In order to conserve fuel,you modify your car by removing 100 kg of excess weight.How much energy is saved each time you drive up a 3 km high mountain? A) 2.94 $\times$ 10⁶ J B) 2.86 $\times$ 10⁴ J C) 3.86 $\times$10⁶ J D) 3.00 $\times$ 10⁵ J

Question

Quizplus · Accepted Answer

The work done to lift the car up a 3 km high mountain is given by: 
work = force x distance 
The force here is the weight of the car and the weight removed, which is 100 kg. Assuming an average weight of 1500 kg, the force is (1500 + 100) x 9.8 = 16,520 N. 
The distance is 3 km, which is 3000 m. 
The work done is therefore: 
work = force x distance = 16,520 x 3000 = 49,560,000 J

Removing 100 kg of weight reduces the force by (100/1600) x 16,520 = 1032 N. 
The work saved is therefore: 
work saved = force saved x distance = 1032 x 3000 = 3,096,000 J

Therefore, the energy saved each time you drive up a 3 km high mountain is 3.86 x 10^6 J, which is closest to option C (3.86 x 10^16 J).

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