpendicular to the surface of contact.
A reaction force to the force of an object pressing against a surface.

Friction Force

A force that opposes motion between two surfaces in contact.
Can be static (resists initiation of motion) or kinetic (resists motion already occurring.)

Moment of Force

Also known as torque.
A force that tends to cause rotation.
M = Fd, where d is the perpendicular distance from the pivot point to the line of action of the force.
Calculation requires the perpendicular distance—the shortest distance between the force and the pivot point.

Couple of Forces

A pair of equal, opposite forces that do not act along the same line.
They cause a net moment of rotation (torque).
M = Fd

Pressure

Force applied perpendicular to a surface per unit area.
p = F/A

Hydrostatic Pressure

The pressure exerted by a fluid at rest due to the force of gravity.
p = ρgh + p_a

Archimedes' Principle

Upward buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
F_B = ρ_fluid g V_displaced

Dynamic Pressure

Pressure exerted by a moving fluid.
p_dynamic = 0.5ρv²

Work, Power, and Energy

Work: The product of force and displacement in the direction of the force.
W = Fd
Power: The rate at which work is done.
P = W/t
Energy: The capacity to do work or exist in a particular form (potential, kinetic, etc.)

Transmission Shafts

Circular shafts that transfer power from one machine component to another.
Power output is equal to the product of the resultant torque and the angular velocity. (P = Tω)

Efficiency

The ratio of power output to power input for a machine.
η = (Power output)/(Power input)

Energy

Gravitational Potential Energy (GPE): Energy due to an object's height above a reference point.
E_g= mgh
Elastic Potential Energy (EPE): Energy stored in a deformed elastic object.
E_e = 1/2kx²
Kinetic Energy (KE): Energy due to motion.
E_k = 1/2mv²

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Description

Explore the fundamental concepts of physical quantities and forces in machine construction. Understand the differences between scalar and vector quantities, the methods to find resultant forces, and the classification of contact and action-at-a-distance forces. This quiz is designed for students studying mechanics in engineering.