The weight of an object on each planet is proportional to the force of gravity in that planet’s atmosphere. The force of gravity on planet Earth is approximately 9.81 m/s2

Question

9.81

m
/
s
2
. The force of gravity on Mars is 0.38 m/s2
0.38

m
/
s
2
. If Hill weighs 128 pounds on Earth, how much would he weigh on Mars? Round the answer to the nearest hundredth.(1 point) .

Answer 1

To find Hill's weight on Mars, we can use the ratio of the gravitational forces on Mars and Earth. We start by converting Hill's weight from pounds to a mass in kilograms, then we can convert that mass back to weight on Mars.

1. Convert Hill's weight from pounds to kilograms:

   \[ \text{Weight in kg} = \frac{\text{Weight in pounds}}{2.20462} = \frac{128}{2.20462} \approx 58.06 \text{ kg} \]

2. Calculate the weight on Mars using the ratio of gravity:

   \[ \text{Weight on Mars} = \text{Weight in kg} \times \text{Gravity on Mars} \]

   The weight on Earth (in Newtons) can be calculated as:

   \[ \text{Weight on Earth} = \text{Weight in kg} \times g_{\text{Earth}} \approx 58.06 \times 9.81 \approx 570.53 \text{ N} \]

   Now, to find the equivalent weight on Mars:

   \[ \text{Weight on Mars} = \text{Weight in kg} \times g_{\text{Mars}} = 58.06 \times 0.38 \approx 22.06 \text{ N} \]

3. Convert this weight back to pounds:

   \[ \text{Weight on Mars in pounds} = \text{Weight on Mars} \times 0.224809 = 22.06 \times 0.224809 \approx 4.96 \text{ pounds} \]

Thus, Hill would weigh approximately 4.96 pounds on Mars, rounded to the nearest hundredth.