Physics Chapter on Vectors and Moments

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Questions and Answers

What does it mean for vectors to be represented by sides of a polygon in the same order?

The vectors are all perpendicular to each other.

The vectors' tail of each vector starts at the head of the previous one. (correct)

The vectors are all parallel to each other.

The vectors form a closed shape, and their resultant is always non-zero.

If a set of vectors arranged in order forms a closed polygon, what is their resultant?

The resultant is equal to zero. (correct)

The resultant is equal to the sum of the magnitudes of the vectors.

The resultant cannot be determined.

The resultant is equal to a vector of the largest magnitude among the given vectors.

A vector R makes an angle θ with the x-axis. What is the correct expression for its horizontal component (x)?

$x = R \cos \theta$ (correct)

$x = R \sin \theta$

$x = \frac{R}{\cos \theta}$

$x = R \tan \theta$

A vector R makes an angle θ with the x-axis. What is the correct expression for its vertical component (y)?

$y = R \sin \theta$ (C) Signup and view all the answers

What is the correct formula to calculate the moment of a force?

Moment = Force x Perpendicular distance (C) Signup and view all the answers

What are the units for the moment of a force?

Nm (B) Signup and view all the answers

What is the condition for rotational equilibrium of a body, according to the principle of moments?

The total clockwise moment must be equal to the total anticlockwise moment. (B) Signup and view all the answers

What causes the weight of an object?

The gravitational attraction between the Earth and the small particles in the object (D) Signup and view all the answers

What can gravitational potential energy be expressed as?

$GPE = mgh$ (D) Signup and view all the answers

Which statement best describes the law of conservation of energy?

Energy is constant in an isolated system. (D) Signup and view all the answers

How is power defined in the context of work and energy?

Power is the rate of work done. (A) Signup and view all the answers

In terms of efficiency, how can it be expressed?

Both as a percentage and as a decimal. (C) Signup and view all the answers

Which equation represents momentum?

$p = mv$ (D) Signup and view all the answers

What occurs in the stress-strain behavior of rubber when it is subjected to loading?

The stiffness decreases and the chains uncoil. (C) Signup and view all the answers

What is represented by the area of the hysteresis loop in a stress-strain graph for rubber?

The total energy absorbed during loading. (C) Signup and view all the answers

Which of the following best describes hysteresis in the context of rubber?

The behavior during loading differs from that during unloading. (A) Signup and view all the answers

When two springs are connected in series, what must be considered to analyze their behavior under a load?

The equivalent force constant depends on both springs. (C) Signup and view all the answers

What effect can be felt when repeatedly stretching and releasing a rubber band due to hysteresis?

Heating occurs because of energy absorption. (B) Signup and view all the answers

What does the gradient of a velocity-time graph represent?

Acceleration (D) Signup and view all the answers

For an object moving with constant velocity, what would its acceleration-time graph look like?

A horizontal line at zero (A) Signup and view all the answers

What does the area under an acceleration-time graph represent?

Velocity (D) Signup and view all the answers

An object is moving with constant deceleration. Which describes its displacement-time graph?

A curve with a decreasing gradient (C) Signup and view all the answers

In the context of the bouncing ball example, what does a positive value of acceleration represent when considering the short time of contact with the ground?

The upward force exerted by the surface on the ball (B) Signup and view all the answers

For an object thrown upwards, what does the acceleration-time graph look like assuming the upward direction is positive?

A horizontal line at approximately -9.81 $ms^{-2}$ (C) Signup and view all the answers

In the bouncing ball example, what happens to the time of contact with ground after each bounce?

It increases each time because the force decreases. (C) Signup and view all the answers

What is true about the acceleration of the bouncing ball (ignoring time of contact with ground)?

It is always negative (C) Signup and view all the answers

What does the area under a velocity-time graph represent?

Displacement (D) Signup and view all the answers

If an object's displacement-time graph is a straight line with a positive gradient over a period, what is true about its velocity?

It is constant and positive (D) Signup and view all the answers

An object is dropped from a height. If upward direction is positive, which statement is true regarding its displacement?

The displacement decreases negatively over time. (B) Signup and view all the answers

Which of the following is true regarding the gradient on a displacement-time graph?

It represents the object's velocity. (B) Signup and view all the answers

For an object moving with constant acceleration, which graph would be a horizontal line?

Acceleration-time (C) Signup and view all the answers

An object is undergoing constant deceleration. Which best describes the shape of its velocity-time graph?

