Question

1. a martian weighs 38 n on the surface of mars. the acceleration due to gravity on mars is 3.8 m/s² and the acceleration due to gravity on jupiter is 23.1 m/s². find the following:

a. the martians mass
b. the martians weight on earth
c. the martians weight on jupiter.

Explanation:

Part a: The Martian’s mass

Step1: Recall the weight formula

Weight \( W = m \times g \), where \( W \) is weight, \( m \) is mass, and \( g \) is acceleration due to gravity. To find mass, we rearrange the formula to \( m=\frac{W}{g} \).

Step2: Substitute the values

Given \( W = 38\space N \) (weight on Mars) and \( g = 3.8\space m/s^{2} \) (gravity on Mars). Substitute into the formula: \( m=\frac{38}{3.8} \).

Step3: Calculate the mass

\( \frac{38}{3.8}= 10\space kg \).

Step1: Recall the weight formula

Weight \( W = m \times g \), where \( m \) is mass (found in part a as \( 10\space kg \)) and \( g \) is acceleration due to gravity on Earth (\( 9.8\space m/s^{2} \)).

Step2: Substitute the values

Substitute \( m = 10\space kg \) and \( g = 9.8\space m/s^{2} \) into the formula: \( W=10\times9.8 \).

Step3: Calculate the weight

\( 10\times9.8 = 98\space N \).

Step1: Recall the weight formula

Weight \( W = m \times g \), where \( m = 10\space kg \) (mass from part a) and \( g = 23.1\space m/s^{2} \) (gravity on Jupiter).

Step2: Substitute the values

Substitute into the formula: \( W = 10\times23.1 \).

Step3: Calculate the weight

\( 10\times23.1=231\space N \).

Answer:

The Martian’s mass is \( \boldsymbol{10\space kg} \).

Part b: The Martian’s weight on Earth