Question

question 18 (1 point)
object a weighs 40 n on earth, and object b weighs 40 n on the moon. the moons gravity is one sixth of earths. compare the masses of the objects.
a has 6 times the mass of b.
b has 6 times the mass of a.
a and b have equal mass.
the situation as stated is impossible.

Explanation:

Step1: Recall the formula for weight

Weight \( W = mg \), where \( m \) is mass and \( g \) is gravitational acceleration.

Step2: Find mass of Object A

For Object A on Earth: \( W_A = m_A g_E \), so \( m_A=\frac{W_A}{g_E} \). Given \( W_A = 40\ N \), so \( m_A=\frac{40}{g_E} \).

Step3: Find mass of Object B

For Object B on Moon: \( W_B = m_B g_M \), and \( g_M=\frac{1}{6}g_E \). Given \( W_B = 40\ N \), so \( m_B=\frac{W_B}{g_M}=\frac{40}{\frac{1}{6}g_E}=\frac{240}{g_E} \).

Step4: Compare masses of A and B

Find the ratio \( \frac{m_B}{m_A}=\frac{\frac{240}{g_E}}{\frac{40}{g_E}} = 6 \). So \( m_B = 6m_A \), meaning B has 6 times the mass of A.

Answer:

B has 6 times the mass of A.