[1.] t=5s || s(5)=200 s(0)=5 s=200m-5m=195m ||V=ds/dt= (5+4t+2t^2+t^3) ` / (t) ` =(4+4t+3t^2)/1 || 4[m/s]+ 20[m/s]+ 75[m/s]= 99[m/s]=V || a=dv/dt= (4+ 4t+ 3t^2) ` / (t) ` = (4+6t) / 1 || 4[m/s^2]+ 6*5[m/s^3…*s]= 34[m/s^2] [2.] m1=1kg, m2=2kg, M=2kg, a=?, Q=m*g {Fw1=N1-Q1; ||-Fw2=N2-Q2→Fw2= Q2-N2} {m1*a=N1-m1*g || m2*a=m2*g-N2} Z zas. dyn. dla br. sztywnej: Mw=J*ε || M>=r>*F> || Mw= M2-M1=N2*ru-N1*ru= ru*(N2-N1) || ru*(N2-N1)=J*ε || a= dv/dt= dw/dt*ru=ru*ε→ ε=a/ru || J=1/2*M*ru^2 || ru*(N2-N1)= 1/2*M*ru^2*a/ru || {N2-N1= 1/2*M*a || m1*a=N1-m1*g→N1= m1*a+ m1*g || m2*a=m2*g - N2→N2=m2*g - m2*a} m1*a+m1*g - (m2*g - m2*a)= 1/2*M*a || m1*g - m2*g= 1/2*M*a - m1*a - m2*a || g*(m1-m2)=a*(1/2*M-m1-m2) || [g*(m1 - m2)]/[1/2*M - m1 - m2]=a || [(m/s^2)*kg]/[kg]= m/s^2

[3.] mezon ł=10^-8 s || v=0,999c || s=? || c=300000000 m/s = 3*10^8 m/s || t=ł / [1 - (v^2/c^2)] - z def. o dylatacji czasu || V=ds/dts=v*t || s=v*ł / [1 - (v^2/c^2)]= (0,999*3*10^8*10^-8) / 1-[(0,998001 c^2) / c^2]= 0,999*3 / 0,001999= 2,997/0,0447101= 67,03 || [m/s*s] / [(m^2/s^2) / (m^2/s^2)]=m [4.] ??? [5.] a=?, N=?, f=0,01, m1=1kg, m2=2kg {Fw1=N-T || -Fw2=N-Q2 Fw2=Q2-N} {m1a=N-T N=m1a+T || m2a= Q2-N} T=f*Fn, Fn=Q1 ⇒ T=m1*g*f || m2a=Q2-(m1a+T) || m2a=m2g-m1a-m1gf || m2a+m1a= m2g-m1gf || a(m2+m1)=g(m2-m1f) || a=[g(m2-m1)] / [m2*m1] jednostki [(m/s^2)*kg] / [kg]= m/s^2 ||N=m1a+T= m1*[g(m2-m1f)] / [m2+m1]…+m1gf jednostki [kg*(m/s^2)*kg] / kg…+kg*m/s^2= N+N=N [6.] po2x || po= mo/v= mo/a^3 || p=m/v '=m/a^2*a ' bo długość zmienia tylko jeden bok || m=mo* [1]/ [1-(v^2/c^2)] || a ` = a*[1-(v^2/c^2)] ||

2po=p || 2*(mo/a^3)= mo / [1-(v^2/c^2)] /a^2*a*[1-(v^2/c^2)] || 2mo/a^3= mo / a^3*[1-(v^2/c^2)] || 2p= p*([1] / [1-(v^2/c^2)]) || 2p*[1-(v^2/c^2)]=p || 1-(v^2/c^2)= p/2p || 1-(1/2)= v^2/c^2 || (1/2)*c^2=v^2 || v=c/2 [7.] α=45, h=10m Ciało wykonuje 2 ruchy: jednost. prostoliniowy w poziomie i jednost. przyśpieszony w pionie. ↓V1u ↘Vu →Vo || mgh=(mv^2)/2 || V1u=√(2gh) || sinα= (V1u)/Vu || Vo=V1u/sinα= √(2gh)/√2/2 || cosα=Vo/Vu || Vu=Vo/cosα= 2*√(2gh)/√2/(√2/2)= [2*√(2gh)/√2]- 2/√2= [4*√(2gh)]/2= 2√(2gh) || √[(m/s^2)*m]= √(m^2/s^2)= m/s [8.] M=2, m=1, Fw=m*a, Q=N, Q-N=m*a, m*g-N=m*a || a=dv/dt=(w*ru)/dt=ε*ru⇒ε=a/ru || J=0,5M*r^2 || Mw=N*ru || Mw=ε*J || N*ru=(a/ru)*J || N*ru=(a/ru)*1/2*M*ru^2 || N=1/2*a*M→ a=2*(N/M) || m*g-N=m*a || m*g-N=m*2*(N/M) ||

