Mechanics and Materials

What is a vector?

Any physical quantity that has direction as well as magnitude, such as velocity, force and displacement.

1 of 96

What is the scalar of velocity?

Speed (has no direction)

2 of 96

How do you add two vectors acting at 90o to each other?

Use Pythagoras: a2 + b2 = c2 (the resultant is the hypotenuse)

3 of 96

Two forces; 8N and 3N, act on each other. Which of these is NOT a possible resultant force? 10N; 8.5N; 4N; 11N

4N - the smallest force possible is 8-3 = 5N ; thus a resultant force of 4N is too small.

4 of 96

How do you resolve a force into horizontal and vertical components?

Use SOHCAHTOA (Fcos0 horizontal ; Fsin0 vertical)

5 of 96

What is an object doing if it's in equilibrium?

Not moving OR moving at a constant velocity. It has no resultant forces acting on it (Newton's First Law)

6 of 96

A box is stationary on a hill of angle 0 (theta). Three forces, W (weight), R (reaction) and F (friction) act on it. How is F calculated?

F = Wsin0 (The angle 0 in the equilibrium triangle is between the weight (hypotenuse) and the reaction force.)

7 of 96

For an object in equilibrium acted upon by three forces, the resultant of F1 + F2 =.....

F3 (or more correctly, -F3 ; so the total is 0N)

8 of 96

Define a moment.

Force x perpendicular distance from the line of action of the pivot

9 of 96

What is the unit of a moment?

Nm

10 of 96

What is the principle of moments?

For an object in equilibrium; the sum of the clockwise moments = sum of the anticlockwise moments

11 of 96

What is the centre of mass?

The point through which a single force on a body has no turning effect; where the mass is thought to act.

12 of 96

If a question refers to a uniform plank, what can you deduce?

The centre of mass is directly in the centre of the body

13 of 96

What is a couple? What is its equation?

A pair of equal and opposite forces acting on a body to produce a turning effect: force x perpendicular distance between the line of action of the two forces

14 of 96

What is stable equilibrium?

When an object will return to its base if titled and released : i.e. the line of action of the weight remains within the base.

15 of 96

What is needed for an object to topple?

The line of action of the weight needs to fall outside the base, so a resultant turning effect is produced. Fd > Wb/2 ; where F is the force applied, d is the distance to the base, W is the weight and b/2 is half the width of the base

16 of 96

Why is a bus full of passengers on the upper deck unstable?

Because it has a high centre of mass, and a narrow base (for its height) so a smaller angle is needed for the weight to fall outside the base and the bus to turn.

17 of 96

If an object weight W is suspended in the middle of a string, what can be said about the tension in both halves?

The vertical components of the tensions added together = W. Note that both strings have the same horizontal tensions, as there is no net horizontal "swing".

18 of 96

How is average speed found from a distance/time graph of a changing speed?

total distance travelled / total time

19 of 96

How is the instantaneous velocity found?

By drawing a tangent to the graph at the point t and calculating its gradient.

20 of 96

When is it necessary to consider velocity rather than speed?

When an object's direction is changing, such as a bouncing ball (-ve velocity on the bounce up, for example).

21 of 96

What is acceleration?

Change in velocity per unit time

22 of 96

How is it found from a velocity time graph?

The gradient of the line. (It it is non uniform, use a tangent to the curve).

23 of 96

How is displacement found from a velocity-time graph?

The area under the graph. If it drops below the x axis this is negative displacement. When the areas are added, the final displacement is found. If it equates to zero, the object returned to the starting position.

24 of 96

What do the SUVAT equations assume?

Acceleration is constant.

25 of 96

Give the SUVAT equation used to find s if v isn't known.

S = ut + 1/2at2

26 of 96

Give the SUVAT equation that doesn't include a

s = ( (u + v)/2 )t

27 of 96

Give the SUVAT equation that is a direct rearrangement of the acceleration equation

v = u+ at

28 of 96

Give the equation used to find final veolocity of an object accelerating by a over distance s from an initial velocity of u.

v2 = u2 + 2as

29 of 96

Does a heavy object fall faster than a lighter one?

No. They both fall with acceleration g, 9.81 ms-2

30 of 96

How can g be determined?

Measure the time taken for a ball to drop a known distance s (use a slow-motion camera, or light gates). Use s = ut + 1/2 at2 ; but as u is 0 (dropped from rest) this is s=1/2gt2. A graph of s on y and t2 on x will have gradient g/2

31 of 96

In projectile motion, horizontal and vertical components are _(a)_. Acceleration is _(b)_ in _(c)_ but zero in _(d)_. Therefore, _(e)_ velocity is the _(f)_ throughout.

