AQA GCSE Physics. Topic 5: Forces. Notes. (Content in bold is for Higher Tier only)

Transcription

1 AQA GCSE Physics Tpic 5: Frces Ntes (Cntent in bld is fr Higher Tier nly)

2 Vectrs A Vectr has magnitude and directin A Scalar has just magnitude - Generally, scalars cannt be negative, but vectrs can be, as a certain directin is psitive Examples - Speed is scalar - Velcity is vectr - Distance is scalar - Displacement is vectr - Time is scalar - Acceleratin is vectr - Frce is vectr - Mass is scalar - Mmentum is scalar - Energy is scalar Imagine a ball thrwn ff a cliff, displacement is 0 at height f cliff, abve the cliff the ball has psitive displacement, and belw the clifftp the ball has negative displacement. - In lng answer questins, yu may be able t decide where the 0 pint f a vectr may lie, fr example yu culd set zer t be bttm f cliff, s the ball will never have negative displacement - Speed is nly velcity when given a directin, s thrwn 10mmss 1 is its speed but thrwn 10mmss 1 at 30 abve the hrizntal is the velcity Imagine a car travelling rund a rundabut at cnstant speed. While its speed is cnstant, its directin is cnstantly changing s its velcity is cnstantly changing therefre it is accelerating. Vectrs can be represented by arrws, with their size/length representing the vectr magnitude Object Interactin - A frce is a push r pull that acts n an bject due t the interactin with anther bject. All frces between bjects are either: - Nn-Cntact - the bjects are physically separated. Electrstatic The charges cause a frce f attractin/repulsin Gravitatinal attractin The mass creates a frce f attractin - Cntact - the bjects are physically tuching Nrmal cntact frce, which is felt in ppsite directin t cntact The frce is nrmal t the planes f cntact Frictin The surfaces and their rughness cause frictin when mved in cntact

3 Gravity All matter has a gravitatinal field, and attracts all ther matter - The larger the mass, the strnger the field, the greater the attractin Weight - The frce exerted n a mass by the gravitatinal field, in Newtns weight = mass gravitatinal field strength W = mg = m 10 Weight, W, in newtns, N and mass, m, in kilgrams, kg - Measured by a frce meter (als knwn as calibrated spring-balance) Weighing scale measures the frce yu exert, and then divides by 10 t give mass - Yu need t recall that n earth, g = 10 Same persn, n tw different planets? - Their mass is the same - The gravitatinal field strength, g, at the tw planets will be different (i.e. nt 10 fr bth) S their weight will be different n bth Acceleratin in free fall is due t gravity, and is the same as g, i.e. 10mmss 2 The weight f an bject is cnsidered t act at the bject s centre f mass Resultant Frce - This is a single frce representing the sum f all the frces acting n an bject - If mre than ne frce act alng a straight line, the resultant can be fund by adding (acting in the same directin) r subtracting (acting in ppsite directins) them Skydiver example - Frces that act are air resistance and weight - Initially, the skydiver has n air resistance and the nly frce acting n him is weight

4 - As he falls, he accelerates, increasing his speed (A) Resultant is simply 833N dwn - As air resistance increases, the resultant frce frm weight decreases (B) Resultant is = 483N dwn - S acceleratin decreases, s he is nt speeding up as quickly (C) Resultant is 133N dwn - Eventually they are equal and balance, s there is n resultant frce (D) Resultant = 0 - S there is n acceleratin when the resultant frce is 0 they travel at terminal velcity. - Free Bdy Diagrams shw the frces (and their directins) acting n an bject, like fr the skydiver abve Reslving Frces - A frce F at angle θθ t the grund can be reslved parallel and perpendicular t the grund - Using Pythagras Rule, the tw cmpnents are as shwn aa 22 + bb 22 = cc 22 FF 22 = (FFFFFFFFFF) 22 + (FFFFFFFFFF) 22 θθ FF FF cs θθ FF sin θθ Wrk Wrk Dne = Frce Distance W = Fs - Where Wrk Dne, W, is in jules J, the frce, F is in newtns N and the distance, s is in metres m. - Where distance is distance mved alng the line f actin f the frce - Wrk dne is when energy is transferred frm the bject ding the wrk t anther frm If a bk is lifted 1m in the air, and 2m t the right Wrk is dne (against gravity) when mving 1m vertically, as that is in the directin f the frce (gravity) Energy is transferred frm yur muscles t the bk, increasing its gravitatinal ptential. - One jule f wrk is dne when a frce f ne newtn causes a displacement f ne metre. 1 jule = 1 newtn-metre Wrk dne against frictinal frces causes a rise in temperature f the bject Springs - T stretch, bend r cmpress an bject, mre than ne frce has t be applied - If a single frce is applied t an bject, it will just mve in that directin If it is pulled in ppsite directins n either side f the bject, it will stretch If it is fixed at ne pint and stretched, a frce is still being applied by the fixed pint Defrmatin - This means changing shape