A straight line with a negative gradient. (D) Signup and view all the answers

In the bouncing ball example, when considering the short contact time, the time for which the ball is in air:

decreases after each bounce. (B) Signup and view all the answers

What does the gravitational field strength represent?

The amount of gravitational force acting per unit mass (B) Signup and view all the answers

Which of the following energy types is associated with a body’s position relative to the ground?

Gravitational potential energy (A) Signup and view all the answers

What is efficiency calculated as?

Useful energy output divided by total energy input times 100 (A) Signup and view all the answers

Which factor does NOT affect the rate of flow in a fluid?

Color of the fluid (B) Signup and view all the answers

What condition is necessary for Stoke’s law to apply?

The object should be spherical (B) Signup and view all the answers

What effect does increasing speed have on the drag experienced by a falling object?

Drag increases as speed increases (A) Signup and view all the answers

Which of the following best describes terminal velocity?

When the upward forces equal the weight of the object, resulting in zero resultant force (A) Signup and view all the answers

What does viscosity measure in fluids?

The resistance to flow (D) Signup and view all the answers

What equation represents Newton's second law when force is constant?

𝐹 = 𝑚(𝑣 − 𝑢)/𝑡 (B) Signup and view all the answers

What is the definition of impulse in the context of a constant force?

Impulse = force × time (A) Signup and view all the answers

In the law of conservation of momentum, what condition must be met for momentum to be conserved?

No external forces should be acting on the system. (C) Signup and view all the answers

What happens to the momentum during a coalescence collision?

Masses of colliding objects are added. (C) Signup and view all the answers

What is the relationship between initial momentum and final momentum in an isolated system?

Initial momentum equals final momentum provided no external forces are acting. (B) Signup and view all the answers

What defines the density of a fluid?

Density is defined as mass over volume. (D) Signup and view all the answers

During an explosion, what is a key principle that applies to momentum?

Momentum is always conserved in explosions. (C) Signup and view all the answers

In a scenario with a constant force, what is impulse equivalent to?

Change in momentum (B) Signup and view all the answers

For a body under the influence of a variable force, which statement is true regarding average force?

Average force is the change in momentum divided by time. (A) Signup and view all the answers

Study Notes

Mechanics and Materials

Motion
- Distance is a scalar quantity, measured in meters (m).
- Displacement is a vector quantity, measured in meters (m).
- Speed is the rate of change of distance, measured in meters per second (ms⁻¹).
- Velocity is the rate of change of displacement, measured in meters per second (ms⁻¹).
- Acceleration is the rate of change of velocity, measured in meters per second squared (ms⁻²).
- Acceleration occurs when speed changes, direction changes, or both.
- Constant circular motion involves changing velocity, thus acceleration.

Motion Graphs

Constant Gradient (Straight Line)
- Gradient = (y₂ - y₁)/(x₂ - x₁)
- Gradient = zero, if gradient is zero then gradient is horizontal
- Gradient = infinite, if gradient is vertical then gradient is infinite
- Constant positive gradient, if gradient is positive then it slopes upwards.
- Constant negative gradient, if gradient is negative then it slopes downwards, or constant slope downwards.
Varying Gradient (Curves)
- The gradient of a curve at any given point can be determined by drawing a tangent to the curve at that point.
- Displacement-time graph, gradient = velocity
- Velocity -time graph, gradient = acceleration.
- The area under the graph represents displacement and velocity; acceleration-time.

Graphs of Motion

Object with Constant Velocity
- Displacement graph is a straight line with a constant positive gradient.
- Velocity graph is a horizontal line at a constant value..
- Acceleration graph is a horizontal line with a value of zero.
Object with Constant Acceleration
- Displacement graph is a curve, concave upwards.
- Velocity graph is a straight line.
- Acceleration graph is a horizontal line at a constant value.
Object with Constant Deceleration
- Displacement graph is a curve, concave downwards.
- Velocity graph is a straight line.
- Acceleration graph is a horizontal line at a constant value.

Object Dropped and Thrown Upwards

Dropped Object
Assumes upward direction as positive.
Displacement graph is a curve.
Velocity graph has negative gradient, decreasing linearly.
Acceleration graph is a horizontal line at a constant value -9.81 ms⁻².
Thrown Upwards
Assumes upward direction as positive.
Displacement graph is a curve.
Velocity graph is decreasing linearly with negative gradient.
Acceleration graph is a constant value of -9.81 ms⁻².

