[tex]Given[/tex]
[tex]m=0.2kg[/tex]
[tex]m_{t}=0.750kg[/tex]
[tex]{h}=0.86m[/tex]
[tex]{v}=0.97m/s[/tex]
[tex]~Powered~ Phase~ \Delta d=4.53m[/tex]
[tex]~Coasting~ Phase~ \Delta d=2.02m[/tex]
[tex]Required[/tex]
[tex]{E}_{k},Power,{F}_{f} ~On ~Coasting ~Phase ~and~{F}_{f} ~On ~Powered ~Phase[/tex]
[tex]Solution[/tex]
[tex]Initial Energy= Gravitational Potential Energy[/tex]
[tex]{E}_{g}={m}g\Delta h[/tex]
[tex]={0.2kg}*9.8N/kg*0.86m[/tex]
[tex]{E}_{g}=1.68J[/tex]
[tex]Maximum Kinetic Energy[/tex]
[tex]{E}_{k}=(1/2)m{v}^2[/tex]
[tex]=(1/2)0.200Kg(0.97m/s)^2[/tex]
[tex]{E}_{k}=0.1J[/tex]
[tex]Calculating ~{F}_{f} ~On ~Powered ~Phase[/tex]
[tex]\vec a=v/ \Delta t[/tex]
[tex]\vec a=\frac{0.97m/s}{4.63s}}[/tex]
[tex]\vec a=0.21m/s^2[/tex]
[tex]\vec F_{app}=mg[/tex]
[tex]\vec F_{app}=0.200Kg*9.8N/Kg[/tex]
[tex]\vec F_{app}=1.96N[/tex]
[tex]\vec F_{Net}=m \vec a[/tex]
[tex]=0.750Kg*0.21m/s^2[/tex]
[tex]\vec F_{Net}=0.16N[/tex]
[tex]\vec F_{Net}=\vec F_{app}+\vec F_{f}[/tex]
[tex]\vec F_{f}=0.16N-1.96N[/tex]
[tex]\vec F_{Net}=-1.80N[/tex]
[tex]\vec F_{Net}=1.80N[/tex]
[tex]Calculating ~{F}_{f} ~On ~Coasting ~Phase[/tex]
[tex]{E}_{T}={m}g\Delta h[/tex]
[tex]={0.2kg}*9.8N/kg*0m[/tex]
[tex]{E}_{T}=0J[/tex]
[tex]{E}_{T}={E}_{k}+{W}_{f}[/tex]
[tex]0J=0.35J+\vec F_{f}\Delta d[/tex]
[tex]0J=0.35J+\vec F_{f}*2.02m[/tex]
[tex]\vec F_{f}=-0.35J/2.02m[/tex]
[tex]\vec F_{f}=-0.17N[/tex]