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Question 2

$\begin{gathered} mass_{}ofthecablecar=m_c=2500\operatorname{kg} \\ massofthepeople=m_P=80(70\operatorname{kg})=5600\text{ kg} \\ g=9.81m/s^2 \\ h=950\text{ m} \\ t=\text{ }6\text{ minutes= 6(60s)=360 s} \\ A) \\ For\text{ total gain gravitational potential energy for the car} \\ P_C=\text{ }m_cgh \\ P_C=\text{ (}2500\operatorname{kg}\text{)(}9.81m/s^2\text{)(}950\text{ m)} \\ P_C=\text{ 23,298,750 J} \\ \text{The total gain gravitational potential energy for the car is 23,298,750 J} \\ \\ For\text{ total gain gravitational potential energy for the people} \\ P_P=\text{ }m_Pgh \\ P_P=\text{ (}5600\text{ kg)(}9.81m/s^2\text{)(}950\text{ m)} \\ P_P=\text{ 52,189,200 J} \\ \text{The total gain gravitational potential energy for the people is 52,189,200 J} \\ \\ B)\text{ } \\ \text{The total work is the sum of gain gravitational potential energy for the} \\ \text{car and people} \\ W_T=\text{23,298,750 }J+\text{52,189,200 J} \\ W_T=75,487,950\text{ J} \\ \text{The total work done by the motor }is\text{ }75,487,950\text{ J} \\ \\ C) \\ For\text{ the minimun power} \\ \text{Powe}=(W_T)/(t)=\frac{75,487,950\text{ J}}{\text{360 s}}=209,688.75\text{ W} \\ \text{The minimun power is }209,688.75\text{ W} \end{gathered}$

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