mechanics Flashcards

Question

how do you increase the accuracy of the method used in the practical for g? MECHANICS

Answer 1

increasing accuracy in method: ⋅ in the experiment , using a computer to automatically release and time the ball bearing's fall removes the random error that might arise if you timed a ball bearing manually by eye with a stopwatch, reducing the uncertainty in the time measurement

Answer 2

you could do a similar experiment with light gates: ⋅ drop a ball bearing from a height h so it falls through the light gate. the light gate then automatically calculates the velocity of the falling object ⋅ you can then use (v^2) = (u^2) + 2as to calculate the acceleration due to gravity, g

Answer 3

⋅ both methods give less uncertainty in g than measuring the time of the ball manually by the eye would ⋅ light gates can calculate the velocity of the ball automatically, instead of it being calculated from the time measurements, which could reduce systematic error ⋅ this means that the main uncertainty would now only be caused by measuring h (instead of t)

Answer 4

1) set up a video camera in front of a metre rule and record the ball as it is dropped from the top of the ruler 2) once the ball hits the floor, you can stop recording and analyse the video with video editing software 3) go through the video frame by frame, making note of the distance the ball has travelled every 0.1 seconds 4) create a table to calculate the ball's velocity. you can then calculate the average value for g from the table or plot a graph of velocity against distance. the gradient of this graph will give acceleration due to gravity

Answer 5

you can use a regular camera in a dark room with a strobe light to find g 1) set the camera to take long exposure 2) while the camera is taking the photo, turn on the strobe light and drop the ball 3) as the ball falls, it will be lit up at regular intervals by the strobe light 4) this means the ball will appear multiple times in the photograph, in a different position each time 5) calculate the change in distance between each location of the ball and create a table (shown) 6) the frequency the strobe light flashes at gives you the time interval between distances 7) work out the velocity of the ball using the table and plot a graph of velocity against time - g will be the gradient

Answer 6

1) the main cause of uncertainty in this experiment is in measuring the distance fallen by the ball - other sources of uncertainty are small bc you're not timing the ball yourself (bc video is measuring time) 2) a parallax (systematic error due to looking at the ruler at an angle) will also affect your distance measurements, so make sure your camera is at a right angle to the ruler (and use multiple cameras if the ruler is large) 3) an uncertainty caused by the time interval between pictures can be reduced by either increasing the frequency of the strobe light, or using a camera with a higher frame rate 4) repeating the experiment and calculating the average value of g can also increase the accuracy of the experiment 5) measuring over a larger distance or using smaller time increments means you will average over more values, which is likely to give a more accurate value for g

Answer 7

you can just replace a with g in equations of motion (suvat) when talking about projectiles

Answer 8

as g is a constant acceleration, you can use the equations of motion (suvat) in projectiles

Answer 9

⋅ g acts in the vertical plane (NOT THE HORIZONTAL PLANE) and acts downwards ⋅ g does NOT act in the horizontal plane ⋅ so also note that g doesn't affect the horizontal component, only the vertical, because g acts vertically

Answer 10

1) resolve the initial velocity of the object into the horizontal and the vertical components 2) use the vertical component to work out how long an object is in the air and/or how high it goes 3) use the horizontal component to work out how far the object goes horizontally while it's in the air

Answer 11

⋅ a graph of displacement against time for an accelerating object always produces a curve ⋅ if the object is accelerating at a uniform rate, then the rate of change of the gradient will be constant (the second derivative will be constant)

Answer 12

⋅ different accelerations have different gradients ⋅ for example, when comparing the green example (the one on the front of the flashcard) and the pink examples (shown below), if the lion has a different acceleration it'll change the gradient of the curve ⋅ decelerating has a decreasing gradient, instead of an increasing gradient like positive acceleration

Answer 13

speed-time graphs and velocity-time graphs are pretty similar - the big difference is that the velocity-time graphs can have a negative part to show negative velocity (negative velocity = something travelling in the opposite direction/backwards)

Answer 14

the gradient of a velocity-time graph tells you the acceleration

Answer 15

1) uniform acceleration is always a straight line 2) the steeper the gradient, the greater the acceleration

Answer 16

⋅ v = u + at ⋅ because... (look at image)

Answer 17

⋅ the equation for a straight line is y = mx + c ⋅ you can rearrange the acceleration equation (v = u + at) into the same form, getting v = at + u ⋅ this means that on a linear v-t graph, acceleration (a) is the gradient (m) and initial speed (u) is the y-intercept (c)

Answer 18

⋅ the area under a velocity-time graph tells you the displacement of an object ⋅ areas under any negative parts of the graph count as negative areas, as they show the object is moving back toward its starting point

Answer 19

the area under a speed-time graph gives the total distance travelled

Answer 20

⋅ non-uniform acceleration is a curve on a v-t graph ⋅ as acceleration is changing, the gradient of the v-t graph will also be changing (bc a = Δv/Δt) - so you won't get a straight line

Answer 21

1) an increasing acceleration is shown by an increasing gradient - like in the curve (1) 2) a decreasing acceleration is shown by a decreasing gradient - like in curve (2)

Answer 22

⋅ as the v-t graph is no longer a simple straight line, you have to estimate the area under the curve (bc s = area) ⋅ if the graph is on squared paper, an easy way to do this is to just count the number of squares under the curve and multiply the area by what the area of one square represents (so eg, 2 m s^-1 x 1 s, so area of 1 square = 2 m) ⋅ another way is to split the curve up into the trapezia and calculate the area of each trapezium and add them all up

Answer 23

1) to investigate how the distance a trolley has travelled affects its speed, set up the experiment shown in the diagram 2) measure the length of the trolley 3) mark a start line on the ramp to make sure the trolley always starts from the same position 4) measure the angle of the ramp (°) and the distance from the start line to the light gate (d) 5) place the trolley on the ramp and line it up with the start line. let go of the trolley so its initial velocity, u, is 0 6) the data logger will record the time taken for the trolley to pass through the light gate and calculate the velocity of the trolley as it passes through the light gate 7) change the starting position of the trolley, so that d is varied 8) repeat this experiment 3 times and average the recorded velocities to reduce the error in your final result

Answer 24

using a light gate gives a much lower uncertainty in the measurement than using a stopwatch and calculating the velocity manually

Answer 25

⋅ you can use the same setup as in the experiment to investigate other factors ⋅ eg) you could change the angle of the ramp or material it's made from - or change the mass, the size or the shape of the trolley

Answer 26

⋅ you can use a ticker timer instead of a data logger ⋅ ticker timers create holes in (or make dots on) a long piece of paper (ticker tape) at regular time intervals ⋅ this is usually about every 50th of a second

Answer 27

1) you can calculate how long it takes the trolley to travel down the ramp by attaching the ticker tape to the back of the trolley and threading it through the timer 2) switch the ticker timer on when you release the trolley, and switch it off when the trolley reaches the end of the ramp 3) the time taken can then be calculated from the number of holes punched into the ticker tape (50 holes = 1 second)

Answer 28

1) ticker timers are able to measure the time very accurately but rely on manually turning the machine on and of, which will add uncertainty to measurements eg) human error/reaction time 2) uncertainty can also be introduced when having to count the total number of dots

Answer 29

data loggers do not have this human error and can calculate the velocity and display it in real-time - saving time and allowing comparisons between experiments to easily be made

Answer 30

you can use the air glider experiment to measure how the mass and velocity of a glider just before the collision affects the velocities of both gliders after the collision 1) set up the experiment as shown in the diagram, with a video camera positioned side-on with the motion of the gliders 2) measure the length and the mass of both gliders 3) turn on the video camera and start recording 4) push one glider so it hits the second glider 5) when both gliders have come to a stop, stop recording (if you use the velocities you can find to work out the total momentum before and after the collision, you should find it is the same)

Answer 31

1) using the video analysis software, you can view your videos frame-by-frame. pick a point of reference on the metre rule and count how many frames it takes the slider to pass that point 2) by knowing how many frames per second the video is shot at (the frame rate of the video), you can calculate the time taken (t) for the whole glider to pass that point. you recorded the length (L) of each glider, and so you can calculate their velocities

Answer 32

⋅ using the equations of motion for constant acceleration, you can model how a uniformly accelerating body's velocity and displacement vary over time ⋅ to do this, use an iterative method, where velocity and displacement of the body are calculated over lots of small time increments to model the body's behaviour over a longer time period

Answer 33

1) create a spreadsheet [/table] like the one shown below (the one shown below models the motion for a body accelerating from rest at 4 m s^-1 over increments of 1 s) 2) for each row, the change in velocity (Δv) will be constant (as Δv = aΔt = 4 x 1 = 4 m s^-1) 3) add this Δv to the velocity (v) from the previous row, giving you the new velocity for each increment 4) to find the change in displacement (Δx) for each row use Δx = uΔt + 0.5a(Δt)^2 (where u is the value of v from the previous row). add this to the previous x value to get a new displacement at the end of each time interval 5) repeat these calculations to build up a full model of a body's motion over time. if you enter the correct formulae into the spreadsheet, then it can automatically complete as many rows (iterations) as you want 6) you can then plot a graph if v against t (which should be a straight line through the origin with a gradient equal to the body's acceleration) and x against t (which should be a curve)

Answer 34

1) consider an object fired horizontally, so that it begins to move with the projectile motion under the influence of gravity 2) initially, the object has the horizontal speed v0 and the vertical speed 0. following the first time increment, the object still has the horizontal speed v0, but its vertical speed has increased by Δv. this gives the resultant velocity of v1 as shown 3) following the second increment, the horizontal speed has remained constant (because gravity doesn't act on the horizontal component of speed) and the vertical speed has again increased by Δv. the new resultant velocity is v1 + Δv = v2 4) the pattern continues for each time increment. the resultant velocity increases for each increment (the blue arrow gets longer each time), as the object is accelerating

Answer 35

1) free-body force diagrams show a single body on its own 2) the diagram should include all the forces that act on the body, but not the forces it exerts on the rest of the world 3) remember forces are vector quantities and so the arrow labels should show the magnitude and the direction of the forces 4) if the body is in equilibrium (i.e. not accelerating) the forces on it will be balanced

Answer 36

resolving a force means splitting it into its components

Answer 37

⋅ forces can be in any direction, so they're not always perpendicular to each other ⋅ this is sometimes a bit awkward for calculations ⋅ to make an 'awkward' force easier to deal with, you can think of it as two separate, independent forces, acting at right angles to each other

Answer 38

resolved forces have no effect on each other as they are perpendicular (eg, the horizontal force will have no vertical effect, and vice versa)

Answer 39

⋅ to find the size of a component force in a particular direction ⋅ forces are vectors, so you treat them in the same way as a velocity or displacement - put them end to end (tip to tail) as shown in diagram ⋅ so using trigonometry you get: F horz = Fcosθ and F vert = Fsinθ ⋅ remember that cos90° = 0 (so Fcos90° (which would be vert force in terms of cos) = 0 , so forces which act at 90° to each other are independent (i.e. they have no effect on each other)

Answer 40

1) if two forces act on an object, you find the resultant force by adding the vectors together and creating a closed triangle, with the resultant force represented by the third side 2) forces are vectors, so use vector addition - draw the forces as vector arrows 'tip-to-tail' 3) then use trigonometry to find the angle and the length of the third side

Answer 41

⋅ choose the most sensible axes for resolving ⋅ use directions that make sense fo the situation you're dealing with ⋅ if you have an object on a slope, choose your directions[/axes] along the slope and at right angles to it (not any other direction) ⋅ you can turn paper to an angle if that helps [make the diagram make more sense]

Answer 42

examiners like to call a slope an 'inclined plane'

Answer 43

linear momentum is just the momentum in a straight line (not in a circle or anything complicated like that)

Answer 44

the object's mass and its velocity

Answer 45

momentum = mass x velocity p = mv

Answer 46

⋅ assuming no external forces act, momentum is always conserved (this is the principle of the conservation of momentum) ⋅ this means the total momentum of two objects before they collide equals the total momentum after the collision

Answer 47

the principle of the conservation of momentum can be handy for working out the velocity of objects after a collision:

Answer 48

⋅ yes, the conservation of momentum can be applied in explosions ⋅ eg) if you fire an air rifle, the forward momentum gained by the pellet equals the backward momentum of the rifle, and you feel the rifle recoiling into your shoulder

Answer 49

collisions can be elastic or inelastic

Answer 50

a perfectly elastic collision is one where the momentum is conserved and the kinetic energy is conserved - i.e. no energy is dissipated as heat, sound, etc

Answer 51

if a collision is inelastic it means that some of the object's kinetic energy is converted into other forms during a collision (but momentum is still conserved)

Answer 52

momentum is always conserved, no matter if the collision is elastic or inelastic

Answer 53

you can use the principle of the conservation of momentum to predict the behaviour of real-world objects, eg) balls in sports games

Answer 54

⋅ newton's first law of motion state that the velocity of an object will not change unless a resultant[/external] force acts on it ⋅ this means the body will remain at rest or moving in a straight line at a constant speed[/velocity], unless acted on by a resultant force

Answer 55

⋅ if any forces acting on a body aren't balanced, the overall resultant force will cause the body to accelerate ⋅ if you gave the apple in the example a shove, there would be a resultant force acting on it and it would roll off the table

Answer 56

newton's first law of motion states: "a body will remain stationary or move at a constant velocity unless acted upon by a resultant force"

Answer 57

⋅ the resultant force on an object is equal to its rate of change of momentum ⋅ F = ma

Answer 58

1) the greater the net resultant force acting on a body of a certain mass, the greater the acceleration of the body (F ∝ a) 2) for a given [resultant] force, the greater the mass of the body it acts on, the less acceleration the body will experience (a = F/m)

Answer 59

⋅ F = ma ⋅ 1 N = 1 kg m s^-2 ⋅ 1 Newton is 1 kilogram metre per seconds squared

Answer 60

⋅ all objects fall at the same rate (if you ignore air resistance) ⋅ on earth, the force that causes objects to accelerate toward the ground is the gravitational pull of the earth ⋅ the gravitational field strength on the earth (g) is pretty much constant - so all objects should accelerate toward the ground at the same rate, no matter what their mass is

Answer 61

⋅ newton's second law explains how all objects fall at the same rate (if you ignore air resistance) ⋅ consider two balls being dropped at the same time - ball 1 being heavy, and ball 2 being light ⋅ then use newton's second law to find their acceleration (as balls are free-falling)

Answer 62

netwon's third law is a consequence of the conservation of momentum

Answer 63

newton's third law states that: "if an object A exerts a force on object B, then object B exerts an equal but opposite force on object A" OR ⋅ "if body A exerts a force on body B, then body B exerts an equal force back on body A but in the opposite direction"

Answer 64

the two forces mentioned in newton's third law actually represent the same interaction, just seen from two different perspectives (not two forces being applied to one object)

Answer 65

if you (body A) push against a wall (body B), the wall will push back against you, just as hard (an equal force exerted back on body A in the opposite direction)

Answer 66

if you pull the cart, whatever force you exert on the rope, the rope exerts the exact pull on you

Answer 67

⋅ when you go swimming, you push back against the water with your arms and legs, and the water pushes you forward with an equal-sized force ⋅ so the backward momentum of the water is equal to your forward momentum

Answer 68

newton's third law applies in all situations and to all types of forces - but the pairs of forces in question are always the same type, eg) they are both gravitational or both are electrical

Answer 69

* the resultant force acting means a change in mass or acceleration (F = ma) - which means a change in momentum (as p = mv and p = Ft) * momentum is always conserved when no external force acts, so whenever one object exerts a force on another (and changes its momentum), the second object must exert an equal-sized force back on the first object so that the overall change in momentum is zero

Answer 70

friction is a force that opposes motion

Answer 71

1) contact friction between solid surfaces (what we usually mean when we just used the word 'friction') 2) fluid friction (known as drag or fluid resistance or air resistance)

Answer 72

a 'fluid' is a word that means either a liquid or a gas - something that can flow

Answer 73

1) the force depends on the thickness [/viscosity] of the fluid 2) the drag force increases as the speed of the object increases (for simple situations, drag force is directly ∝ to the speed of the object) 3) the drag force also depends on the size and the shape of the object moving through the fluid - the larger the area pushing against the fluid, the greater the resistance force

Answer 74

1) frictional forces always act in the opposite direction to the motion of the object 2) frictional forces can never speed things up or start something moving 3) frictional forces convert kinetic energy into heat

Answer 75

* terminal velocity - when the frictional force equals the driving force * you will reach terminal velocity at some point, if you have: 1) a driving force that stays the same all the time[/constant] 2) a frictional or a drag force (or collection of resistance forces) that increases with speed

Answer 76

⋅ yes, things falling through the air or water reach terminal velocity too EG) ⋅ when something is falling through the air, the weight of the object is a constant force accelerating through the air ⋅ in this case, air resistance is the frictional force opposing this motion, which increases with speed (for something falling through water, frictional force is water resistance)

Answer 77

the v-t graph for the terminal velocity of a parachutist is a bit different from that of a regular object because you have a new terminal velocity being reached, after the parachute is opened, which you also have to calculate

Answer 78

1) put elastic bands around tube of viscous liquid at fixed distances using ruler 2) drop ball bearing into tube, + use stopwatch to record time at which it reaches each band. record your results in table below: 3) repeat this few times to reduce effect of random errors on your results. you can use strong magnet to remove ball bearing from tube 4) calculate times taken by ball bearing to travel between consecutive elastic bands + calculate average for each reading. use average times + distance between bands to calculate average velocity between each pair of elastic bands 5) you should find that average velocity increases at first, then stays constant - this is ball bearing's terminal velocity in viscous liquid used

Answer 79

you could also investigate the terminal velocity by dropping paper cones through the air and using a light gate to get a more accurate velocity readings

Answer 80

⋅ you can change parts of your experiment to see what effect they have on terminal velocity and the time taken to reach the terminal velocity ⋅ you could EG) 1) change the liquid used in the experiment -> the terminal velocity will be lower in more viscous (thicker) liquids because the drag force is greater -> try mixing the water into wallpaper paste and see how much the terminal velocity increases when drag is lower 2) change the size of the ball -> what happens if the ball is larger? or smaller? 3) change the shape of the thing you are dropping -> the drag force will be greater 4) change the mass of the thing you are dropping, while keeping the size the same (by using more dense materials?) -> you should find that heavier objects reach a faster terminal velocity because a greater drag force is needed to balance the extra weight (remember, objects with different masses only fall at the same rate if the drag is ignored)

Answer 81

1) use your average velocity data from the experiment for investigating terminal velocity to plot a graph of velocity against time 2) draw a smooth curve (curved line of best fit) and use it to estimate the terminal velocity of the ball bearing

Answer 82

remember that the forces are balanced when the ball reaches terminal velocity

Answer 83

⋅ work is done whenever energy is transferred OR ⋅ work is done if a force is applied to an object and the object is displaced as a result

Answer 84

'work' in physics means an amount of energy is transferred from one form to another when a force causes a movement of some sort

Answer 85

1) usually you need the force to move a body of some kind because you're having to overcome another force 2) the thing being moved has kinetic energy while it's moving 3) the kinetic energy has been transferred to another form of energy when the movement stops

Answer 86

ΔE = FΔs or work done = force causing motion x displacement

Answer 87

1) work is the energy that's been changed from one form to another - it's not necessarily the total energy ⋅ eg) moving a book from a lower shelf to a higher one will increase the book's GPE, but it had some PE to start with -> here, work done would be the increase in the PE not the total PE of the book 2) 3) the force F will be a fixed value in any calculations, either because it's constant or because it's the average force 4) ΔE = FΔs assumes that the direction of the force is the same as the direction of the movement 5) ΔE = FΔs gives you the definition of the Joule (J):

Answer 88

⋅ remember that the displacement needs to be in metres (when s is measured and for calculations) ⋅ if you have the displacement in centimetres or kilometres, you need to convert it to metres first

Answer 89

ΔE = FΔs gives you this definition of the joule (J): "one joule is the work done when a force of 1 newton moves an object through a distance[/displacement] of 1 metre"

Answer 90

no, the force isn't always in the same direction as the displacement of the object

Answer 91

1) to calculate the work done in a situation like the one shown on the front of the flashcard, you need to consider the horizontal and vertical components of the force 2) the only displacement is in the horizontal direction ⋅ this means that the vertical force is not causing any displacement (and hence not doing any work) - it's just balancing out some of the object's weight, meaning there's a smaller reaction force 3) the horizontal force is causing the displacement - so to calculate the work done, this is the only force you need to consider. which means you get: ΔE = FΔscosθ ⋅ where θ is the angle between the direction of the force and the direction of the displacement

Answer 92

⋅ power is the rate of work done OR ⋅ power: the amount of energy transferred from one form to another per second

Answer 93

power = work done/time OR P = (ΔE)/t

Answer 94

the definition of the watt (W) is defined as a rate of energy transfer equal to 1 joule per second (J s^-1)