Mechanics and materials

Question 1

What is the difference between scalars and vectors?

Answer 1

Scalars describe only a magnitude while vectors describe magnitude and direction.

Examples of scalars include distance, speed, mass, and temperature; examples of vectors include displacement, velocity, force/weight, and acceleration.

Question 2

How do you find the resultant vector when two vectors are perpendicular?

Answer 2

Use Pythagoras’ theorem: R = √(A² + B²).

For example, if two forces have magnitudes of 5 N and 12 N, the resultant force is R = 13 N.

Question 3

What is the method used to find the direction of a resultant vector?

Answer 3

Use trigonometry, specifically the tangent function: tan θ = opposite/adjacent.

In the context of vectors, θ is the angle from the horizontal.

Question 4

What is resolving vectors?

Answer 4

Resolving vectors involves breaking a vector into its components using trigonometry.

For a vector V, the components can be found using: x = V cos θ and y = V sin θ.

Question 5

What is the formula for calculating the moment of a couple?

Answer 5

Moment of a couple = Force × Perpendicular distance between the lines of action of forces.

A couple consists of two equal and opposite forces acting on an object.

Question 6

What is the principle of moments?

Answer 6

For an object in equilibrium, the sum of anticlockwise moments about a pivot is equal to the sum of clockwise moments.

Question 7

What defines the center of mass of an object?

Answer 7

The center of mass is the point at which an object’s mass acts.

In a uniform object, the center of mass is located at its geometric center.

Question 8

What is instantaneous velocity?

Answer 8

Instantaneous velocity is the velocity of an object at a specific point in time.

It can be found from a displacement-time graph by calculating the gradient at that point.

Question 9

Define average velocity.

Answer 9

Average velocity is the total displacement divided by the total time taken.

Question 10

What is uniform acceleration?

Answer 10

Uniform acceleration is when the acceleration of an object is constant.

Question 11

What is the equation for calculating displacement with uniform acceleration?

Answer 11

s = ut + (1/2)at².

Where s is displacement, u is initial velocity, a is acceleration, and t is time.

Question 12

What does a velocity-time graph represent?

Answer 12

The gradient of a velocity-time graph represents acceleration, and the area under the graph represents displacement.

Question 13

What happens to the vertical and horizontal components of a projectile’s motion?

Answer 13

They are independent and can be evaluated separately using uniform acceleration formulas.

Question 14

What is terminal velocity?

Answer 14

Terminal velocity occurs when the frictional forces and driving forces are equal, resulting in no resultant force and constant speed.

Question 15

State Newton’s 1st law of motion.

Answer 15

An object will remain at rest or travel at a constant velocity until it experiences a resultant force.

Question 16

What is Newton’s 2nd law of motion?

Answer 16

The acceleration of an object is proportional to the resultant force acting on it: F = ma.

Question 17

What is Newton’s 3rd law of motion?

Answer 17

For every action, there is an equal and opposite reaction.

Question 18

What is momentum?

Answer 18

Momentum is the product of mass and velocity: Momentum = mass × velocity.

Question 19

What is the principle of conservation of momentum?

Answer 19

Total momentum before an event is equal to total momentum after the event in the absence of external forces.

Question 20

What does impulse refer to in physics?

Answer 20

Impulse is the change in momentum, which is also equal to the area under a force-time graph.

Question 21

Fill in the blank: The vertical component of velocity can be calculated using _______.

Answer 21

V sin θ.

Question 22

Fill in the blank: The horizontal component of velocity can be calculated using _______.

Answer 22

V cos θ.

Question 23

What is momentum?

Answer 23

The product of mass and velocity of an object

Momentum = mass × velocity

Question 24

What is the principle of conservation of momentum?

Answer 24

Momentum before an event is equal to momentum after the event when no external forces act

This is used to find the velocity of objects after collisions.

Question 25

How do you calculate total momentum before a collision?

Answer 25

Total momentum before = (mass1 × velocity1) + (mass2 × velocity2) ## Footnote Example: A car with mass 500 kg and velocity 4 m/s collides with a stationary truck of mass 1500 kg.

Question 26

What is power in the context of work and energy transfer?

Answer 26

Power (P) is the rate of energy transfer ## Footnote P = ΔW/Δt = F × Δs/Δt

Question 27

Define work done (W).

Answer 27

Work done is defined as the force causing a motion multiplied by the distance travelled in the direction of the force ## Footnote W = F × s × cos(θ)

Question 28

What is impulse?

Answer 28

Impulse is the change in momentum, calculated as the product of force and time ## Footnote F × Δt = Δ(mv)

Question 29

What are the two types of collisions?

Answer 29

* Elastic - both momentum and kinetic energy are conserved * Inelastic - only momentum is conserved, some kinetic energy is converted into other forms ## Footnote Example: An explosion is an inelastic collision.

Question 30

What is the formula for kinetic energy?

Answer 30

Kinetic energy (KE) = 1/2 mv² ## Footnote Where m is mass and v is velocity.

Question 31

What does the principle of conservation of energy state?

Answer 31

Energy cannot be created or destroyed, only transferred from one form to another ## Footnote Total energy in = Total energy out

Question 32

How is efficiency calculated?

Answer 32

Efficiency = (useful power output / total power input) × 100 ## Footnote This gives the efficiency as a percentage.

Question 33

What is density?

Answer 33

Density is the mass per unit volume of a material ## Footnote It measures how compact a substance is.

Question 34

What does Hooke's law state?

Answer 34

Extension is directly proportional to the force applied, given constant environmental conditions ## Footnote This is shown by a straight line graph in a force-extension graph.

Question 35

What is the elastic limit?

Answer 35

The elastic limit is just after the limit of proportionality, beyond which a material deforms plastically ## Footnote If the force applied exceeds this limit, the material will be permanently stretched.

Question 36

Define tensile stress.

Answer 36

Tensile stress is the force applied per unit cross-sectional area ## Footnote Stress = F/A

Question 37

Define tensile strain.

Answer 37

Tensile strain is the extension over the original length ## Footnote Strain = ΔL/L

Question 38

What is the Young modulus?

Answer 38

The Young modulus describes the stiffness of a material, defined as the ratio of stress to strain ## Footnote E = Stress/Strain

Question 39

What is breaking stress?

Answer 39

Breaking stress is the value of stress at which the material will break apart ## Footnote This value depends on the conditions of the material, such as temperature.

Question 40

What happens when a material is stretched beyond its elastic limit?

Answer 40

The material will not return to its original shape and will deform plastically ## Footnote The area between the loading and unloading lines on a force-extension graph represents the work done to permanently deform the material.

Question 41

What is elastic strain energy?

Answer 41

The energy stored when work is done on a material to stretch or compress it ## Footnote Elastic strain energy = 1/2 F × ΔL