To investigate the relationship between the work done to accelerate a trolley and the energy stored in the moving trolley.

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1 SP2h.1 Aelerating trolleys Your teaher may wath to see if you an follow instrutions safely take areful measurements. Introdution The work done y a fore is a measure of the energy transferred when a fore moves through a distane. The energy stored in a moving ojet is alled kineti energy. Aim work done = fore distane moved in the diretion of the fore kineti energy = ½ mass (speed) 2 To investigate the relationship etween the work done to aelerate a trolley and the energy stored in the moving trolley. Method Apparatus trolley ramp loks (to prop up the end of the ramp) string pulley masses stiky tape ard stiky tak or modelling lay alane one light gate datalogger lamps and stand Safety Make sure masses annot fall on your feet. A Set up your apparatus as shown in the diagram elow. Prop up one end of the ramp and plae a trolley on it. Adjust the slope of the ramp until the trolley just starts to move on its own. Gravity pulling the trolley down the slope is now ompensating for frition in the trolley s wheels. B C D E Stik a piee of ard to the top of the trolley using stiky tak or modelling lay. Leave enough spae to stak some masses on top of the trolley. Measure the length of the ard and write it down. Find the mass of the trolley and write it down. Fasten the pulley at the ottom end of the ramp, and arrange the string and masses as shown aove. Set up a light gate near the ottom of the ramp. Adjust its position so that the ard on the top of the trolley passes through the gate as it reahes the end of the ramp. 1

2 F G H I SP2h.1 Aelerating trolleys Draw a line on the ramp (or mark it with stiky tape). This will e the start line for your trolley. Measure how far the ard on the trolley will move from when the trolley is on the start line until the ard passes through the light gate. Write down this distane. Put a mass on the end of the string. Write down the mass that you use. Release the trolley from the top of the ramp and write down the speed of the trolley (from the datalogger) as it passes through the light gate. Repeat step H for other masses on the trolley and other masses on the string. Deide what masses to use, how many different masses you are going to test, and whether you need to repeat any of your tests. Reording your results 1 Draw a tale like this for reording your results. (i) (ii) (iii) (iv) (v) Work done to Mass on Fore on aelerate pulley (kg) string (N) trolley (J) Mass added to trolley (kg) Total mass of trolley, masses on trolley and masses on string (kg) Speed of trolley at end (m/s) Kineti energy stored in moving the trolley at the end of the ramp (J) 2 Calulate the fore on the string for eah run y multiplying the numer in olumn (ii) y 10 N/kg. 3 Calulate the work done to aelerate the trolley y multiplying the distane you measured in step F y the fore in olumn (iv). 4 Calulate the kineti energy of the trolley at the end of eah run using the equation at the top of the first page of this worksheet. You need to use the values in olumns (iii) and (v). You need to inlude the masses on the string, eause they are eing aelerated as well as the trolley. 5 Plot a satter graph to show your results. Put the work done on the horizontal axis and the kineti energy on the vertial axis. Draw a line or urve of est fit through your points. Considering your results/onlusions 6 What relationship etween work done and kineti energy does your graph show? Evaluation 7 a How lose are the points on your graph to the line of est fit? What does this tell you aout the quality of your data? 8 If the work done = kineti energy, your line of est fit should e a straight line through the origin with a gradient of 1. a How does the graph of your results ompare with this desription? Suggest reasons for any points that do not lie on a straight line through the origin. 2

3 SP2h.2 Fators affeting raking distane We an use satter graphs to help us to find out whether there is a relationship etween two variales. If the points form a straight line, then there is a linear relationship etween the two variales. If the straight line goes through the origin, then one variale is diretly proportional to the other. If the two variales are in diret proportion, we know that if one variale doules the other one doules too. The tale shows the raking distanes for ar A at different speeds. The ar has a mass of 1500 kg. 1 Plot a graph to find out if there is a linear or diretly proportional relationship etween the speed of the ar and its raking distane. Plot speed on the horizontal axis and raking distane on the vertial axis. Draw a line or urve of est fit through the points. 2 a Desrie the shape of the line on your graph. Desrie the relationship etween speed and raking distane. The energy stored in a moving vehile is alled kineti energy. The equation on the right shows how to alulate this from the vehile s mass and speed. Braking distane (m) Speed (m/s) ar A kineti energy = ½ mass (speed) 2 3 a Copy the tale aove and add a olumn for kineti energy. Calulate the kineti energy of ar A for the speeds given in the tale aove. Plot a satter graph to investigate the relationship etween kineti energy and raking distane. Put kineti energy on the horizontal axis and raking distane on the vertial axis. Join your points with a line or urve of est fit. Desrie the relationship etween the kineti energy of the ar and its raking distane. H The momentum of a moving ojet is found using the equation on the right. momentum = mass veloity 4 H Plot a satter graph of raking distane against momentum and desrie any relationship that your graph shows. 5 Any relationships you have identified aove are for just one set of data. Use the information in the tale on the right to hek whether or not your onlusions apply to the data given for the other vehiles. Mass of ar B = 1200 kg Mass of ar C = 1500 kg Mass of ar D = 3500 kg Braking distane (m) Speed (m/s) ar B ar C ar D

