Thinking about Newton's Laws
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- Mabel Bruce
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1 Newtonan modellng In ths actvty you wll see how Newton s Laws of Moton are used to connect the moton of an object wth the forces actng on t. You wll practse applyng Newton s three laws n some real contexts. Informaton sheet In 1687, Isaac Newton publshed the Prncpa. In ths book he brought together hs understandng of mathematcs and the scence we now call physcs. Newton recognsed that, when forces act, they change the moton of objects. Before ths, datng as far back as Arstotle ( BC), t was thought that forces caused moton. If Arstotle and Newton were to slde stones across the ce, Arstotle would suggest they need a force to keep them gong. Newton would argue that, f a force acts on the stones, they wll accelerate. The stones actually decelerate, slowng down so that they eventually stop. Thnkng about Newton's Laws Read the statements about each of Newton s Frst, Second and Thrd Laws. Thnk about how t apples n each of the stuatons descrbed n each secton. Wrte down your thoughts about the questons asked. Draw dagrams to help explan your thnkng. Newton's Frst Law A partcle wll reman at rest or contnue to move unformly n a straght lne unless acted upon by a non-zero resultant force. Apple attached to tree T In Newton's words: 'Every body perseveres n ts state of rest, or of unform moton n a rght lne, unless t s compelled to change that state by forces mpressed thereon.' Modellng the apple as a partcle, the forces actng on t are the tenson n ts stalk and ts weght. There s no resultant force, so the apple remans at rest. W Nuffeld Free-Standng Mathematcs Actvty Newtonan modellng Student sheets Copable page 1 of 7
2 Notes on Newton s Frst Law Unform moton s moton wth constant velocty. As velocty ncludes speed and drecton, unform moton s moton wth constant speed and always n the same drecton. A body wth no resultant force actng on t s n equlbrum. It s n statc equlbrum f t s not movng; t s n dynamc equlbrum f t s movng wth constant velocty. A The dagram shows a book lyng on a table. What forces are actng on the book? What does Newton s Frst Law tell you about them? B Ths pcture shows a ball thrown through the ar. Neglect ar resstance. What forces are actng on the ball? What s the resultant force actng on the ball? Consder horzontal and vertcal forces separately. Apply Newton's Frst Law n each drecton. What does Newton's Frst Law suggest wll happen to the ball? What effect does gnorng ar resstance have on the answer? C A space probe s shown here travellng freely, wthout usng ts rockets, n deep space. What does Newton's Frst law predct wll happen to the space probe? D The Moon travels n a nearly crcular orbt about the Earth. What does Newton's Frst law tell you about the moton of the Moon? It was by thnkng about such moton that Newton arrved at hs three Laws. He was able to explan the moton of the Moon rotatng about the Earth, and the moton of an apple fallng to the ground, usng the same underlyng prncples. Nuffeld Free-Standng Mathematcs Actvty Newtonan modellng Student sheets Copable page 2 of 7
3 Newton's Second Law If a non-zero resultant force acts on a partcle, then the partcle wll not be n equlbrum. A resultant force, F newtons, actng on a partcle of mass m klograms, wll gve rse to acceleraton, a m s 2, of the partcle. The acceleraton s n the drecton of the resultant force and the magntude of the acceleraton s gven by the relatonshp: F = ma One newton s defned as the force requred to gve a mass of 1 kg an acceleraton of 1 m s 2. Modellng the apple as a partcle, the resultant force actng on t s ts weght, mg newtons. It accelerates vertcally downwards; a = g = 9.8 m s 2 when ar resstance can be consdered neglgble. In Newton's words: 'The alteraton of moton s ever proportonal to the motve force mpressed; and s made n the drecton of the rght lne n whch that force s mpressed.' Apple fallng from a tree W= mg Notes on Newton s Second Law Newton's Second Law brngs together the deas of a gravtatonal force and acceleraton due to gravty. The weght of an object s the force of attracton due to the Earth. It s the weght of an object that causes t to accelerate. If you apply Newton's Second Law to a mass of m klograms near the Earth's surface, you fnd that t has a weght, W = mg. W = mg a = g = 9.8m s -2 E The pcture shows a ball thrown through the ar. Neglect ar resstance. What s the resultant force actng on the ball? Apply Newton's Second Law n both the horzontal and vertcal drectons to explan the moton of the ball. F One end of a lght nextensble strng s attached to an empty tool box whch s lyng on a smooth table. The strng passes over a smooth pulley and s ted at the other end to a heavy bag as shown. When ths system s released from rest the bag falls vertcally to the ground. Use Newton's Second Law to explan the moton of the tool box. Use Newton's Second Law to explan the moton of the bag. Nuffeld Free-Standng Mathematcs Actvty Newtonan modellng Student sheets Copable page 3 of 7
