Physics Practical guideline

7/30/2019 Physics Practical guideline

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Summary of Case Study


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Introduction/ Background

Ski jumping is a sport that requires great skills and fitness by the athletes and very careful design and construction by

the organisers of the sport. It is generally considered a dangerous sport and there have been many injuries as well

as fatalities over the years. The sport requires a skier to speed up down a specially designed slop and fly in the air as

the slop finishes and land in the correct area. Skiers who jump further from the end of the ramp gain the higher

mark. The current records are between 80 to 250 metres. Diagram below shows the different sections of the

facility. Skiers start at top of the inrun to gain speed and then during the transition section the direction of motion ischanged to horizontal. At take off point the skier starts his flight until landing on the slopes below . The angle of this

slope is designed to reduce the impact of the landing. After landing the slope is gradually changed during the

transition section until it becomes totally horizontal known as outrun. The speed at the take off point and the forces

applied during the projectile motion determines the horizontal distance travelled.(S3)(1)

(S6)

Implication of Physics Theory

Ski jumping relies on the potential energy gained by the skier positioning themselves at top of the ramp.

This stored energy can provide the necessary velocity at the bottom of the ramp in the form of kinetic energy

for the flight to take place.

The gravitational potential energy at top of the ramp is

GPE= mgh where m is the mass g is the gravitational field strength and h is the height

The kinetic energy at the bottom of the ramp is

KE = mv2

where m is the mass and v is the velocity

In ideal situation (no friction or drag forces)

KE = GPE

mv2

= mgh therefore V= (2gh)
http://en.wikipedia.org/wiki/File:Einsiedeln_IMG_2768.JPGhttp://en.wikipedia.org/wiki/File:Einsiedeln_IMG_2768.JPGhttp://en.wikipedia.org/wiki/File:Einsiedeln_IMG_2768.JPG


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V is the initial horizontal velocity for the skier to launch him/herself as a projectile. The horizontal distance

that the skier lands depends on its initial horizontal velocity and the time of flight. The time of flight can be

calculated by considering the skier is in free fall in the vertical direction.

S = ut + at2

Where S is the vertical height dropped after the take-off

u the vertical component of velocity

t the flight time

since u is zero at the start, therefore

t = (2S/9.81)

by knowing t and V, we can calculate the horizontal distance from the take-off point.

Distance = Vx t (S4 & S5)

Historically Ski jumping started at the beginning of the 19th

century somewhere in Norway. The initial

attempts were much smaller in size than the modern ski jumping taking place for example at the winter

Olympics taking place in Canada. The distances jumped started at as little as 10 meters to the present

records of over 250 meters. (S7)

Ski jumping is a dangerous sport and there are hundreds of injuries every year as the result of this sport.

There are also some fatalities but not at any higher rate than any other comparable sports (1 in 100000 runs).

These dangers could be caused either by bad management of the facilities or bad design. In every

engineering project the designers make certain assumptions about different variables (e.g. the wind speed is

not going to be more than 150 Km/h). These assumptions play a major role in the construction of thefacilities and have a large impact on its safety. Sometimes the designers are forced to work with a very tight

budget and therefore they calculate the values for the different components to be very close to the minimum

acceptable. In this type of design there is a possibility that one of the parameters to exceed its assumed value

and cause a disaster.(S8)

The experiment that we have chosen to do is very closely linked to the ski jumping sport. In this experiment

a roller ball is placed at the top of a ramp where it gains gravitational potential energy and use this energy to

gain speed and take off from the bottom of the ramp and land in sand tray. However there are couple of

differences that although important but dont affect the outcomes significantly. One is the first transitionsection which in the experiment is very short and very sudden. The second difference is the landing point in

the experiment that is a sand pit and stops the ball suddenly rather than a gradual stop in reality. Otherwise

there are very close resemblance between reality and the experiment. (S9)

References:

1- http://en.wikipedia.org/wiki/Ski_jumping, including Access Date2- Class notes and discussions (Projectile hand outs)3- Physics by K. Dobson, D. Grace, D. Lovett Pub: Collins Educational,

ISBN:0-00-322328-0

(S1, S2)
http://en.wikipedia.org/wiki/Ski_jumpinghttp://en.wikipedia.org/wiki/Ski_jumpinghttp://en.wikipedia.org/wiki/Ski_jumping


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(R1, R2)Awarded for heading and spelling in the case study

PlanningThe experiment that is closely related to the ski jumping sport is a ramp representing theski slope and a small ball representing the skier. The landing distance i.e. the horizontaldistance between the end of the ramp and where the ball contacts the ground, depends onthe height of the ramp and the drop height at end of the ramp. The aim of the experiment isto investigate the relationship between the horizontal distance and the horizontal velocityat the end of the ramp.

