Chapter 5: rce and Mtin I-a rce is the interactin between bjects is a vectr causes acceleratin Net frce: vectr sum f all the frces n an bject. v v N v v v v v ttal net = i = + + 3 + 4 i= Envirnment respnse f the bject +... = v ma
rce Examples Gravitatinal rictin tensin spring nrmal mmentum change electrstatic magnetic nuclear etc... Srry Gerge Lucas, it s nt...
Newtn s first law Newtn s first law: If n frce acts n a bdy, then the bdy s velcity cannt change, that is, the bdy can nt accelerate if at rest, remains at rest if mving, cntinues mving with same velcity Inertial reference frame is ne in which Newtn s laws hld
Dg + Car rm the picture, did the car decelerate, velcity remain cnstant, r accelerate? Assume the dg was peacefully sitting n the seat befre this event.. car decelerated. car s velcity remained cnstant 3. car accelerated
Symbl: m Mass Definitin: The mass f an bject is a measure f its resistance t being accelerated. SI Base unit: kg (by the way, the English unit fr mass is the slug ) Scalar quantity!
Mass Definitin: The mass f an bject is a measure f its resistance t being accelerated. Mass is an intrinsic characteristic (srt f...) f an bject, hwever its value des change at high speeds (Special Relativity) Has t d with that speed limit c thing... The clser an bject is mving tward a speed f c, the less it accelerates fr a given frce. m = m v c Mre abut that later (i.e., in Phys40). r nw, (Phys30) m is a cnstant...
Newtn s Secnd Law Newtn s secnd law: The net frce n a bdy is equal t the prduct f the bdy s mass and the acceleratin f the bdy Σ = m a Σ : vectr sum f all the frces that act n that bdy Σ x = m a x Σ y = m a y Σ z = m a z Units: N = (kg)(m/s ) = kg. m/s
Example: An bject experiences three frces as shwn in the figure. What is the bject s acceleratin (a) in unit vectr ntatin and as (b) a magnitude and a directin y 0 3 x Befre starting, set up crdinate system and free bdy diagram. Only the frces are imprtant, nt the actual bdy!
Example: An bject experiences three frces as shwn in the figure. What is the bject s acceleratin (a) in unit vectr ntatin and as (b) a magnitude and a directin y 0 3 x (a) Break the prblem int x- and y-cmpnents = (4N cs 60 ) i + ( 4N sin 60 ) j = (55N) i + (0) j 3 = (3N cs 30 ) i + (3N sin 30 ) j net = (03.N) i + ( 9.5N) j
Example: An bject experiences three frces as shwn in the figure. What is the bject s acceleratin (a) in unit vectr ntatin and as (b) a magnitude and a directin y 0 3 x (b) ind and use net tan θ = net j net i net = net = (03.N) + ( 9.5N) = 05.0N net j tan θ = = 9.5N = 0.89 net 03.N i tan θ = 0.7
The gravitatinal frce near the surface f a very large bject (i.e., the Earth): g = m g Weight (gravitatinal frce) W = g = m g g varies with altitude, planet, etc... weight and mass are different, e.g. 7 kg ball, same mass n earth and mn, weighs 706 N n earth but 8 N n the mn Gravitatinal mass = Inertial mass (General Relativity)
ebruary, 00 Cnsider a traffic light f m = 4kg held by ne rpe which in turn is supprted by tw ther rpes as shwn with angles θ = 30 θ = 45, Which f the three rpes has the greater tensin? θ =30 θ =45 3
.. 3. 3 Which f the rpes has the greater tensin? 4. all have the same 5. nne f the abve θ =30 θ =45 3 mg
Traffic Light Cnsider a traffic light f m = 4kg held by ne rpe which in turn is supprted by tw ther rpes as shwn with angles θ = 30 θ = 45, Which f the three rpes has the greater tensin? Rpes & help share the weight, but rpe 3 carries all the weight. ) rpe ) rpe 3) rpe 3 θ =30 4) All rpes have the same tensin 3 θ =45
Traffic Light ebruary, 00 Cnsider a traffic light f m = 4kg held by ne rpe which in turn is supprted by tw ther rpes as shwn with angles θ = 30 θ = 45, Which f the three rpes has the greater tensin? x y = = cs30 sin 30 cs30 sin 30 cs30 sin 30 = + = + + + cs 45 sin 45 cs 45 sin 45 cs 45 sin 45 = = 3 3 = 3 0 = 3 0 =.00 θ =30 = 0.73 3 3 = 0.896 3 θ =45 3
The nrmal frce: N Special rces When a bdy presses against a surface, the surface defrms and pushes n the bdy with a nrmal frce N that is perpendicular t the surface N des nt always equal mg rictin: f is the resistance frce n a bdy when the bdy slides r attempts t slide alng a surface Always ppses mtin
Tensin: T When a crd is attached t a bdy and pulled taut, the crd pulls n the bdy with frce T CP : The bdy in fig (c) has a weight f 75 N, Is T equal t, greater than, r less than 75 N when the bdy is mving upward (a) at cnstant speed (b) at increasing speed (c) at decreasing speed?
Newtn s Third Law Newtn s third law: When tw bdies interact, the frces n the bdies frm each ther are always equal in magnitude and ppsite in directin AB = BA They d nt cancel each ther since they act n different bdies (different perspective)
If a sprts car and a semi-truck cllide headn, which vehicle experiences the greater frce? Remember that a mdern semi-truck has a mass f 0 cars!. car. truck 3. bth experience the same frce
If a sprts car and a semi-truck cllide headn, which vehicle experiences the greater acceleratin? Remember that a mdern semi-truck has a mass f 0 cars!. car. truck 3. bth experience the same acceleratin
Sample prblem 5-4. M = 3.3 kg, m =. kg, frictinless surface H falls as S accelerate t the right (a) What is the acceleratin f S? T = Ma T Acceleratin a links the tw masses tgether rces n m unbalanced frces n M mg T = ma T = Ma g = mg mg Ma = ma a = m g M + m
Assume = 0 N, surface frictinless. What is the acceleratin? = ( m + m + m 3 + m 4 )a = (0kg)a = 0N ==> a = 0N/0kg =.0 m/s Hw abut T? T = m a = (0kg)(.0 m/s ) = 0N
General scheme fr slving Newtn s law prblems - Islate the bjects in the prblem - r each bject f interest, identify all the external frces n that bject and draw a freebdy diagram fr this bject - establish a cnvenient crdinate system fr each bject and find the cmpnent f the frces alng thse axes. - Apply Newtn s nd law in the x and y directins fr each bject. ( e.g. Σ x = ma x, Σ y = ma y ) - Slve the resulting set f equatins.