Bouncing Ball

Displacement, Velocity, and Acceleration graphs: The graphs of a bouncing ball display parallel lines due to constant acceleration.
Area under Displacement Graph: the area represents total height
Gravity is constant, negative acceleration for the upwards motion and positive upwards motion.

Vectors

Vectors: Quantities that have both magnitude and direction.
Addition of Vectors in a Straight Line: Add magnitudes; direction of the resultant is the direction of the original vectors.
Vectors in Opposite Lines: Subtract magnitudes. Direction of the resultant is in the direction of the vector with the larger magnitude.
Vectors Perpendicular to Each Other: Pythagoras' Theorem to find the resultant vector.

Parallelogram and Polygon Laws

Parallelogram Law: If two vectors are represented as the sides of a parallelogram, the diagonal represents the resultant.
Polygon Law: Used for adding more than two vectors arranged as the sides of a polygon; the resultant vector can be drawn as a closing side of a polygon.

Resolving Vectors

Resolving a Vector: Finding two perpendicular components.
Components: are the projections along the x and y axes. (x- and y- components).
Cosine and sine are used for calculating components.
Finding the Resultant The combination of components.

Moments

Moment of a Force: A measure of the tendency for rotation.
Principle of Moments: Total clockwise moments = total anticlockwise moments for equilibrium.
Centre of Mass/Centre of Gravity (COG): The point where an object's weight appears to act.

Equations of Motion

Equations:
- v = u + at
- v² = u² + 2as
- s = ut + ½at²
- s = ½(u + v)t
- Where:
  - v = final velocity
  - u = initial velocity
  - a = acceleration
  - t = time
  - s = displacement

Projectile Motion

Vertical Motion: Under the influence of gravity, initial vertical velocity and final vertical velocity at the highest point are 0.
Horizontal Motion: Constant horizontal velocity in the absence of air resistance.

Forces

Contact Forces: Forces acting between objects in physical contact.
Normal Contact Force: The support force exerted by a surface on an object resting on it.
Friction Force: The force opposing motion between surfaces in contact.
Drag Force: The force resisting motion of an object moving through a fluid; dependent on viscosity of fluid and speed.
Tension Force: A force transmitted through a string, rope, cable, etc.
Gravitational force: force of attraction between objects with mass.
Magnetic Force: Attraction force/repulsion force between magnets or magnetic materials.
Electrostatic Force: Attractive/repulsive force between electrostatically charged objects.
Free Body Diagrams: Diagrams showing all forces acting on an object.

Work Done

Work Done: Product of force and displacement in the direction of the force.

Energy

Energy: Ability to do work.
Kinetic Energy: Energy of motion.1/2mv²
Potential Energy: Energy of position.
Gravitational Potential Energy: Energy due to position relative to a gravitational field.
Conservation of Energy: Energy cannot be created or destroyed, only changed from one form to another.
Law of Conservation of Energy: All forms of energy in a closed system remain constant unless acted upon by external forces.

Power

Power: Rate of doing work, or rate of energy transfer.

Efficiency

Efficiency: Ratio of useful work output to total work input.

Momentum

Momentum: Product of mass and velocity.
Impulse: Change in momentum.
Conservation of Momentum: Total momentum in a closed system remains constant.

Fluids

Density: Mass per unit volume.
Upthrust: Upward buoyant force exerted by a fluid on an immersed body.
Archimedes' Principle: Upthrust = weight of fluid displaced.
Viscosity: Resistance to flow in a fluid.
Drag Force: Force opposing motion of an object moving through a fluid, increasing with speed.
Stokes' Law: Describes the viscous drag on a small sphere moving at low speeds through a fluid.
Laminar flow: smooth, orderly flow in a fluid.
Turbulent flow: Unordered, chaotic flow in a fluid.

Solids Materials

Hooke's Law: Stress is proportional to strain in the elastic region.
Elastic Strain Energy: energy stored in a stretched spring or material.
Stress: Force per unit cross-sectional area.
Strain: Change in dimension divided by original dimension.
Young's Modulus: a material property equal to the ratio of stress to strain in the elastic region.
Stiffness: A measure of a material's resistance to deformation.
Malleable materials: deform under compression with little or no brittle behaviour.
Ductile materials: deform under tension with little or no brittle behaviour.
Brittle materials: break or fracture without much deformation first.

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Description

This quiz tests your understanding of vectors, their representation as polygon sides, and concepts related to moments in physics. It includes questions on vector components, resultant vectors, and conditions for rotational equilibrium. Prepare to apply your knowledge of forces and moments in various scenarios.