A dump truck uses a hydraulic cylinder, as the drawing illustrates. When activat

Question

A dump truck uses a hydraulic cylinder, as the drawing illustrates. When activated by the operator, a pump injects hydraulic oil into the cylinder at an absolute pressure of 3.91 x 106 Pa and drives the output plunger, which has a radius of 0.130 m. Assuming the plunger remains perpendicular to the floor of the load bed, find the torque that the plunger creates about the axis identified in the drawing. A paperweight, when weighed in air, has a weight of W = 27.1 N. When completely immersed in water, however, it has a weight of Win water = 18.9 N. Find the volume of the paperweight. A solid concrete block weighs 150 N and is resting on the ground. Its dimensions are 0.380 m x 0.170 m x 0.120 m. A number of identical blocks are stacked on top of this one. What is the smallest number of whole bricks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block? (Hint: First decide which face of the brick is in contact with the ground.) The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is 1/22 of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1022 kg/m3.

Explanation / Answer

1)

T = r x F  sin

= r (PA)sin

F = P x A = 3.91 x 10^6 Pa x pi (0.13)^2 m^2

F = 2.07 x 10^5 N

T = 3.5m x 2.07 x 10^5 N x sin 90 =7.2 x 10^5 Nm

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2)

Weight of water displaced when the paperweight is submerged inside water = 27.1 N -18.9N = 8.2 N
Mass of the water displaced = 8.2/g = 8.2/9.8 = 0.636 kg
Volume of water displaced = mass of water displaced/density of water
= 0.836/1000 (because density of water = 1000 kg/m^3)
= 0..836 x 10^-3 m^3
= 8.36x 10^-4 m^3

Since the paperweight is completely submerged inside water, therefore the volume of the paperweight
= 8.36 x 10^-4 m^3

Ans: 8.36 x 10^-4 m^3
If you need answer in liter, then multiply by 1000. You get 8.36 x 10^-1 L OR 0.836 L
If you need answer in mL, then multiply the value in m^3 by 10^6. You get 836 mL

I have rounded off the answers.
That 836 which you got is actually in mL. 836 mL, which approximately equals 836 mL

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3)

Use the smallest area "face"
0.12 x 0.17 = 0.02 m^2

Pressure = Force / Area

101000 . 0.02 = Force = 2020 N

Number of blocks = 2020 / 150 = 13.4

So 13 blocks are needed to produce a pressure of at least one atmosphere.

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4)

1)
p=gh
then
h=p/(g)
p=101325/22=4605.68 Pa
then
h=4605.68/(1022*9.8)=0.45m

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