Question

1. A certain lake, filled with fresh water, is 60 m deep and located at sea level. What is the absolute pressure (in kPa) at the bottom of the lake? 2. A cylindrical barrel of mass 30 kg and diameter 90 cm is floating in a bay. A 70 kg person steps onto the barrel, causing it to descend a little farther into the water. Find the distance the barrel sinks (in cm) after this additional weight is added. 3. A hydraulic press in a garage is attached to a platform that is used to lift cars. The press includes a small piston that is attached to a fluid-filled pipe, which opens into a larger chamber under the platform (see image below). If the platform has a radius of 2 m and the piston has a radius of 2 cm, how much force (in N) must be applied to the piston in order to raise an 1800 kg car?

          1. A certain lake, filled with fresh water, is 60 m deep
and located at sea level. What is the absolute pressure (in kPa) at
the bottom of the lake?
2. A cylindrical barrel of mass 30 kg and diameter 90 cm is
floating in a bay. A 70 kg person steps onto the barrel, causing it
to descend a little farther into the water. Find the distance the
barrel sinks (in cm) after this additional weight is added.
3. A hydraulic press in a garage is attached to a platform
that is used to lift cars. The press includes a small piston that
is attached to a fluid-filled pipe, which opens into a larger
chamber under the platform (see image below). If the platform has a
radius of 2 m and the piston has a radius of 2 cm, how much force
(in N) must be applied to the piston in order to raise an 1800 kg
car?

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Added by Josefina Y.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Penny Riley

07/21/2022

Step 1

8 m/s^2, h = 60 m, atmospheric pressure = 1.013 * 10^5 Pa Absolute pressure = 1000 * 9.8 * 60 + 1.013 * 10^5 Absolute pressure = 588000 + 101300 Absolute pressure = 689300 Pa Step 2: Calculate the distance the barrel sinks in the water after the additional weight Show more…

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1. A certain lake, filled with fresh water, is 60 m deep and located at sea level. What is the absolute pressure (in kPa) at the bottom of the lake? 2. A cylindrical barrel of mass 30 kg and diameter 90 cm is floating in a bay. A 70 kg person steps onto the barrel, causing it to descend a little farther into the water. Find the distance the barrel sinks (in cm) after this additional weight is added. 3. A hydraulic press in a garage is attached to a platform that is used to lift cars. The press includes a small piston that is attached to a fluid-filled pipe, which opens into a larger chamber under the platform (see image below). If the platform has a radius of 2 m and the piston has a radius of 2 cm, how much force (in N) must be applied to the piston in order to raise an 1800 kg car?

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Transcript

00:01 What's the absolute pressure at the bottom of the lake? we're given our depth is 60 meters.

00:06 Our atmospheric pressure is equal to 1 .03 times 10 to the 5 pascels.

00:14 So our absolute pressure is equal to our gauge pressure plus our atmospheric pressure, which is equal to our density of water times g plus h plus our atmospheric pressure.

00:26 So we plug in 10 to the 3 times 9 .8 times our temperature.

00:31 60 plus 1 .013 times 10 to the 5 and our absolute pressure is equal to 6 .89 times 10 to the 5 pascels.

00:44 Now in this problem we also have a question 2.

00:49 Our question 2 tells us we have a cylindrical barrel, find the distance that the barrel sinks in centimeters after this additional weight is added.

01:03 Okay, so we'd like to find the distance that it sinks after this additional weight is added.

01:14 Okay.

01:15 So to solve this problem, our buoyant force is equal to m times g.

01:25 And our height is equal to 4 times mass divided by pi d squared times the density of our water.

01:37 So we want to multiply four times our 30 kilogram mass, 4 times our 30 kilogram mass, 4 times our 30 kilogram mass, divided by pi times our d, we're given that it's 90 or 0 .90 squared times 1 ,000.

02:01 So that's 4 .7 centimeters.

02:04 Assuming that it goes down by a distance of x, the total height is equal to h plus x...

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