Force & Motion: Newton s Laws

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1 oce & otion: Newton Law ( t Law) If no net foce act on a body then the body velocity cannot change. Zeo net foce implie zeo acceleation. The ma of an object detemine how difficult it i to change the object velocity. a ha nothing to do with ize! xample: If a foce of N i applied to a paticle with a ma of kg, what i it acceleation? If the ame foce i applied to a paticle with a ma of kg, what i it acceleation? oce i meaued fom the acceleation it poduce. If the velocity of an object change (eithe in magnitude o diection), then it wa acted upon by a net extenal foce in the diection of the acceleation. Inetial ma! ( nd Law) The net foce on a body i equal to it ma time it acceleation. net all = i i= dv = m dt In the SI ytem foce i meaued in Newton, N, whee N = kg m/. v = ma R. ield /6/0 PHY 053 Page

2 ou undamental oce Gavity : Attactive foce between any two o moe object that have ma (Sola Sytem, Galaxie, Cuved Space-Time, Black Hole). lectomagnetim: Attactive o epulive foce between two o moe object that cay electic chage (Atom & olecule, Chemical Reaction). Weak oce: Attactive o epulive foce between two o moe object that cay weak chage (Neuton Decay, Beta Radioactivity). Stong oce: Attactive o epulive foce between two o moe object that cay tong chage (bind the quak within hadon and meon, Atomic Nuclei, iion & uion). neuton u d d W - Qweak Actually all object that have enegy inteact with gavity! a i one fom of enegy. Qweak u d u νe e - poton R. ield /6/0 PHY 053 Page

3 undamental oce: Gavity m gav m G ( h + R gav = = ) mg gav = G m Gavity i an attactive foce between two object that have ma. Nea the uface of the ath the gavitational foce i appoximately by gav = mg, ince g = G ( h + R ) = G G 9.8m / R ( + h / R ) R Gavitational ma! y-axi m h R x-axi The eaon all object (nea the uface of the eath) fall with the ame contant acceleation, g 9.8 m/, independent of ma i becaue the inetial ma of an object i equal to it gavitational ma (i.e. thee i only one type of ma). The weight of an object i equal to the magnitude of the gavitational foce on the object. Nea the uface of the ath, weight = mg. R. ield /6/0 PHY 053 Page 3

4 oce: Nomal, iction, Tenion When a body pee againt a uface, the uface puhe on the object with a nomal foce, N, that i pependicula to the uface. N gav If one eithe lide o attempt to lide an object ove a uface, thee i a fictional foce, f, poduced that i diected along the uface, oppoite to the diection of the intended motion. f Diection of lide When a cod (o a ope, cable, o othe uch object) i attached to a body and pulled taut, the cod pull on the body with a foce T diected away fom the body and along the cod. The foce i called the tenion foce. T T Thee thee foce ae not fundamental. They aie fom the fou fundamental foce! R. ield /6/0 PHY 053 Page 4

5 Applying Newton Law: xample (3 d Law) When two bodie inteact, the foce on the bodie fom each othe ae alway equal in magnitude and oppoite in diection. xample: (ig. ) A contant hoizontal foce, a, i applied to block A, which puhe againt block B with a foce diected hoizontally to the ight. (ig. ) The ame foce, a, i applied to block B; now block A puhe on block B wa a foce diected hoizontally to the left. If the block have a combined ma um and if thee i no fiction between the block and the uface, what ae the magnitude of thei acceleation in (ig. ) and (ig. ) and what i the magnitude of the foce a? What i the ma of block A and block B? (expe the anwe in tem of,, and um ) a = ( ) / + um a + a a ig. ig. = A = um B um + + B A = A B ictionle! ictionle! R. ield /6/0 PHY 053 Page 5

6 Applying Newton Law: xample xample: (ig. ) A block of ma on a fictionle hoizontal uface i connected by a cod ove a male, fictionle pulley to a econd block of ma. What ae the magnitude and diection of the acceleation of each block and what i the tenion in the cod? (expe the anwe in tem of,, and g) a = g + xample: (ig. ) A block of ma on a fictionle plane inclined at an angle θ i connected by a cod ove a male, fictionle pulley to a econd block of ma. What ae the magnitude and diection of the acceleation of each block and what i the tenion in the cod? (expe the anwe in tem of,, θ, and g) R. ield /6/0 a = inθ g + T = + T g ( + inθ ) = g + ictionle! ictionle! ig. ig. PHY 053 Page 6 θ

7 oce & otion: iction Coefficient of tatic fiction μ : Cae : v = 0 & a = 0 If on object doe not move (i.e. v = 0 a = 0) then the tatic fictional foce, f, and the component of the extenal foce ext that i paallel to the uface balance each othe and the maximum value of the magnitude of f i given by f N ext f μ N and max ext = f max = μ = μ g N g aximum extenal foce without the block liding! Cae : v not 0 Coefficient of kinetic fiction μ k : If the object begin to lide along the uface (i.e. v 0) then the magnitude of the fictional foce, apidly deceae to a value f k, whee f N v ext f k = μ k N and ext = ( a + μ g) k g Note that μ k < μ. R. ield /6/0 PHY 053 Page 7

8 iction: xample xample (tatic fiction): (ig. ) A block of ma i at et on a plane inclined at angle θ to the hoizontal. If the coefficient of tatic fiction between the block and the uface of the plane i μ, what i the laget angle θ without the block liding? ig. θ tanθ = μ xample (kinetic fiction): (ig. ) A block of ma lide along the floo while an extenal foce ext i applied at an upwad angle θ. If the coefficient of kinetic fiction between the block and the floo i μ k, what angle θ give the maximum value of the block acceleation a (while till keeping the block on the table)? ig. θ ext tanθ = μ k R. ield /6/0 PHY 053 Page 8

Phys 201A. Homework 6 Solutions. F A and F r. B. According to Newton s second law, ( ) ( )2. j = ( 6.0 m / s 2 )ˆ i ( 10.4m / s 2 )ˆ j.

Phys 201A. Homework 6 Solutions. F A and F r. B. According to Newton s second law, ( ) ( )2. j = ( 6.0 m / s 2 )ˆ i ( 10.4m / s 2 )ˆ j. 7. We denote the two foces F A + F B = ma,sof B = ma F A. (a) In unit vecto notation F A = ( 20.0 N)ˆ i and Theefoe, Phys 201A Homewok 6 Solutions F A and F B. Accoding to Newton s second law, a = [ (