5 - Elastic Defrmatin The bject returns t its riginal shape when the lad has been remved Elastic band - Plastic Defrmatin The bject des nt return t its riginal shape when the lad has been remved A spring when pulled t far Hke s Law The extensin f an elastic bject, such as a spring, is directly prprtinal t the frce applied, prvided that the limit f prprtinality is nt exceeded. where: - F is the frce applied t the spring, NN - K is the spring cnstant, NNmm 1 - X is the extensin, mm FF = kkkk Linear line fr a Frce/Extensin Graph - This is elastic regin - It is fllwing Hke s Law - Gradient is k The pint it stps being linear is the limit f prprtinality. - Frm then n, it des nt bey Hke s Law Nn-Linear line - There is plastic behaviur here - It is nt fllwing Hke s Law - If shallw Lts f extensin fr nt a lt f frce Easy t stretch If graph is just linear, with n nn-linear end sectin, the material is brittle, s snaps instead f stretches after the elastic limit Wrk Dne Wrk Dne = 1 2 kkxx2 - When a frce stretches/cmpresses a spring, the spring des wrk Elastic ptential energy is stred in the spring Prvided it des nt inelastically defrm: The wrk dne n the spring = the elastic ptential energy stred Mments and Rtatin (Physics nly) - Fr an bject attached t a pivt pint (a pint which it can rtate abut, but cannt mve away frm); If a frce is applied alng a line passing thrugh the pivt (see diagram), the bject des nt rtate, and is just held still.

6 If there is a distance between the pivt and the line f actin f the frce, the bject rtates abut the pivt, in the directin f the frce applied. - If the Frce is applied nt perpendicular t the bject we need t cnsider the perpendicular distance frm pivt t line f frce Mment f a Frce = frce perpendicular distance Still rtates clckwise Nthing happens Rtates clckwise MM = FFFF where mment f a frce, M, in newtn-metres Nm, frce F in newtns N and distance d is the perpendicular distance frm the pivt t the line f actin f the frce, in metres m. Example f mments: Bike Riding pressing yur ft dwn n the pedal, causes a mment abut the pivt, turning the pedal arms. Equilibrium is when: sum f anticlckwise mments = sum f clckwise mments Levers and Gears (Physics nly) - Gears can change speed, frce r directin by rtatin Fr an example when the first gear is supplying the frce - If cnnected t a gear with fewer teeth (i.e. a smaller gear) The secnd gear will turn faster But with less frce In ppsite directin t first gear - If cnnected t a gear with mre teeth (i.e. a larger gear) Turns slwer Mre frce In ppsite directin The secnd gear will always turn in the ppsite directin - Blue gear is supplying the pwer - T increase the pwer, a larger gear is used fr the secndary (red) As the frce n the red gear is a further distance frm its pivt, the mmentum f the larger gear is greater

7 Pressure (Physics nly) Particles in a gas mve randmly in every directin and they exert frces n their cntainer, which is felt as pressure. pressure, p = frce area = F A Where the pressure, p, is in pascals Pa, the frce, F, in newtns N and the area, A, in metres squared, m 2. - Remember, pressure prduces a net frce at right angles t any surface Pressure in a Fluid (Physics nly) Factrs that influence flating and sinking An bject flats if its weight is less than the weight f the water it displaces - S a 1000kg bat will sink int the water until it has displaced 1000kg f water Prviding the bat desn t cmpletely submerge befre it displaces this amunt, then it will flat. Pressure in a liquid varies with depth and density, and this leads t an upwards frce n a partially submerged bject. - The buyancy frce is the upwards frce that cunteracts the weight f the flating bject - This is equal t the weight f the fluid displaced by the bject A ping png ball flats n water as its density is less than the density f the water, s fr the vlume displaced, the weight f the equivalent amunt f water is greater than the weight f the ping png ball, s the resultant frce is buyancy, s it flats Increasing the depth, the greater the weight f the water abve yu, s greater frce felt, s greater pressure pppppppppppppppp dddddd tttt aa cccccccccccc llllllllllll = hhppllhhhhhh cccccccccccc dddddddddddddd llllllllllll gg pp = hhρρρρ Where pressure p is in pascals Pa, the height f the clumn h in metres m, the density ρ in kilgrams per metre cubed kg/m 3 and the gravitatinal field strength g is in newtns per kilgram N/kg which is nrmally Upthrust: A partially (r ttally) submerged bject experiences a greater pressure n the bttm surface than n the tp surface. This creates a resultant frce upwards which is knwn as upthrust. - Earth s Atmsphere: A thin layer (relative t size f the earth) f air arund the Earth. The atmsphere gets less dense with increasing altitude - The atmsphere is a thin layer (relative t the size f the Earth) f air rund the Earth. The atmsphere gets less dense with increasing altitude.

