mechanics one Flashcards by pen 6816

What is the relationship between all the angles between a vector and all the axies?

cos^2(x) +cos^2(y) +cos^2(z)=1

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How do you find magnitude of vector in a certain direction?

cos(x) = Ax / |A|

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What is the definition of force?

The rate of change of momentum

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What is centripetal force?

F=-mω^2r

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Does acceleration change with inertial frame of reference?

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When an object is undergoing circular motion, what is the equation for position?

i*r*cos(ωt) + j*r*sin(ωt)

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When an object is undergoing circular motion, what is the equation for velocity?

-i*r*ωsin(ωt)+jωrcos(ωt)

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What is the transpose of a matrix?

Shown my M^t

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Which way are elements numbered in a matrix?

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A 6x5 matrix is what size?

6 rows and 5 columns

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What is the equation to find the kinetic energy of a rotating object?

0.5*I*ω²

=0.5*m*v²

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What is the difference between shear stress and tensile stress?

Both are force / area. With tensile, surface of area and direction of force are perpendicular. With shear they are parralel.

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What is shear strain a measure of?

The angle of deflection γ that defines the change in shape. Also dimentionless.

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Symbol of shear stress

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Symbol for shear modulus?

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What is engineering stress?

Stress found with the intial area. Very similar to true stress when strain is small and before strain hardening happens.

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What is poisson’s ratio?

When a rod is pulled, the radius falls. Laterial strain is change in radius divided by original radius.

Poisson’s ratio is laterial strain / longitudinal strain.

Constant only in elastic range.

Typically between 0.25 and 0.33. Max value of 0.5

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What is torque?

M= r X F

all are vecters and the order can’t change.

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What is the 2nd moment of area of a rectangular cross section?

h³w/12

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What is the second momenet of area of a triangle with an axis through the base?

b*h³ /12

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In the elastic range, what is the relationship between shear stress and shear strain?

T/υ =G

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What is the equation for shear stress?

τ=Vay / Ib

V=total shear force

I= 2nd moment of area

b=breadth of cross sectional area

ay= 1st moment of area about neutral axis

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What is the equation for bending stress in a beam?

σ=m*y / I

m =internal bending moment about the neutral axis

I 2nd moment of area and y the 1st.

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How do you tell the difference between a mechanism and statical determinacy and indeterminacy?

m+r=2j

m=no. of axial forces you could find, r=external reactions and j no. of joints.

m+r=2j means determinate, m+r>2j means indeterminate and m+r<2j means collapse

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How do you find true strain?

ε_t=ln(1+ε)

True stress?

True stress=engineering stress\*(1+engineering strain)

If you have two vectors defining the sides of qudralterial, how is the area found?

Cross product togther and find magnitude The area of a triangle can be found by then diving by 2.

What is the moment of interia of a disk with the axis perpendicular to the sides goind through the centre?

0.5\*m\*r²

How is I found for a compound shape?

Find the centre of gravity and put the neutral axis through it. For each bit of the shape, use the standard formula to find I and add area\*(distance of C of M of bit of shape to C of M of the whole)² Add all together.

How do you find the shape factor

Shape factor=Z_p/Z_e Z_p=A(y₁+y₂)/2 Z_e=second moment of area/ Y_max

What is the plastic deformation section on a stress strain graph?

A flat plateu after the small fall.

What is the equation for the bending moment in beam?

bending moment=(stress\*2nd moment of area of whole shape) / distance to neutral axis Tension is + so ensure the sign of the distance to neutral has the right sign.

At complete plastic deformation, what is the area above the neutral axis?

The area below the neutral axis.

How do you find the plastic moment M_p

Find the neutral axis. Each section above and each section below will feel a force R Each R is found by multiplying the area of the section by the yield strength of the material. M_p is found by multiplying the R for each section by the distance of the centre of mass of the section by the distance to the neutral axis and adding all together.

How do you find Z_e

Find neutral axis and second moment of area for the whole shape. Y is the maximum distance any part of the shape is from the NA Divide I by y

How do you find Z_p?

Find total area of the shape. The neutral axis will divide the the shape into 2 sections. Y₁ and Y₂is the distance between the C of M of each section and the neutral axis. Z_p=0.5\*A\*(Y₁+Y₂)

There is a simply supported beam, of 4.0m span, carrying a uniformly distributed load of 6 kN/m. What is the maximum bending moment?

ωL² /8 6\*4² /8=12 kNm

What is the equation for centre of gravity?

What is the equation for moment of inertia? (with respect to area?)

I_y is the moment about the y axis. Same for x.

What is the equation that gives the extention of an object with a changing diameter?

If an object is on the point of slipping on a slope, what is the relationship between the coefficient of friction and the angle of slope?

tan (ø)=coefficient of friction

What is the equation for the energy in a spring?

0.5\*sping constant\*extention²

What is the gravitational force of attraction between two masses?

F=G\*m₁\*m₂\*r^-2

What is the escape velocity?

The speed where the gpe = ke

What is an auxmetic material?

One with a negative poissions ratio

When I is found for an object, it is the resitance to a force acting in what direction?

A direction perpendicular to the axis where I was found around.

What is the parallel axis theorem?

I_x=ï_x+Ad²_y I_x is the moment of interia to find, ï_x is a moment of interia that is known and goes through the centroid, A is the total area of the shape and d_y is the perpendicular distance between the axises.

What is the equation for the moment of interia with respect to mass?

How is moment of interia with respect to mass found from radius of gyration?

I=mk²

How do you find the work done by a torque?

Multiply by angle in radiens

What is the rotaional interia for a sphere with the axis going through the center?

0.4\*m\*r²

What is the relationship between angular speed and linear speed?

𝜔 =v/r

How do you find the maximum bending stress?

Use the normal bending stress equation but make y the perpendicular distance from the neutral axis to the furthest edge.

What is the perpendicular axis theorem?

Only applies to laminar (flat objects) The moment of inertia about an axis perpendicular to the plane is the sum of the moments of inertia of two perpendicular axes through the same point in the plane of the object.

What is the maximum deflection on a catilever beam with a force at the end?

FL³/3EI F is force at the end, L is length, I is second moment of area of cross section

If torque is positive, what direction does it go?

Anti-clockwise.

What is the relationship between shear modulous and young's modulous?

G=E/2(1+υ) G=shear mod E=young mod υ=poissons ratio.

What is the x and the y with the wigly bar on top with centre of mass questions?

The centre of mass co-ordinates of the finite element used for the integration.

What does a negative tensile stress mean?

Compression

What is the second moment of area of a circle?

π\*0.25\*r⁴

When drawing a bending moment diagram, where do you take the moment from?

The cut. The moment of the reaction force= moment of load + M

How do you find the 1st moment of area?

Divide into sections, multiply area of each section the distance to the neutral axis and add together.

How do you find the moment of inertia of a mass rotaing a distance r from the origin?

mass\*r²

mechanics one Flashcards

(63 cards)