4 SP2h.3 Braking distane and energy Strengthen Name Class Date 1 a Car rakes apply a fore. What does this fore do to the ar? The rakes transfer energy stored in the moving ar (kineti energy). Where is the energy transferred to? d e f What is the equation for alulating kineti energy? If the speed of the ar doules, what happens to the kineti energy? When the speed doules, how muh more energy must the rakes transfer? How does the raking distane at 30 m/s ompare with the raking distane at 15 m/s? Use your answers to question 1 to write a paragraph to answer question S1. S1 A ar travels at 15 m/s for one part of a journey and at 30 m/s for another part of the journey. The driver rakes to a stop using a raking fore of 9000 N eah time. Explain how the raking distane will e different at the two speeds. 2 Cross out the inorret words to omplete these sentenes. When the mass of a moving ojet inreases, its kineti energy (inreases/dereases). When the mass doules, the kineti energy (halves/doules/is multiplied y 4). When the speed of a moving ojet inreases, its kineti energy (inreases/dereases). When the speed doules, the kineti energy (halves/doules/is multiplied y 4). 3 A ar has a mass of 1200 kg and its rakes an apply a fore of 9000 N. It is travelling at 30 m/s. Calulate its stopping distane. kineti energy = ½ kg ( m/s) 2 = J work done to stop the ar = J distane = = J N = m four times as long four times as muh energy it is multiplied y 4 KE = ½ mass (speed) 2 makes it deelerate thermal energy in the rakes and surroundings 4

5 SP2h.4 Braking distanes and energy Homework 1 Name Class Date 1 Fill in the gaps in these sentenes using words from the ox. You an use eah word one, more than one or not at all. Work is the transferred when a fore ats over a. The unit for work done is the (J). The work done is alulated from the multiplied y the. Kineti energy is the name for energy stored in ojets. The amount of kineti energy stored depends on the of the ojet and on its squared. Kineti energy is alulated using this equation: kineti energy = ½ When a vehile rakes, the kineti energy stored in it is transferred to thermal energy in the and the surroundings. The work done is the kineti energy transferred. We an use this idea to alulate the distane of a vehile if we know its mass, speed and the raking. rakes raking distane energy equal to fore greater than high joule less than mass moving speed speed 2 stopping weight 2 A lorry has a mass of kg. It is travelling at 20 m/s, and its rakes an apply a fore of N. a Calulate the energy stored in the moving lorry. kineti energy = ½ kg ( m/s) 2 kineti energy = ½ mass (speed) 2 work done = fore distane moved in the diretion of the fore = J Write down the equation for alulating the distane from the work done (energy) and the raking fore. distane = Calulate the stopping distane. 3 The same lorry as in question 2 takes on an extra load, so its total mass is now kg. Calulate its stopping distane from a speed of 20 m/s if the same raking fore is applied. stopping distane = m 5

6 SP2h.5 1 A Japanese ullet train has a mass of kg and travels at a top speed of 275 km/h. Its raking distane from this speed is 4 km. Calulate the raking fore. 2 Use your answer to question 1 to alulate the stopping distane if the same train were travelling at 350 km/h when the rakes were applied. 3 An airliner has a mass of kg when it lands at a speed of 75 m/s. The overall raking fore (from the rakes and from drag fores) is N. Calulate how muh runway it needs to ome to a omplete stop. Braking distanes and energy Homework 2 1 km/h = m/s kineti energy = ½ mass (speed) 2 work done = fore distane moved in the diretion of the fore 4 The tale on the right shows details of some different lorries. Calulate the stopping distane for eah lorry. 5 a Using your results from question 4, suggest what the relationship is etween the mass of the lorry and its raking distane. Using your results from question 4, suggest what the relationship is etween the raking fore of the lorry and its raking distane. Lorry Mass (kg) Speed (km/h) Braking fore (kn) A B C D d You annot work out a relationship using only two results. Suggest what further alulations you would need to do to onfirm your answer in part a. How would you deide whether your results do show a diretly proportional relationship? How would you show whether or not the relationship you suggested in part is orret? Extra hallenge 6 A ar has a mass of 1200 kg. It rakes with a fore of 9500 N and travels 25 m while oming to a stop. Calulate the speed at whih it was travelling efore the rakes were applied. 7 Use algera to show how the raking distane is related to lorry mass and to raking fore. 6

7 SP2h Name Class Date Progression questions Progression hek Answer these questions. 1 What is work done and how is it alulated? 2 What is kineti energy and how is it alulated? 3 How are work done and kineti energy related to raking distanes? Now irle the faes in the Start row in the tale showing how onfident you are of your answers. Question Start Assessment Using a different olour, orret or add to your answers aove. You may need to use the ak of this sheet or another piee of paper. Then irle the faes in the Chek row in the tale. Question Chek Feedak What will you do next? Tik one ox. strengthen my learning strengthen then extend extend Note down any speifi areas you need to improve. _ Ation You may now e given another ativity. After this, note down any remaining areas you need to improve and how you will try to improve in these areas. 7