8 - This is because it is the ttal weight f the air abve a unit area at a certain altitude. The weight f the air is the frce which causes the pressure S with higher elevatin, there are fewer air mlecules abve the unit area than the same area at lwer heights, s there is a smaller weight, s less pressure Idealised Assumptins, fr a simple mdel f the atmsphere: - Isthermal, s it is all at the same temperature - Transparent t slar radiatin - Opaque t terrestrial radiatin Frce and Mtin Distance is hw far an bject mves. Distance des nt invlve directin. Distance is a scalar quantity. Displacement includes bth the distance an bject mves, measured in a straight line frm the start pint t the nish pint and the directin f that straight line. Displacement is a vectr quantity. Speed des nt invlve directin. Speed is a scalar quantity. Velcity, which is a vectr quantity, is speed in a given directin. If an bject was travelling in a circular mtin, the bject is cnstantly changing directin, therefre the velcity, which is a vectr that depends n the mvement and the directin, is cnstantly changing. A change in velcity is defined as acceleratin, s althugh the bject isn t speeding up, it is accelerating due t the changing directin. The speed f a mving bject is rarely cnstant. When peple walk, run r travel in a car their speed is cnstantly changing. Typical Speeds: - Wind - 5 7mmss 1 - Sund - 330mmss 1 - Walking - ~ 1.5mmss 1 - Running - ~3mmss 1 - Cycling - ~6mmss 1 - Bus - 14km/h - Train - 125miles/h - Plane - 900km/h Distance measured in mm, cm, m and km and time measured in ms, s, mins and hurs. - Depending n lengths invlved, use apprpriate units speed = distance time vv = d t Remember t cnvert units t make sure everything is equivalent! Average speed fr nn-unifrm mtin: - Wrk ut TOTAL TIME and TOTAL DISTANCE - Then use: ttal distance average speed = ttal time - E.g. 3 sectins f different speeds t travel distances, use tttttttt = dddddddddddddddd t wrk ut ttal ssssssssss time, then sum the different distances, then use abve.

9 Graphs Displacement-Time Graphs - Gradient is velcity - Sharper gradient means faster speed - Negative gradient is returning back t starting pint - Hrizntal line means statinary - 0 Distance means that it is back t starting pint - Area under line = nthing - Curved Line means that the velcity is changing (acceleratin) - If an bject is accelerating, its speed can be determined by drawing a tangent and calculating the gradient f the distance-time graph. Velcity-Time Graphs - Gradient is acceleratin - Sharper gradient means greater acceleratin - Negative gradient is deceleratin - Hrizntal line means cnstant speed - 0 Velcity means that it is statinary - Area under line = distance travelled Smetimes cunting the squares is the best methd fr a curved line - Curved Line means that the acceleratin is changing Average Speed? - This is fr when the speed changes during the mtin - Use verall distances and timings t wrk ut average speed Falling in a fluid (Physics nly) - Initially, the bject will fall freely under gravity (9.8 m/s 2 ) Hwever drag frces will act (see skydiver) And then the bject will mve at terminal velcity - The graph shws an initial steep gradient, which dies ff t a flat gradient acceleratin decreases as drag increases, until n acceleratin at terminal velcity, ~40mmss 1 in this case Equatins Average Speed = aa = Ttal Distance Ttal Time vv uu tt vv 2 = uu 2 + 2aaaa Kinetic Energy = 1 2 mmvv2

