ENG1011 Study

What is the Pythagorean theorem?

$$a²+b²=c²$$

What is the equation for spring potential energy?

$$PE_s=\dfrac{1}{2}kx²$$

What is the SUVAT equation for distance (where there is constant acceleration)?

$$s=ut+\dfrac{1}{2}at²$$

What is the equation for weight?

$$W=mg$$

What is the Pythagorean identity?

$$\sin^{2}\left(\theta\right)+\cos^{2}(\theta)=1$$

What is the SI unit for time?

Second (s)

What is the SI unit for length?

Metre (m)

What is the SI unit for mass?

Kilogram (kg)

What is the derived unit for speed?

$\dfrac{dx}{dx}$ (m/s)

What is the derived unit for acceleration?

$\dfrac{dv}{dx}$ (m/s²)

What is the unit for area?

m²

What is the unit for density?

kg/m³

What is the unit for Force?

Newton (N)

What is the unit for pressure and stress?

Pascal (Pa)

What is the unit for energy, work and heat?

Joule (J)

What is the unit for power?

Watt (W)

What does the prefix Giga (G) represent?

$$10^9$$

What does the prefix Mega (M) represent?

$$10^6$$

What does the prefix Kilo (k) represent?

$$10³$$

What does the prefix Milli (m) represent?

$$10^-3$$

What does the prefix Micro ($\mu$) represent?

$$10^{-6}$$

What does the prefix Nano (n) represent?

$$10^{-9}$$

What does dimensional homogeneity mean?

Each term on both sides of the equation must be expressed in the same dimensions

How many sigfigs are in 12.34N?

4 sigfigs (precision of 0.01N)

How many sigfigs are in 12N?

2 sigfigs (precision of 1N)

How many sigfigs are in 146?

3 sigfigs

How many sigfigs are in 0.0045?

2 sigfigs

How many sigfigs are in 1002?

4 sigfigs

How many sigfigs are in 45.600?

5 sigfigs

How many sigfigs are in 4500?

2 sigfigs

When does a value have infinite sigfigs?

When the value is known exactly. For example, we know there is 12 in a dozen, so 12 has infinite sigfigs.

What is a scalar value?

A positive/negative quantity described completely by its magnitude.

What is a vector?

Any quantity that is completely described by both a magnitude and direction.

Length, mass, time, speed, volume are examples of (scalar/vector)

Scalar

Force, displacement, velocity, acceleration are examples of (scalar/vector)

Vector

For an object to be in equilibrium what is the resultant force ($F_R$ )?

$$F_R=0$$

What is the law of cosines?

$$C=\sqrt{A^{2}+B^{2}-2AB\cos\left(c\right)}$$

What is the law of sines?

$$\dfrac{A}{\sin\left(A\right)}=\dfrac{B}{\sin\left(B\right)}=\dfrac{C}{\sin\left(C\right)}$$

If you have the x and y forces, how do you calculate the magnitude of the total resultant force?

$$|F_R|=\sqrt{(F_{R,x})^2+(F_{R,y})^2}$$

What is the definition of Force?

An action that causes a body to accelerate

What is the definition of Mass?

a measure of a body’s inertia or its amount of substance

What is Newton’s First Law?

If a particle is at rest (or moving with constant velocity), it will remain at rest (or continue to move with constant velocity) unless acted on by a force.

What is Newton’s Second Law?

A particle acted on by a force will accelerate in the direction of the force. The magnitude of the acceleration is proportional to the magnitude of the force and inversely proportional to the mass of the particle ($F=ma$)

What is Newton’s Third Law?

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

What is static equilibrium?

A body is at rest ($<span>v=0, a=0</span>$ )

What is dynamic equilibrium?

body moving at a constant velocity $v\ne0, a=0$

What are springs?

Springs are elastic members that exert a force or torque, and absorb energy which are usually stored for later release

What is Hooke’s Law?

$$F=kx$$

Where is Hooke’s law valid?

In the elastic region of the material

What are the equations for springs in series (2 equations)?

$$x_{total}=x_1 + x_2+ x_3$$

$$\dfrac{1}{K_e}=\dfrac{1}{K_1}+\dfrac{1}{K_2}+\dfrac{1}{K_3}$$

What are the equations for springs in parallel (2 equations)?

$$F_{total}=F_1+F_2+F_3$$

$$K_e=K_1+K_2+K_3$$

What is a fixed pulley attached to?

A stationary object

What is a movable pulley attached to?

A load that needs to be lifted or moved

What is the equation for Mechanical Advantage?

$$MA=\dfrac{F_{load}}{F_{input}}=\dfrac{d_{input}}{d_{output}}$$

What is the elastic region?

The initial phase of material deformation where the material returns to its original shape upon removal of the load.

What is a plastic region?

The phase beyond the elastic limit where a material undergoes permanent, non-reversible deformation under load.

What direction is a positive moment (clockwise/counter-clockwise)?

Counter-clockwise

Where is the equivalent point force located for a uniformly distributed load?

At the centroid of the uniformly distributed load.

What can a support (in general) prevent?

Translation of a body, and rotation of a body.

How many reaction forces are in a fixed support?

3 Reaction Forces — M, F_x, F_y

A fixed support cannot:

Rotate, translate horizontally, translate vertically

How many reaction forces does a pinned support have?

2 Reaction Forces — F_x and F_y

What does a pinned support do?

Allows rotation, restricts any translation.

How many reaction forces does a roller support have?

1 Reaction Force — $F_\perp$

What does a roller support do?

Allows translation along the surface, allows rotation

Restricts translation perpendicular to the surface

In a two force member, equilibrium is achieved if:

• The forces are equal and opposite

• The forces share the same line of action

What forces can two force members experience?

Tension and compression

In a three force member, equilibrium is achieved if:

• $$\sum F_R=0$$

• $$\sum M_R=0$$