Question

1. an astronaut has a mass of 68-kg. what is the acceleration due to gravity on the moon, if her weight is 110.16-n? 4) a 49-kg child is standing on earth. what is his weight? 5) what is the weight of an 18-kg dog on earth?

Explanation:

Problem 3

Step1: Recall the formula for weight

The formula relating weight (\(W\)), mass (\(m\)), and acceleration due to gravity (\(g\)) is \(W = m \times g\). We need to solve for \(g\), so we can rearrange the formula to \(g=\frac{W}{m}\).

Step2: Substitute the given values

We are given that the mass \(m = 68\space kg\) and the weight \(W = 110.16\space N\). Substituting these values into the formula for \(g\), we get \(g=\frac{110.16}{68}\).

Step3: Calculate the value of \(g\)

Performing the division \(\frac{110.16}{68}=1.62\space m/s^2\).

Step1: Recall the formula for weight on Earth

The acceleration due to gravity on Earth, \(g_{Earth}=9.8\space m/s^2\). The formula for weight is \(W = m \times g\).

Step2: Substitute the given values

We are given that the mass \(m = 49\space kg\) and \(g = 9.8\space m/s^2\). Substituting these values into the formula, we get \(W=49\times9.8\).

Step3: Calculate the weight

Performing the multiplication \(49\times9.8 = 480.2\space N\).

Step1: Recall the formula for weight on Earth

The acceleration due to gravity on Earth, \(g_{Earth}=9.8\space m/s^2\). The formula for weight is \(W = m \times g\).

Step2: Substitute the given values

We are given that the mass \(m = 18\space kg\) and \(g = 9.8\space m/s^2\). Substituting these values into the formula, we get \(W = 18\times9.8\).

Step3: Calculate the weight

Performing the multiplication \(18\times9.8=176.4\space N\).

Answer:

The acceleration due to gravity on the moon is \(1.62\space m/s^2\).

Problem 4