Mass — Question 2

Question 2

Mass remains fixed when local gravitational field changes

A sample has inertial mass 4 kg. Use weight magnitude $W=mg$. Compare sites with $g=10$ and $g=2$ m/s$^2$. A separate horizontal test uses net force 12 N.

1. Find the sample’s weight at each site.

2. Find its horizontal acceleration under the test force at each site.

3. What would a force scale calibrated to display $W/(10\ \mathrm{m/s^2})$ show at the second site?

Question 2 - Solution

Mass remains fixed when local gravitational field changes

(a) Change weight with field.

$$\boxed{W_1=4(10)=40\,\mathrm N},\quad\boxed{W_2=4(2)=8\,\mathrm N}$$ The weights are 40 N and 8 N. Gravity’s force changes while the sample’s mass remains 4 kg.

(b) Use inertial response.

$$a_1=a_2=\frac{F_x}{m}=\frac{12}{4}=3\,\mathrm{m/s^2}$$ The test acceleration is $12/4=3$ m/s$^2$ at both sites, assuming all horizontal contributions are included in the specified net force.

(c) Distinguish a display calibration from mass.

$$m_{\mathrm{display}}=\frac{W_2}{g_{\mathrm{calibration}}}=\frac8{10}=0.8\,\mathrm{kg}\ne4\,\mathrm{kg}$$ The scale would display 0.8 kg under that uncorrected calibration. This is a misleading mass estimate caused by assuming the wrong local g, not an actual reduction of the sample’s inertial mass.