In the opening scenes of the movie Raiders of the Lost Ark....

In the opening scenes of the movie Raiders of the Lost Ark. Indiana Jones tries to remove a gold idol from a booby-trapped pedestal. He replaces the idol with a bag of sand of approximately equal volume. (Density of gold $=19.32 \mathrm{~g} / \mathrm{cm}^{3} ;$ density of sand $\approx 2 \mathrm{~g} / \mathrm{cm}^{3}$.) a. Did he have a reasonable chance of not activating the masssensitive booby trap? b. In a later scene he and an unscrupulous guide play catch with the idol. Assume that the volume of the idol is about $1.0 \mathrm{~L}$. If it were solid gold, what mass would the idol have? Is playing catch with it plausible?

In the opening scenes of the movie Raiders of the Lost Ark. Indiana Jones tries to remove a gold idol from a booby-trapped pedestal. He replaces the idol with a bag of sand of approximately equal volume. (Density of gold $=19.32 \mathrm{~g} / \mathrm{cm}^{3} ;$ density of sand $\approx 2 \mathrm{~g} / \mathrm{cm}^{3}$.)
a. Did he have a reasonable chance of not activating the masssensitive booby trap?
b. In a later scene he and an unscrupulous guide play catch with the idol. Assume that the volume of the idol is about $1.0 \mathrm{~L}$. If it were solid gold, what mass would the idol have? Is playing catch with it plausible?

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Key Concepts

Mass Calculation via Density and Volume

Mass can be calculated by multiplying the density of a material by its volume. This concept is used to deduce the mass of the gold idol and the bag of sand. It plays a critical role in assessing whether the substitution would avoid triggering a booby trap that is sensitive to weight changes.

Mass-Sensitive Mechanisms

Certain systems or devices, such as the booby trap in this scenario, are designed to respond to changes in mass. Understanding how the mass of the substituted object compares to the original enables an analysis of whether the device might be triggered inadvertently when an object of significantly lower mass but equal volume is used.

Density

Density is a fundamental physical property defined as mass per unit volume. It helps determine how much mass is contained in a given volume of a material. In this context, comparing the densities of gold and sand is crucial to understand how swapping them affects the overall mass while keeping volume constant.

Volume

Volume is the measure of the amount of space an object occupies. Here, maintaining the same volume when substituting a gold idol with a bag of sand is a key factor, as it ensures that the disguise fits the cavity or pedestal, even if the mass is significantly different.

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