Aim-

In this experiment you are going to

Measure the height of the ramp and the horizontal distance the ball travels

Investigate the relationship between the two variables-Horizontal distance and the speed ofa ball rolling down the ramp (V)

Horizontal Distance = Vx t

P1. List all of the materials required. (Use a diagram P13)

RampLab JackBallStopclockMetre ruler

Set squareSand trayBlue-tac to fix the lab jack to bench

ramp

Ball

Jack

and tray

Distance travelled by

the ball = 1.00m

Maximum

height 30cm

approx.


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P2, P3, P4, P5, P6. Describe your method for each part of the experiment. You must explain yourchoice and appropriateness of measuring instruments and demonstrate correct measuringtechniques.

Method

P2To measure the average speed of the ball, we need to measure the time that it takes to travel fromthe moment of release from the top of the ramp to the point where it reaches the bottom of thetamp. The instrument that is available for measuring time is a stop watch that can measure time to100th of a second.

P3Stop- watch measures to one hundredth of a second, that is precision of 0.01s and uncertainty ofmeasuring time is 0.01s. The time that takes for the ball to travel from top of the ramp to thebottom at its shortest (maximum height) is just over 1 second. It is therefore a suitable device for

this purpose. Time is measured for 6 different height of the ramp.

P4we need to measure the height from the top of the bench to the centre of the ball (h). This can bedone with a meter rule that is placed at 90 degrees to the bench

P5Measuring the height of the ramp using a meter ruler is justified as the meter rule can measurewithin a millimeterand the height varies 80 mm to 200mm. The precision of measurement is 1mm(or 0.1cm) and uncertainty of measuring length is 1mm ( 0.1cm). The height is varied for 6different values.

P61- The meter rule must be at right angles with the table. This can be done by using a set

square against the ruler(refer to a diagram showing how a meter rule and set square areused).

2- The values of the height must be read with the eye at right angles to the meter ruler toavoid parallax errors (refer to a diagram showing how to read the scales)

3- The distance the ball travels down the ramp must be read looking perpendicular to thescales on the metre-rule (refer to a diagram showing how to read the scales)

4- You must start the stopwatch as you let the ball go (initial speed of the ball =0)

5- Set the stop watch to zero before start timing

6- Describe techniques for measuring the horizontal distance correctly (refer to a diagram)

7- You must be standing near the bottom of the ramp as the ball reaches there and pressingthe stop button while looking at 90 degrees to the ball and the ramp to avoid parallax errors.


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P7 and P8. Identify the key variables in each part the investigation and state how it is made a fairtest. (Adjust and number of tables or number of rows in each table to suit your investigation)

Independent Variable Dependent Variable Fixed Variables

Horizontal Velocity of the ball atthe moment it leaves the ramp

Horizontal distancebetween the table andthe landing location of

the ball.

Length of rampmass of the bass

shape of the ball to controldrag

friction force between theramp and ball

height of the benchgravitational field strength

P8- Length of the ramp is kept constant by marking the start and finish points of

balls motion on the ramp.- All other factors such as equipment used, same ball used (-mass and shape

of ball kept constant). Same ramp used (keep friction force constant). Thebench height is fixed so as g value.

P9 Comment on whether repeat readings are appropriate in this case.

Because we are using a stopwatch to read the time and the stopwatch is controlled by humanaction and because human introduce reaction time which is random value, therefore our readingsare going to be random too. In order to check reliability of measured time and reduce randomuncertainties we need to repeat the experiment at least three times and find the average time ofthe decent.Repeat the horizontal distance where the ball lands from the vertical height for each timemeasurements, since the uncertainty in measuring the distance is poor. Averaging the valuesreduces the effect of random error.

The height measurement does not require repeat measurement because there is no reaction timeis involved and if we make sure that we have used the correct measuring method one reading is

sufficient.

P10 .There are no high risk activities in this experiment. The medium risk could be the fall of the rampto the floor. This risk can be reduced by setting the ramp away from the edge of the table. The labjack slipping (-use blue-tac to stick the jack to the bench). There are number of low risk activitiesthat include relatively sharp edges of the instrument used. You must take care in using the jack,the square and meter rulers.


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P11. Discusses how the data collected will be used:-

Distance travelled along the ramp by the ball = d

Heightcm

Time1s

Time2s

Time3s

TimeAvs

Hor d1cm

Hor d2cm

Hor d3cm

Hor davcm

h1

h2

.

.

.

h6

The average value of time of decent and the value of the length of the ramp will be used to

calculate the average velocity (average velocity =distance/time). The final velocity will be

calculated by (final velocity at the end of the ramp = 2 x average velocity). The average horizontal

distance travelled by the ball is calculated. A graph is plotted to show the relationship between the

final velocity and the horizontal distance. The graph should be straight line going through the

origin. The gradient is the flight time (time taken for the ball leaving the ramp to landing in the

sand).