(m*g)/m= 2*(N/M)+N || g=2*(N/M)+N || g=2(N/M)+(MN)/M= (2N+MN)/M || gM=2N+MN || gM=N(2+M) || (gM)/(M+2)=N [9.] √[1-(v^2/c^2)]= ♥ || Eu=Ec-Eo→ mo*c^2 || Ec→ (mo*c^2)/ ♥ || En=[(mo*c^2)/ ♥]- mo*c^2= mo*c^2*[(1/♥)-1] || kg*m^2/s^2=kJ [JA] Ek=1/2*mv^2 || m(v)= m.spocz./♥ || Ek=1/2*v^2*(m.spocz./♥) || (m^2/s^2)*kg=kJ [10.] Vo=?, h=10, V1=10m/s || Ec=Ek+Ep, Eko+Epo=Ek1+Ep1, Eko=1/2*m*vo^2, Epo=0, Ek1=1/2*m*v1^2, Ep=mgh|| 1/2*m*vo^2= [1/2*m*v1^2]+ mgh || vo^2=v1^2+2gh || vo=√(v1^2+2gh)= √(100+200)= √300 [11.] Fw1=Q-N || Fw2=N || ma=QN || ma=N || ma=Q-ma || 2ma=Q || a=Q/(2m)⇒a=(mg)/(2m)=(1/2)g [12.] P=m*v || m(v)-masa relatywistyczna, m(v)= m.spocz./♥ || P=v*(m.spocz./♥) || (m/s)*kg

[1.] t=5s || s(5)=200 s(0)=5 s=200m-5m=195m ||V=ds/dt= (5+4t+2t^2+t^3) ` / (t) ` =(4+4t+3t^2)/1 || 4[m/s]+ 20[m/s]+ 75[m/s]= 99[m/s]=V || a=dv/dt= (4+ 4t+ 3t^2) ` / (t) ` = (4+6t) / 1 || 4[m/s^2]+ 6*5[m/s^3…*s]= 34[m/s^2] [2.] m1=1kg, m2=2kg, M=2kg, a=?, Q=m*g {Fw1=N1-Q1; ||-Fw2=N2-Q2→Fw2= Q2-N2} {m1*a=N1-m1*g || m2*a=m2*g-N2} Z zas. dyn. dla br. sztywnej: Mw=J*ε || M>=r>*F> || Mw= M2-M1=N2*ru-N1*ru= ru*(N2-N1) || ru*(N2-N1)=J*ε || a= dv/dt= dw/dt*ru=ru*ε→ ε=a/ru || J=1/2*M*ru^2 || ru*(N2-N1)= 1/2*M*ru^2*a/ru || {N2-N1= 1/2*M*a || m1*a=N1-m1*g→N1= m1*a+ m1*g || m2*a=m2*g - N2→N2=m2*g - m2*a} m1*a+m1*g - (m2*g - m2*a)= 1/2*M*a || m1*g - m2*g= 1/2*M*a - m1*a - m2*a || g*(m1-m2)=a*(1/2*M-m1-m2) || [g*(m1 - m2)]/[1/2*M - m1 - m2]=a || [(m/s^2)*kg]/[kg]= m/s^2

