Question

1. which of the following statements are true of the quantity weight? list all that apply.

a. the weight of an object is dependent upon the value of the acceleration of gravity.
b. the weight of an object would be less on the moon than on the earth.
c. a person could reduce their weight significantly by taking an airplane ride to the top of mount everest.
d. two objects of the same mass can weigh differently.
e. to gain weight, one must put on more mass.
f. the weight of an object can be measured in kilograms.
g. the weight of an object is equal to the force of gravity acting upon the object.
h. when a chemistry student places a beaker on a balance and determines it to be 84.3 grams, they have weighed the beaker.

Explanation:

• Option A: Weight formula is \(W = mg\) (\(m\) - mass, \(g\) - acceleration of gravity). So weight depends on \(g\).
• Option B: Moon's \(g\) (\(g_{moon}\approx1.62\ m/s^{2}\)) is less than Earth's (\(g_{earth}\approx9.8\ m/s^{2}\)). Using \(W = mg\), weight is less on Moon.
• Option C: Change in height (like going to top of Mount Everest) causes a very small change in \(g\) (due to \(g=\frac{GM}{r^{2}}\), \(r\) - distance from center of Earth). The change in weight is negligible, not significant.
• Option D: If two objects have same \(m\) but are in places with different \(g\) (e.g., one on Earth, one on Moon), \(W = mg\) will be different.
• Option E: From \(W = mg\), if \(g\) is constant (e.g., on Earth's surface), increasing \(m\) increases \(W\).
• Option F: Kilograms is unit of mass. Weight's unit is Newton (\(N\)) (\(W = mg\), \(m\) - kg, \(g\) - \(m/s^{2}\), so \(W\) - \(kg\cdot m/s^{2}=N\)).
• Option G: By definition, weight is the force of gravity on an object (\(W = F_{gravity}=mg\)).
• Option H: When a student places a beaker on a balance and gets 84.3 grams, they measure mass (balance - compares masses, unit grams - mass unit). Weight's unit is Newton.

Answer:

A. The weight of an object is dependent upon the value of the acceleration of gravity.
B. The weight of an object would be less on the Moon than on the Earth.
D. Two objects of the same mass can weigh differently.
E. To gain weight, one must put on more mass.
G. The weight of an object is equal to the force of gravity acting upon the object.