If a 55-gallon drum is completely full of water, what would be the weight of all that water on Mars?
The correct answer and explanation is:
To calculate the weight of the water in a 55-gallon drum on Mars, we need to first determine the weight of the water on Earth and then account for the difference in gravity between Earth and Mars.
- Weight of water on Earth:
- The volume of water is 55 gallons.
- Since 1 gallon of water weighs about 8.34 pounds, the total weight of the water on Earth is: 55 gallons×8.34 pounds/gallon=458.7 pounds55 \, \text{gallons} \times 8.34 \, \text{pounds/gallon} = 458.7 \, \text{pounds}
- Gravity on Earth and Mars:
- The acceleration due to gravity on Earth is approximately 9.8 m/s29.8 \, \text{m/s}^2.
- The acceleration due to gravity on Mars is much weaker, about 3.7 m/s23.7 \, \text{m/s}^2, roughly 38% of Earth’s gravity.
- Weight on Mars:
The weight of an object is the force exerted on it due to gravity. Since weight is directly proportional to the gravitational pull, the weight of the water on Mars will be: Weight on Mars=Weight on Earth×Gravity on MarsGravity on Earth\text{Weight on Mars} = \text{Weight on Earth} \times \frac{\text{Gravity on Mars}}{\text{Gravity on Earth}} Weight on Mars=458.7 pounds×3.79.8=458.7 pounds×0.3776=173.4 pounds\text{Weight on Mars} = 458.7 \, \text{pounds} \times \frac{3.7}{9.8} = 458.7 \, \text{pounds} \times 0.3776 = 173.4 \, \text{pounds}
Thus, the weight of a 55-gallon drum full of water on Mars would be approximately 173.4 pounds.
Explanation:
The key to understanding this problem lies in the difference in gravitational forces. Weight is the measure of gravitational force acting on an object, so when you move from one planet to another, the same object will weigh less on a planet with weaker gravity. Mars has only 38% of Earth’s gravity, so the water in the drum weighs significantly less there. By adjusting the Earth’s weight for the gravity on Mars, we can find the correct weight on that planet.