(a) independent of each other (b) 9.81 ms-2 (c) vertical direction (d) horizontal direction (e)Horizontal (f) constant

32 of 96

What is initial vertical velocity OFTEN taken as in projectile questions?

0 ms-1 (if an object is dropped/fired from rest, i.e. not if it is thrown with a particular velocity)

33 of 96

What is Newton's First Law?

Objects stay at rest or in constant motion unless acted upon by a resultant force.

34 of 96

What is F proportional to?

ma (mass x acceleration)

35 of 96

Which of Newton's Law's is this a simplification of?

The Second Law

36 of 96

How is weight different from mass?

Mass is a physical quantity that is measured in kg and (usually) remains constant for a body. Weight is a force (measured in N) and varies depending on the gravitational field strength. W =mg (an extension of F=ma)

37 of 96

How can F=ma be used when more than one force acts, to find a?

Find the resultant force first (F2-F1, resolving etc), BEFORE putting into F=ma

38 of 96

How may lift problems (to find Tension) be solved in this way?

1.Decide which is greater, weight of the lift or chord tension (i.e moving up or down?) 2. mass x lift acceleration gives the "resultant", rearrange to find T: (T-mg) = ma OR (mg-T) = ma *this is the same as taking -ve a into account

39 of 96

What is another term for air resistance?

Drag / fluid drag

40 of 96

What is terminal speed?

The maximum speed an object can reach; when drag forces=motive forces/weight so the resultant is 0N and no acceleration occurs

41 of 96

Why can streamlined cars move faster?

They experience lower air resistance, so can reach higher terminal speeds as it takes more velocity for the drag forces to equal the car's motive force.

42 of 96

What is thinking distance?

The distance traveled in the time taken for a driver to react to a hazard

43 of 96

What can be used to calculate breaking distance (the distance traveled under the breaking forces)?

The SUVAT equations; like v2 = u2 + 2as

44 of 96

What is the equation for force that explain why a car crash puts great forces on a passenger?

impulse (change in momentum) / time

45 of 96

What is momentum?

Mass x velocity ; unit kgms-1

46 of 96

Is it vector or scalar?

Vector. So an object rebounding off a wall with the same velocity will have a change of momentum of 2mu

47 of 96

What is Newton's Second Law in terms of momentum?

The rate of change of momentum of an object is proportional to the resultant force acting on it.

48 of 96

Thus, what is the unit for rate of change of momentum?

N (It's force!)

49 of 96

What is the unit for impulse (change in momentum) other than kgms-1

Ns (Force x time)

50 of 96

Hence, in a force-time graph, how is impulse found?

Area under the graph, Fxtime

51 of 96

An object hits a wall at an angle 0 (theta) to the normal to the wall and rebounds at the same speed. What was the impact force?

Only the component of the velocity along the normal of the wall is considered, thus the momentum is m x ucos0 . As velocity is the same, the change is -2 mu cos 0 ; so force is -2mu cos 0 / time of impact

52 of 96

What is Newton's Third Law of motion?

When two objects interact, they exert equal and opposite forces on each other.

53 of 96

What is the principle of momentum?

For a system of interacting objects, the total momentum remains constant, provided no external resultant force acts on the system

54 of 96

Object A mass MA collides at velocity VA with stationary Object B mass MB. The move off together What is the velocity after?

MAxVA = V(MA + MB) by conservation of momentum. Thus V of both objects is (MAxVA)/(MB+MA)

55 of 96

In an explosion, what is the total momentum after?

Zero kgms-1. This is as it is 0 before the explosion, and as it must be conserved it is the same after.

56 of 96

Explain why, therefore, shrapnel from an explosion moves off in all directions?

They move off in opposite directions to conserve the zero momentum, as velocity is a vector and will be negative/positive in different directions.

57 of 96

What is an elastic collision? Give an example.

One where no kinetic energy is lost. For example, particles and atoms colliding.

58 of 96

Give an example of an inelastic collision.

A bouncing ball that will not return to its original height and will eventually stop.

59 of 96

What is work?

The energy needed to move a force a distance in the direction of the force.

60 of 96

Energy cannot be (A) but eventually is dissipated as (B)

(A) created or destroyed (B) heat energy

61 of 96

What is the area under a force-displacement graph?

