Question
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
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) .
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) .
Answers
GPT-4o mini
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.
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.
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