[3.] mezon ł=10^-8 s || v=0,999c || s=? || c=300000000 m/s = 3*10^8 m/s || t=ł / [1 - (v^2/c^2)] - z def. o dylatacji czasu || V=ds/dts=v*t || s=v*ł / [1 - (v^2/c^2)]= (0,999*3*10^8*10^-8) / 1-[(0,998001 c^2) / c^2]= 0,999*3 / 0,001999= 2,997/0,0447101= 67,03 || [m/s*s] / [(m^2/s^2) / (m^2/s^2)]=m [4.] ??? [5.] a=?, N=?, f=0,01, m1=1kg, m2=2kg {Fw1=N-T || -Fw2=N-Q2 Fw2=Q2-N} {m1a=N-T N=m1a+T || m2a= Q2-N} T=f*Fn, Fn=Q1 ⇒ T=m1*g*f || m2a=Q2-(m1a+T) || m2a=m2g-m1a-m1gf || m2a+m1a= m2g-m1gf || a(m2+m1)=g(m2-m1f) || a=[g(m2-m1)] / [m2*m1] jednostki [(m/s^2)*kg] / [kg]= m/s^2 ||N=m1a+T= m1*[g(m2-m1f)] / [m2+m1]…+m1gf jednostki [kg*(m/s^2)*kg] / kg…+kg*m/s^2= N+N=N [6.] po2x || po= mo/v= mo/a^3 || p=m/v '=m/a^2*a ' bo długość zmienia tylko jeden bok || m=mo* [1]/ [1-(v^2/c^2)] || a ` = a*[1-(v^2/c^2)] ||

2po=p || 2*(mo/a^3)= mo / [1-(v^2/c^2)] /a^2*a*[1-(v^2/c^2)] || 2mo/a^3= mo / a^3*[1-(v^2/c^2)] || 2p= p*([1] / [1-(v^2/c^2)]) || 2p*[1-(v^2/c^2)]=p || 1-(v^2/c^2)= p/2p || 1-(1/2)= v^2/c^2 || (1/2)*c^2=v^2 || v=c/2 [7.] α=45, h=10m Ciało wykonuje 2 ruchy: jednost. prostoliniowy w poziomie i jednost. przyśpieszony w pionie. ↓V1u ↘Vu →Vo || mgh=(mv^2)/2 || V1u=√(2gh) || sinα= (V1u)/Vu || Vo=V1u/sinα= √(2gh)/√2/2 || cosα=Vo/Vu || Vu=Vo/cosα= 2*√(2gh)/√2/(√2/2)= [2*√(2gh)/√2]- 2/√2= [4*√(2gh)]/2= 2√(2gh) || √[(m/s^2)*m]= √(m^2/s^2)= m/s [8.] M=2, m=1, Fw=m*a, Q=N, Q-N=m*a, m*g-N=m*a || a=dv/dt=(w*ru)/dt=ε*ru⇒ε=a/ru || J=0,5M*r^2 || Mw=N*ru || Mw=ε*J || N*ru=(a/ru)*J || N*ru=(a/ru)*1/2*M*ru^2 || N=1/2*a*M→ a=2*(N/M) || m*g-N=m*a || m*g-N=m*2*(N/M) ||

(m*g)/m= 2*(N/M)+N || g=2*(N/M)+N || g=2(N/M)+(MN)/M= (2N+MN)/M || gM=2N+MN || gM=N(2+M) || (gM)/(M+2)=N [9.] √[1-(v^2/c^2)]= ♥ || Eu=Ec-Eo→ mo*c^2 || Ec→ (mo*c^2)/ ♥ || En=[(mo*c^2)/ ♥]- mo*c^2= mo*c^2*[(1/♥)-1] || kg*m^2/s^2=kJ [JA] Ek=1/2*mv^2 || m(v)= m.spocz./♥ || Ek=1/2*v^2*(m.spocz./♥) || (m^2/s^2)*kg=kJ [10.] Vo=?, h=10, V1=10m/s || Ec=Ek+Ep, Eko+Epo=Ek1+Ep1, Eko=1/2*m*vo^2, Epo=0, Ek1=1/2*m*v1^2, Ep=mgh|| 1/2*m*vo^2= [1/2*m*v1^2]+ mgh || vo^2=v1^2+2gh || vo=√(v1^2+2gh)= √(100+200)= √300 [11.] Fw1=Q-N || Fw2=N || ma=QN || ma=N || ma=Q-ma || 2ma=Q || a=Q/(2m)⇒a=(mg)/(2m)=(1/2)g [12.] P=m*v || m(v)-masa relatywistyczna, m(v)= m.spocz./♥ || P=v*(m.spocz./♥) || (m/s)*kg

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