Question

Geologists place tiltmeters on the sides of volcanoes to measure the displacement of the surface as magma moves inside the volcano. Although most tiltmeters today are electronic, the traditional tiltmeter, used for decades, consisted of two or more water-filled metal cans placed some distance apart and connected by a hose. FIGURE $P14.45$shows two such cans, each having a window to measure the water height. Suppose the cans are placed so that the water level in both is initially at the $5.0cm$mark. A week later, the water level in can $2$is at the $6.5cm$mark.

A. Did can $2$move up or down relative to can $1$? By what distance?

B. Where is the water level now in can $1$?

Short answer

Part (a)

(a) The movement of Can $1$relative to Can $2$in the downward direction is $3cm$

Part (b)

(b) The new level of water in Can$1$is $3.5cm$

Step-by-step solution

Explanation(part A)

(A). The rising water level in the Can $2$denotes that the Can have sunk concerning the Can$1$.

Because the total amount of water remains constant, the rise in water level in Can$2$is the same as the decline in water level in Can$1$.

The water level in the two cans is equalized in the middle of the height change.

As a result, the relative change in height of the cans is equal to half of the change in height of the water.

Hence, the movement of Can $2$relative to Can $1$in the downward direction is $2(6.5cm-5.0cm)=3cm$

To find the fall of water level (part B)

Can $1$'s water level falls at the same time as can $2$'s water level reaches.

The new water level in Can$1$is $(5.0cm-1.5cm)=3.5cm$