Question

challenge: the weight of your pet pony standing still on earth is 400 pounds.
a) what is the pony’s mass? (show all work)
b) how many pounds will the pony weigh on neptune? (show all work)
c) will the pony have more or less mass on neptune?
super challenge: what is a
eally easy\ way to lose weight without losing mass?

Explanation:

Part A

Step1: Recall mass - weight relation

Weight on Earth \( W_E = m\times g_E \), where \( g_E = 32\space ft/s^2\) (approximate gravitational acceleration on Earth) and mass \( m=\frac{W_E}{g_E}\). But also, mass is an intrinsic property, and we can use the fact that on Earth, weight in pounds and mass in slugs: \( m=\frac{W}{g}\), but if we consider the conversion from pounds (weight) to mass in kilograms, we know that \( 1\space pound - force= 4.448\space N\) and \( F = mg\), \( g = 9.8\space m/s^2\). So \( m=\frac{W}{g}\), where \( W = 400\space lb_f\), \( g = 32\space ft/s^2\) (in English units) or \( g=9.8\space m/s^2\) (in SI units). Let's use SI units for clarity. First, convert 400 pounds - force to Newtons: \( W_E=400\times4.448 = 1779.2\space N\). Then mass \( m=\frac{W_E}{g_E}=\frac{1779.2}{9.8}\approx181.55\space kg\). Alternatively, in English units, mass in slugs is \( m=\frac{W}{g}=\frac{400}{32}=12.5\space slugs\). Since mass is constant, the pony's mass is \( 12.5\space slugs\) (or approximately \( 181.55\space kg\)).

Step2: Conclusion

The mass of the pony is calculated by dividing its weight on Earth by the gravitational acceleration on Earth. Using \( m=\frac{W}{g}\) with \( W = 400\space lb\) and \( g = 32\space ft/s^2\), we get \( m=\frac{400}{32}=12.5\space slugs\) (or in SI units, approximately \( 181.55\space kg\)).

Step1: Find gravitational acceleration on Neptune

The gravitational acceleration on Neptune \( g_N\approx11.15\space m/s^2\) (or in English units, \( g_N\approx36.58\space ft/s^2\)). Let's use the English unit approach since the weight on Earth is given in pounds. We know that weight \( W = m\times g\), and mass \( m\) is constant. From part A, \( m = 12.5\space slugs\). So weight on Neptune \( W_N=m\times g_N\).

Step2: Calculate weight on Neptune

Substitute \( m = 12.5\space slugs\) and \( g_N = 36.58\space ft/s^2\) into the formula \( W_N=m\times g_N\). So \( W_N=12.5\times36.58 = 457.25\space pounds\). (If we use SI units: \( m = 181.55\space kg\), \( g_N = 11.15\space m/s^2\), \( W_N=m\times g_N=181.55\times11.15\approx2024.3\space N\), convert back to pounds: \( \frac{2024.3}{4.448}\approx455\space pounds\), the slight difference is due to approximation of \( g_N\) values).

Step1: Recall mass definition

Mass is the amount of matter in an object. It is an intrinsic property and does not depend on the location of the object (like on Earth or Neptune). Weight, on the other hand, depends on the gravitational force at the location (\( W = m\times g\)).

Step2: Conclusion about mass on Neptune

Since mass is independent of the gravitational field, the pony's mass on Neptune will be the same as its mass on Earth. So the mass will be neither more nor less, it will be the same.

Answer:

The pony's mass is \( 12.5\space slugs\) (or approximately \( 181.55\space kg\))

Part B