P12. What are the main sources of uncertainty (systematic or random)?

Random uncertainties are mainly due to Human reaction time in using the stopwatch. Humanreaction time at its worst case is about 0.2 seconds ( 0.1s) in setting the stopwatchThe uncertainty in measured length of the ramp and the height= 1mm (or 0.1cm)The uncertainty in measuring the horizontal distance is much higher than 1mm (or 0.1cm)Uncertainties of digital stopwatch is: plus or minus 0.01 sec

Systematic error include the 0 setting of the stop watch and end points of the meter rulers.

Velocity (m/s)

Horizontal

distance(m)


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Implementation and Measurements

M1. Record all measurements using the correct number of significant figures, tabulatingmeasurements where appropriate.

Create a table with the required number of columns and rows each with appropriateheadings for collecting and recording the results of your experiment/s. Your recordingsmust have the correct number of significant figures

Results

Distance travelled down the ramp =

Heightm

Time1s

Time2s

Time3s

TimeAvs

Hor d1m

Hor d2m

Hor d3m

Hor davm

0.100 1.87 1.84 1.78 1.80 0.453 0.452 0.450 0.4520.140 1.53 1.60 1.50 1.54 0.556 0.540 0.535 0.544

0.180 1.37 1.37 1.34 1.36 0.630 0.626 0.619 0.625

0.220 1.24 1.15 1.22 1.20 0.682 0.708 0.656 0.682

0.260 1.12 1.12 1.15 1.13 0.746 0.754 0.746 0.749

0.300 1.09 1.06 1.09 1.08 0.795 0.790 0.812 0.799

M2. Use correct units throughout.The SI units are used throughout this document, for example in the above table length is

measured in metre and time in seconds.

M3. Obtain an appropriate number of measurements.Six measurements have been taken to make the data appropriate for plotting a graph.

M4. Obtain measurements over an appropriate range.The range of the height is limited to the maximum that the ramp could be set. The sixmeasurements are equally divided to cover the whole range.


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Analysis

Vav = distance travelled down the ramp/ timeVf = 2 x Vav

Heightm

TimeAvs

Hor davm

Vavm/s

Vfm/s

0.100 1.80 0.452 0.560 1.11

0.140 1.54 0.544 0.650 1.30

0.180 1.36 0.625 0.740 1.44

0.220 1.20 0.682 0.830 1.66

0.260 1.13 0.749 0.880 1.76

0.300 1.08 0.799 0.930 1.86

A1: Produces a graph with appropriately labeled axes and with correct units

A2: Produces a graph with sensible scales

A3: Plots points accurately

A4: Draws line of best fit (either a straight line or a smooth curve)


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A5. Comment on the trend/pattern obtained

The graph shows a straight line that passes through the origin. Since the line passes

through the origin therefore the two variables are directly proportional. The gradient is

positive and the slope of the line shows the time taken for the ball to reach the ground. The

graph clearly shows that the horizontal distance increases as the speed of the ball

increases at the bottom of the ramp.

A6. Derive a relation between two variables

The graph is a straight line through the origin. The equation for a straight line that passes

through the origin is: Y = m X + C

Calculate the gradient using all of the line-

Gradient shown on the graph

where C = 0

Applying this equation to our variables in the graph:

Dh = 0.43 Vf

Where Dh stands for the Horizontal distance, m= 0.43 s (unit must be from the graph) and

Vfstands for final velocity of the ball on the ramp.

A7. Discuss/use related physics principles

The movement of a projectile can be analysed by dividing the movement into two different

components. The vertical component that is a free fall and a horizontal component that is a

linear movement at a steady speed. The value of the horizontal speed is equal to the initial

horizontal velocity and the time of flight is determined by the height of the object from the

ground. If the height is kept constant the time of flight will also remain constant. Since the

horizontal movement is a linear motion at a constant velocity we could write

V = Horizontal distance/ time

Time taken for the ball to travel horizontal distance = time taken for the ball to fall the height

of the bench.

Or

Horizontal distance = V x time

This equation shows that the horizontal distance is directly proportional to the initial velocity

of the ball as it leaves the end of the ramp. Also we can see that the gradient of the lineequals the time of the flight.


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In this case the time of the flight could be calculated as follows:

s = ut + a t2

0.92 = 0 + 9.81 t2

t2 = 1.84 / 9.81

t = 0.44 s

This value is almost the same as the gradient of the graph.