4 Newton's Thrd Law Every force arses as the acton of one body on another. The objects are subject to forces that are equal n magntude and act n opposte drectons. The force on the apple due to the table s equal and opposte to the force on the table due to the apple. Apple on a table In Newton's words: 'To every acton there s always opposed an equal reacton: or the mutual actons of two bodes upon each other are always equal and drected to contrary parts.' G Forces on the apple N 1 s the normal contact force actng on the apple. Ths force mantans the apple n equlbrum. Force on the table due to the apple N 2 s the force that acts on the table because of N 1 actng on the apple. N 1 N 2 W = mg What s the magntude of the normal contact force on the apple? What s the magntude of the force that acts on the table because of the apple? What happens to the magntudes of the forces f the mass of the apple s ncreased? How does Newton's Thrd Law apply n ths stuaton? H Thnk about a fallng ball (neglectng ar resstance). What s the resultant force actng on the ball? What causes ths? How does Newton's Thrd Law apply n ths case? Nuffeld Free-Standng Mathematcs Actvty Newtonan modellng Student sheets Copable page 4 of 7
5 Try these Use Newton's Laws to answer the followng questons. Model all objects as partcles. Take the acceleraton due to gravty to be g = 9.8 m s 2. 1 A resultant force of 6 newtons acts on a partcle of mass 3 klograms. What s the acceleraton? 2 What force appled to a mass of 2.5 kg wll cause an acceleraton of 8 m s 2? 3 A car of mass 400 kg travels along a horzontal road wth constant deceleraton 5 m s 2. Fnd the resultant horzontal resstve force, F, actng on the car. resstve force, F a = 5 m s kg drecton of moton 4 A tenns player serves a ball of mass 55 grams. Consder the ball at any pont on ts path before t bounces. Assume that ar resstance s neglgble. a What s the magntude and drecton of the ball's acceleraton? b What s the magntude and drecton of the resultant force actng on the ball? 5 A tran of total mass 150 tonnes decelerates at 2 m s 2 as t approaches a staton along a straght horzontal track. (1 tonne = 1000 kg) Fnd the magntude of the resstve force, F. resstve force, F 2 m s 2 total mass 150 tonnes 6 A woman drags a heavy load of mass 50 kg across a floor wth a force of 70 N. Modellng the floor as smooth and the load as a partcle, and assumng that the rope s horzontal, calculate the acceleraton of the load. 7a A partcle of mass 5 kg s acted upon by a horzontal force of 80 N. Fnd the horzontal acceleraton of the partcle. b A partcle of mass 5 kg s acted upon by a force of 80 N actng vertcally upwards. The only other force on the partcle s ts weght. Fnd the acceleraton. Nuffeld Free-Standng Mathematcs Actvty Newtonan modellng Student sheets Copable page 5 of 7
6 8 A book, of mass 200 g, rests on a table wthn the carrage of a tran. The tran accelerates at 0.5 m s 2 out of a staton. a Draw the forces actng on the book. b If the book does not slp, fnd the magntude of the frcton force actng on the book. 9 A drver of mass 57 kg s sttng n the drvng seat of a car at rest. There s no contact between the drver's back and the seat. a Draw a dagram of the forces actng on the drver. b The drver starts the car, and accelerates at 1 m s 2 along a horzontal road. Draw a new force dagram showng the forces now actng on the drver. Fnd the value of the resultant force actng on the drver, and state where t comes from. 10 Horzontal forces of 5 newtons and 3 newtons act on a partcle of mass 2 klograms. Fnd the acceleraton produced f these forces: a act n the same drecton b act n opposte drectons. 11 A bulder rases brcks to the top of a buldng usng a pulley system. Each platform has a mass of 20 kg. When both platforms are empty they hang n equlbrum, wth the lower platform just off the ground, as shown n the dagram. To lower platform B, the bulder adds to t a load of 10 kg. a Draw force dagrams showng the forces actng on: the lower platform, A the upper platform, B b Use Newton's Second Law to wrte down equatons relatng the forces actng on each platform to the acceleraton of each. Hnt: Assume that the platforms are attached by a lght, nextensble strng passng over a smooth pulley, so that each platform wll have the same acceleraton, and the tenson n both parts of the rope wll be equal. c Calculate the acceleraton of each platform, and the tenson n the rope. A B Nuffeld Free-Standng Mathematcs Actvty Newtonan modellng Student sheets Copable page 6 of 7
7 12 A hotel guest travels by lft from the ground floor to the fourth floor wth her sutcase n her hand. The mass of the hotel guest s 70 kg and the mass of the sutcase s 20 kg. The lft accelerates at 0.5 m s 2 as t sets off from the ground floor, and decelerates at 0.4 m s 2 as t nears the 4 th floor. a Draw force dagrams showng the forces actng on: the sutcase the hotel guest as the lft sets off from the ground floor. b Use Newton's Second Law at the tme the lft sets off from the ground floor to fnd: the force exerted by the hotel guest on her sutcase. the normal reacton between the hotel guest and the floor of the lft. c Use Newton's Second Law at the tme the lft nears the 4 th floor to fnd: the force exerted by the hotel guest on her sutcase. the normal reacton between the hotel guest and the floor of the lft. d Explan brefly when, on her lft journey, the hotel guest wll feel the true weght of her sutcase. Reflect on your work What are Newton s three Laws? If an object s movng, how can you tell f t s n equlbrum? Whch of Newton s Laws are you usng? How s your weght related to your acceleraton due to gravty? Whch of Newton s Laws are you usng? Nuffeld Free-Standng Mathematcs Actvty Newtonan modellng Student sheets Copable page 7 of 7
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