Question

an object has a weight of -135 n. calculate the mass of the object. remember to use -10.0 m/s^2 for the acceleration due to gravity. be sure your answer has the appropriate number of significant figures, include correct units: m, s, m/s, m/s^2, and put a space in between the number & units (example: -10.0 m/s^2).
\\(\vec{f}_g = m\vec{a}_g\\)
a person has a mass of 68.2 kg. calculate the weight of the person on earth in newtons. remember to use -10.0 m/s^2 for the acceleration due to gravity. be sure your answer has the appropriate number of significant figures, include correct

Explanation:

Step1: Recall the formula for weight

The formula given is $\vec{F}_g = m\vec{a}_g$, where $F_g$ is the weight (force due to gravity), $m$ is the mass, and $a_g$ is the acceleration due to gravity. We need to solve for $m$, so we can rearrange the formula to $m=\frac{F_g}{a_g}$.

Step2: Substitute the given values

We know that $F_g = - 135\space N$ and $a_g=- 10.0\space m/s^{2}$. Substituting these values into the formula for $m$:
$$m=\frac{- 135\space N}{- 10.0\space m/s^{2}}$$

Step3: Calculate the mass

When we divide $- 135$ by $- 10.0$, we get $m = 13.5\space kg$ (the negative signs cancel out, and we consider significant figures: $135$ has three significant figures, $10.0$ has three, so the result should have three significant figures).

Answer:

13.5 kg