A8. Consider sources of error in your measurements

The greatest source of uncertainty in this experiment is the reaction time of operating the

stop watch. The second source of uncertainty is the measurement of the horizontal distance

and the least uncertainty is measuring the distance travelled down the ramp and height of

the ramp using a meter rule.

A9. Suggest realistic modifications to reduce error/improve experiment

Since the human reaction time is the greatest uncertainty in this experiment we should try

to reduce it to as low as possible. Since the reaction time itself is more or less constant for

a person we need to alter other factors. The nearer our time measurement is to the value of

the reaction time the worse the uncertainty will be. Therefore we need to increase the time

we need to measure by increasing the length of the ramp so that the ball takes longer to

reach the bottom of the ramp, doing the measurement over the smallest height range aspossible, since greater the height faster the ball rolls, shorter the time. Do go above 20.0cm

height. In this way the reaction time becomes a smaller proportion of the total time

measured.

A10 Calculates uncertainties

The time one Does not satisfy the criteria- Justify uncertainty in one

measurementCould calculate

% uncertainty in the measured time = (largest readingsmallest

reading)/average time *100

Find the largest % uncertainty

The reaction time is different for individuals and it varies between 0.1 to 0.2 seconds. If we

consider the worst case i.e. 0.2 s, and knowing that the time of decent for the ball as its

shortest was 1s, we can calculate the relative uncertainty:

Relative Uncertainty in time measurement = 0.2 x 100 = 20 %

1.0


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This shows that the level uncertainty is unacceptably high.

Uncertainty ofmeasuring height using meter ruler that has mm reading is +/ 1 mm or 2mm

The minimum height measured was 100mm

Relative Uncertainty in height measurement = 2 x 100 = 2 %

100

A11: Provides a final conclusion This must relate to the aim

The aim was to investigate the physics model that the horizontal distance travelled by the

ball is proportional to the initial horizontal velocity of the ball.

In this experiment we have shown that test result is positive and the horizontal distancetravelled bay the ball is indeed directly proportional to the initial horizontal velocity. The

graph of d against v shows a straight line goe through the origin. The equation Dh = 0.43 Vf

shows the constant of proportionality =0.43s which is also that the time of flight and is a

constant value for a certain height and is independent of the horizontal velocity.

R1: Summary contains few grammatical or spelling errors

R2: Summary is structured using appropriate subheadings

A: Summary of case study or physics-based visitRef Criterion Mark

Ref Criterion MarkS1- Carries out a visit OR uses library, consulting a minimum of three

different sources of information (egbooks/websites/journals/magazines/case study provided by Edexcel/manufacturers data sheets)

1

S2- States details of visit venue OR provides full details of sources ofinformation

1

S3 Provides a brief description of the visit OR case study 1

S4 Makes correct statement on relevant physics principles 1S5 Uses relevant specialist terminology correctly 1S6 Provides one piece of relevant information (eg data, graph, diagram)

that is not mentioned in the briefing papers for the visit or case study1

S7 Briefly discusses context (eg social/environmental/historical) 1S8 Comments on implication of physics (eg benefits/risks) 1S9 Explains how the practical relates to the visit or case study 1

Maximum marks for this section 9

AS Assessment Criteria - To be completed by class teacher

B: Planning Ref Criterion Mark

P1 Lists all materials required


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P2 States how to measure one relevant quantityusing the most appropriate instrument

P3 Explains the choice of the measuring instrumentwith reference to the scale of the instrument asappropriate and/or the number of measurementsto be taken

P4 States how to measure a second relevant quantity

using the most appropriate instrumentP5 Explains the choice of the second measuringinstrument with reference to the scale of theinstrument as appropriate and/or the number ofmeasurements to be taken

P6 Demonstrates knowledge of correct measuringtechniques

P7 States which is the independent and which is thedependent variable

P8 Identifies and states how to control all otherrelevant variables to make it a fair test

P9 Comments on whether repeat readings areappropriate in this case

P10 Comments on safety

P11 Discusses how the data collected will be used

P12 Identifies the main sources of uncertainty and/orsystematic error

D: Analysis Ref Criterion Mark

A1 Produces a graph with appropriately labelled axesand with correct units

A2 Produces a graph with sensible scalesA3 Plots points accurately

A4 Draws line of best fit (either a straight line or asmooth curve)

A5 Comments on the trend/pattern obtained

A6 Derives relation between two variables ordetermines constant

A7 Discusses/uses related physics principles

A8 Attempts to qualitatively consider sources of error

A9 Suggests realistic modifications to reduce

error/improve experimentA10 Calculates uncertainties

A11 Provides a final conclusion

E: Report Ref Criterion Mark

R1 Summary contains few grammatical or spelling errors

R2 Summary is structured using appropriate subheadings


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Physics Practical guideline