Find the work (in ft-lb) done in raising 500 lb of ore from a mine that is 1000 ft deep. Assume that the cable used to raise the ore weighs 2 lb/ft. A) $5 \times 10 ^ { 5 }$ B) $2.5 \times 10 ^ { 6 }$ C) $2 \times 10 ^ { 6 }$ D) $6 \times 10 ^ { 5 }$ E)10⁶ F) $1.5 \times 10 ^ { 6 }$ G) $7 \times 10 ^ { 5 }$ H) $4 \times 10 ^ { 5 }$

Question

Quizplus · Accepted Answer

The work done is the sum of the work to lift the ore and the work to lift the cable. The work to lift the ore is $500 \, \text{lb} \times 1000 \, \text{ft} = 5 \times 10^5 \, \text{ft-lb}$. The work to lift the cable is $\int_0^{1000} 2x \, dx = 10^6 \, \text{ft-lb}$. Total work is $5 \times 10^5 + 10^6 = 1.5 \times 10^6 \, \text{ft-lb}$.

Find the Work (In Ft-Lb) Done in Raising 500 Lb 5×1055 \times 10 ^ { 5 }5×105

Find the Work (In Ft-Lb) Done in Raising 500 Lb $5 \times 10 ^ { 5 }$