10 Newtn s First Law An bject has a cnstant velcity unless acted n by a resultant frce - If a resultant frce acts n the bject, it will accelerate Acceleratin is change in velcity ver time S the velcity will change Either the directin r speed f the bject will change (r bth) - If n resultant frce acts n the bject And the bject is statinary, it will remain statinary And the bject is mving, it will cntinue t mve at the same velcity The tendency fr bjects t cntinue in unifrm velcity (r stay at rest) is inertia Newtn s Secnd Law The acceleratin f an bject is prprtinal t the resultant frce acting n the bject, and inversely prprtinal t the mass f the bject. Frce = mass x acceleratin FF = mmmm where F is the frce in newtns N, m is the mass in kg and a is the acceleratin in m/s 2. Inertia - The measure f hw difficult it is t change the velcity f an bject ffffiiccii iiiiiiiiiiiiiiii mmmmmmmm = aaaaaaaaaaaaaaaaaaaaaaaa = ff aa Newtn s Third Law Whenever tw bjects interact, the frces they exert n each ther are equal and ppsite. - Rcket taking ff The rcket exerts a frce n the gases being ejected. The gases apply a frce equal in magnitude but in ppsite directin n the rcket, which lifts it ff the surface. - A bk n a table The weight f the bk (frm the Earth) = the pull f the bk n the Earth Vehicle Stpping Distances - After seeing a hazard Befre yu react, during reactin time yu travel X metres Thinking Distance Then yu react, causing the car t slw dwn and stp ver Y metres Braking Distance stpping distance = thinking + braking distances Thinking Distance - Speed - Affected by reactin time - Cncentratin - Tiredness - Distractins - Influence f drugs/alchl Braking Distance - Speed - Pr rad cnditins (icy, wet) - Bald tires (lw frictin) - Wrn brake pads - Weight (mre passengers)

11 Speed and Braking Distance - Greater the speed, the greater distance travelled during the same time (reactin time) Typical stpping distances (Physics nly): Reactin Times vary ss fr each persn - Measure reactin times by the ruler drp Drp a ruler thrugh the persn s pen hand, the time it takes t catch it can be determined by ss = uuuu aatt2 wwheeeeee uu = 0 aaaaaa aa = gg, ssss tt = 2gggg Where s is the distance the ruler travels thrugh the hand When a frce is applied t the brakes f a vehicle: - Wrk is dne by the brakes (by frictin) nt the wheel S the vehicle s KE reduces And the temperature f the brakes increase - Greater the speed = greater braking frce needed t stp the car (ver the same distance) S greater frce = greater acceleratin This may lead t brakes verheating and a lss f cntrl, which is dangerus Mmentum mmmmmmmmmmmmmmmm = mmmmmmmm vviiiiffccffiivv pp = mmmm Where p is the mmentum in kilgrams metres per secnd kgms -1, m is the mass in kilgrams kg and v the velcity metres per secnd ms Mmentum is always cnserved in a cllisin r explsin (where there are n external frces like frictin, air resistance, electrstatic attractin etc.) - In cllisins: tttttttttt mmmmmmmmmmmmmmmm bbbbbbsseett = tttttttttt mmmmmmmmmmmmmmmm aaaaaaaaaa - S tw marbles clliding, each will have mmentum befre and after the cllisin Remember mmentum is a vectr

12 Changes in Mmentum (Physics nly) Newtn s Scnd Law: Frce is equal t the rate f change f mmentum FFttppccpp = cccccccchhpp iiii ccttccppccttppcc tttttttt (mmmm mmmm) = tt Safety Features (Physics nly) - When braking hard, there is a large deceleratin - S a large frce is felt n the passengers and the cars - This can be dangerus, as the frce felt can cause injury (neck whiplash etc.) - Safety This can be explained by the equatin abve large deceleratin = large change in mmentum ver a shrt time, s a large frce exerted n the bject (persn!) Seatbelts Withut these, when hard braking yu will keep mving and nt decelerate, causing t fly thrugh the windshield These strap yu in, but als stretch under large frces Stretching increases the distance mved slightly, but extends the time taken mre fr passengers t stp This decreases the rate f change f mmentum and therefre reduces the frce Crumple znes Withut these, the car wuld be a slid metal blck, which wuld immediately stp during a crash instead f sftening the blw slightly sfter areas at the frnt f the car, which crumple upn a crash It absrbs energy t defrm and cmpact It increases the time taken fr the car t stp This reduces acceleratin and frce n passengers Air Bags Withut these yur head will whip frward during a crash, hitting the steering wheel r whipping back t hit the back f the head, which wuld cause serius neck energy These inflate instantaneusly upn a crash Yur head hits this and slws dwn Increases the time taken fr the head t stp mving S reduces the frce n the neck