Work done (J)

62 of 96

If an object is acted upon by force F at an angle 0 to the direction of motion, in which it moves s metres, what is the work done?

w = Fxsxcos0

63 of 96

Thus, what is the energy stored in a spring? (Hint: consider the force - extension graph for a wire obeying Hooke's law)

1/2 x F x e , as extension is a displacement (as in W=Fs) and the area under the graph is a triangle, thus as the area is work done 1/2bh = 1/2 F x e

64 of 96

What is the equation for kinetic energy?

1/2mv2

65 of 96

What is Ke gained equal to for a falling object (assume no friction)?

GPE lost, or 1/2mv2 = mgh (so you can cancel mass, if constant, to give 1/2v2=gh)

66 of 96

What is power?

The rate of transfer of energy, P=e/t

67 of 96

How can you find the power of your legs by running up stairs?

Find the vertical height climbed (the force, your weight, is acting vertically). Multiply by your weight (thus mgh) and divide by the time taken to run (P=e/t)

68 of 96

What is another equation for power in terms of velocity?

p=Fv (force x distance moves per second in that direction). This is as Wd = f x d ; so P = fxd/t = f x (d/t) = fv

69 of 96

How is efficiency calculated?

Useful energy transferred/energy supplied to the machine

70 of 96

Define denisty

Mass per unit volume

71 of 96

How do you convert from cm3 to m3 ?

Multiply by x10-6 - which is (x10-2)^3 as the scale factor is cubed

72 of 96

How is the density of an irregular object found?

The mass is recorded on a mass balance. The object is then submerged in water, in a measuring cylinder. The change of volume is noted. Density = mass/volume

73 of 96

What is Hooke's Law?

Force needed to stretch a spring is proportional to the extension of the spring from its natural length.

74 of 96

What point will a wire not obey this beyond?

The limit of proportionality (don't confuse with the elastic limit!)

75 of 96

What is the elastic limit?

The point beyond which, if a wire is stretched, it will not return to its original shape (undergone plastic deformation).

76 of 96

What is the equation relating spring modulus to force?

F = k x e (Force = spring modulus x extension from natural length)

77 of 96

What is the effective spring constant of springs 1 and 2 in parallel?

K = K1 + K2

78 of 96

What is the effective spring constant for springs 1 and 2 in series?

1/k = 1/k1 + 1/k2

79 of 96

Substitute the force-spring modulus equation into the energy equation to find the elastic potential energy where F is not known.

E = 1/2 k e2 (Energy = 1/2 x spring modulus x extension^2)

80 of 96

What is tensile stress?

Tension/cross sectional area . Measured in Pa

81 of 96

What is tensile strain?

Extension/natural length. A ratio with no units.

82 of 96

What is the Young's Modulus?

Stress/Strain (The stiffness of a material). Measured in Pa

83 of 96

What happens at the Yield point 1 on a stress/strain graph?

The wire weakens temporarily and suffers plastic deformation

84 of 96

What happens at Yield point 2?

A small increase in stress causes a large increase in strain, and the material undergoes plastic flow.

85 of 96

What is the UTS?

The Ultimate Tensile Stress, the masximum stress a wire can undergo (its Strength) before it weakens, extends and breaks

86 of 96

What is the gradient of the stress/strain graph?

The Youngs Modulus. Steeper gradient = higher YM

87 of 96

How do you tell how strong a material is from the graph?

Compare the heights of the UTS (maximum height on the y axis) higher = stronger

88 of 96

What will a brittle material exhibit?

It breaks suddenly without deforming first / having any noticeable yield

89 of 96

What is a ductile material?

One that can be stretched out into a wire, has a greater breaking point (withstands more strain)

90 of 96

For a metal wire, on a load-extension graph, the loading and unloading curves are _(a)_ unless _(b)_.

(a) the same (b) The elastic limit is passed

91 of 96

Rubber has a low what?

Limit of proportionality (but NOT elastic limit - it returns to it's original shape

92 of 96

What is the area between a loading/unloading curve?

The energy stored in a material as the internal energy of the molecules (difference between the energy used to stretch the material and that which is recovered).

93 of 96

What is this area if the graph doesn't return to the origin (i.e. is permanently deformed)?

The internal energy AND the energy needed to permanently deform the material (e.g. a polythene *****).

94 of 96

What is the total energy under the curve?

Elastic strain energy (energy to stretch the material)

95 of 96

Give the order of magnitude for the YM of metals, like copper and steel

x10^11

96 of 96

Get Revising

Mechanics and Materials

Comments

Similar Physics resources:

Comments

Related discussions on The Student Room

Similar Physics resources: