mechanics Flashcards
what is the difference between scalar and vector quantities?
MECHANICS
scalars only have magnitude, but vectors have magnitude and direction
list common quantities that are either scalars or vectors
MECHANICS
how do you find the resultant vector?
MECHANICS
⋅ adding two or more vectors is called finding the resultant of them - whatever quantity it is (displacement, force, momentum), the procedure is the same
1) you should always start by drawing a diagram. draw the vectors ‘tip-to-tail’. if you’re doing a vector subtraction, draw the vector you’re subtracting with the same magnitude but pointing in the opposite direction
2) if the vectors are perpendicular to each other, then you can use pythagoras and trigonometry to find the resultant vector
3) if the vectors aren’t perpendicular, you may need to draw a scale diagram
how do you resolve vectors?
MECHANICS
resolving a vector is the opposite of finding the resultant vector - you start from the resultant vector and split it into two components perpendicular to each other (you’re basically working backward from finding the resultant)
why is it useful to resolve a vector?
MECHANICS
⋅ resolving a vector is very useful because the two components of vectors don’t affect each other - this means you can deal with two directions completely separately
(components perpendicular to each other don’t affect each other)
are speed, displacement, velocity and acceleration a scalar or a vector quantity?
MECHANICS
⋅ speed is a scalar quantity
⋅ displacement, velocity and acceleration are all vector quantities
what is the definition for speed?
MECHANICS
speed is how fast an object is moving, regardless of direction (i.e. the magnitude of velocity)
what is the definition for displacement?
MECHANICS
displacement (s) is how far an object has travelled from its starting point in a given direction
what is the definition for velocity?
MECHANICS
velocity (v) is the rate of change of an object’s displacement (an object’s speed in a given direction)
what is the definition for acceleration?
MECHANICS
acceleration (a) is the rate of change of an object’s velocity
what is the average speed?
MECHANICS
during a journey, the average speed is just the total distance covered over the total time elapsed
(average speed = total distance/total time elapsed)
what is the instantaneous speed?
MECHANICS
the speed of an object at any given point in time is known as its instantaneous speed
what is uniform acceleration?
MECHANICS
uniform acceleration is constant acceleration
(in mechanics, uniform = constant)
what could cause acceleration?
MECHANICS
acceleration can mean a change in speed, change in direction or both
what are the four main equations used to solve problems involving uniform acceleration?
MECHANICS
v = u + at
s = 0.5(u + v)t
s = ut + 0.5a(t^2)
v^2 = u^2 + 2as
[less important one: s = vt - 0.5a(t^2)]
how to derive v = u + at?
MECHANICS
how to derive s = 0.5(u + v)t?
MECHANICS
literally adding velocities together and dividing by the number of velocities there are (always just two because you just consider u and v) to find the average velocity (like finding any other average)
how to derive s = ut + 0.5a(t^2)?
MECHANICS
sub v = u + at into s = 0.5(u + v)t
how to derive v^2 = u^2 + 2as?
what is free fall?
MECHANICS
⋅ free fall is defined as the motion of an object undergoing an acceleration ‘g’
⋅ so basically the only force acting on an object is its weight and nothing else
what are 5 things you need to remember when looking at free fall?
MECHANICS
1) acceleration is a vector quantity
2) the magnitude of ‘g’ is usually taken as 9.81 m s^-2, though it varies slightly at different points above the earth’s surface
3) the only force acting on the object in free fall is its weight
4) all objects in free fall fall at the same rate
5) the objects can have an initial velocity in any direction and still undergo free fall as long as the force providing the initial velocity is no longer acting
how do you calculate g? (practical)
MECHANICS
1) set up the equipment as shown in the diagram:
2) measure the height h from the bottom of the ball bearing to the trapdoor
3) flick the switch to simultaneously start the timer and disconnect the electromagnet, releasing the ball bearing
4) the ball bearing falls, knocking the trapdoor down and breaking the circuit - which stops the timer. record the time t shown on the timer
5) repeat this experiment three times and average the time taken to fall from this height. do this for a range of different heights
6) you can then use these results to find g using a
s-(t^2) graph
how do you find g from the graph obtained in the practical? (practical)
MECHANICS
1) use your data from the experiment to plot a graph of height (s) against the time it takes for a ball to fall SQUARED (t^2). then draw a line of best fit
2) you know that with constant acceleration: s = ut + 0.5a(t^2)
3) if you drop the ball [so the ball moves from rest], initial speed u = 0, so s = 0.5a(t^2)
4) rearranging this gives 0.5a = s/(t^2), or 0.5g = s/(t^2)
5) gradient of line of best fit Δs/Δ(t^2) is equal to 0.5g, so: g = 2 x Δs/Δ(t^2)
⋅ eg using this graph) g = 2 x (0.44/0.09) = 9.8 m s^-2 (to 2 sf)
how do you increase the accuracy of the measurements in the practical for finding g?
MECHANICS
to increase the accuracy of the measurements you take, you can:
⋅ use a small and heavy ball bearing so you can assume that air resistance is so small that you can ignore it
⋅ use a ruler with smaller increments and pick a certain point on the ball bearing to measure from to reduce errors in measuring the height
how do you increase the accuracy of the method used in the practical for g?
MECHANICS
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
what could you use instead of an electromagnet and ball in the practical for finding g?
MECHANICS
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
why is using either a computer or light gate instead to find g better in the practical?
⋅ 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)
how can you use video and a ruler to find g? (practical)
MECHANICS
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
how can you use video and strobe lights to find g?
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
what are the main causes of uncertainty in the practical to find g (using video and strobe light) and how do you reduce them?
MECHANICS
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
what can you replace a (acceleration) with in equations of motion (suvat) when talking about projectiles?
MECHANICS
you can just replace a with g in equations of motion (suvat) when talking about projectiles
why can you use equations of motion (suvat) for projectiles?
MECHANICS
as g is a constant acceleration, you can use the equations of motion (suvat) in projectiles
what direction does g act in?
MECHANICS
⋅ 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
how can you use resolving vectors to work out the time of flight of an object and how far an object moves horizontally/vertiaclly through the air (using projectiles)?
MECHANICS
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
what does acceleration look like on a displacement-time graph?
MECHANICS
⋅ 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)
what does the gradient look like for different accelerations
⋅ 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
how can you tell the difference between speed-time graphs and velocity-time graphs?
MECHANICS
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)
what does the gradient of a velocity-time graph tell you?
MECHANICS
the gradient of a velocity-time graph tells you the acceleration
what features of the acceleration can you recognise from the gradient of a velocity-time graph?
MECHANICS
1) uniform acceleration is always a straight line
2) the steeper the gradient, the greater the acceleration
since you know acceleration is just the gradient of a velocity-time graph, what suvat equation can you generate using this information?
MECHANICS
⋅ v = u + at
⋅ because… (look at image)
since the equation of a straight line (y = mx +c) and the suvat equation v = u + at look similar, what does this mean?
MECHANICS
⋅ 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)
how do you plot a v-t graph by calculating v as t increases?
MECHANICS
why does the area under a velocity-time graph give?
MECHANICS
⋅ 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
what does the area under a speed-time graph give?
MECHANICS
the area under a speed-time graph gives the total distance travelled
what does a non-uniform acceleration also look like on a velocity-time graph?
MECHANICS
⋅ 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
how do you know if the acceleration is increasing or decreasing from a velocity-time graph?
MECHANICS
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)
how do you estimate the displacement from a curved velocity-time graph?
⋅ 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
how do you investigate what affects the motion of a trolley? (practical)
MECHANICS
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
how could you lower the uncertainty in the measurement for the velocity of the trolley?
MECHANICS
using a light gate gives a much lower uncertainty in the measurement than using a stopwatch and calculating the velocity manually
how can you investigate other factors using the trolley experiment?
MECHANICS
⋅ 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
what could you use instead of a data logger in the trolley experiment?
MECHANICS
⋅ 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
how can you investigate what happens to the motion of an air glider when two gliders collide? (practical)
MECHANICS
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)
how can you analyse the results from the air glider experiment? (practical)
MECHANICS
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
how can you use vectors for iterative methods?
MECHANICS
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
what do free-body force diagrams show?
MECHANICS
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
what does it mean if you resolve a force?
MECHANICS
resolving a force means splitting it into its components
how do you find the size of the component force in a particular direction?
⋅ 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)
how do you find the resultant force?
MECHANICS
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
what do you need to consider when resolving forces?
MECHANICS
⋅ 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]
what is the equation for momentum?
MECHANICS
momentum = mass x velocity
p = mv
how can you use the principle of the conservation of momentum?
MECHANICS
the principle of the conservation of momentum can be handy for working out the velocity of objects after a collision:
what can the conservation of momentum be used for?
MECHANICS
you can use the principle of the conservation of momentum to predict the behaviour of real-world objects, eg) balls in sports games
considering newton’s first law, what happens if the forces on a body aren’t balanced
⋅ 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
what is newton’s second law of motion?
MECHANICS
⋅ the resultant force on an object is equal to its rate of change of momentum
⋅ F = ma
what do you need to consider for F = ma?
MECHANICS
what is the definition of a newton?
MECHANICS
⋅ F = ma
⋅ 1 N = 1 kg m s^-2
⋅ 1 Newton is 1 kilogram metre per seconds squared
how does netwon’s second law explain how objects fall at the same rate (if you ignore air resistance)?
MECHANICS
⋅ 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)
what does netwon’s third law look like when you push a wall?
MECHANICS
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)
what does newton’s third law look like when pulling a cart?
MECHANICS
if you pull the cart, whatever force you exert on the rope, the rope exerts the exact pull on you
in newton’s third law, are pairs forces always the same type?
MECHANICS
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
what are the three main stages to reaching terminal velocity?
MECHANICS
what does the velocity-time graph look like for an object reaching terminal velocity?
MECHANICS
what does the acceleration-time graph look like for an object reaching terminal velocity?
MECHANICS
what happens once a parachutist jumps out of a plane? and what happens once their parachute opens?
MECHANICS
what does the velocity-time graph look like for a parachutist?
MECHANICS
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
how do you calculate the terminal velocity of a ball bearing (a little steel ball) in a viscous (thick) liquid, using the set up shown? (PRACTICAL)
MECHANICS
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
what are some examples of work done and the energy changes that can happen?
MECHANICS
what is the equation to find how much work is done when a force is applied by body A to body B (usually with the purpose of moving body B?
MECHANICS
ΔE = FΔs
or
work done = force causing motion x displacement
is the force doing work on an object always acting in the same direction as the displacement of the object?
MECHANICS
no, the force isn’t always in the same direction as the displacement of the object
how do you calculate the work done when the force isn’t in the same direction as the displacement (of the object)?
MECHANICS
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
