Worksheet: Pascal’s Principle

In this worksheet, we will practice using Pascal’s principle to analyze the magnitude and direction of fluid pressure on an object.

Q1:

A cubic container holds water. The lid of the container can be pushed downward, exerting pressure on the water in the container. Which of the following statements most correctly describes how the pressure exerted by the water is changed when the lid is pushed downward?

  • AThe pressure exerted on the cube’s vertical sides is increased.
  • BThe pressure exerted on the base of the cube and its lid is increased.
  • CThe pressure exerted on the base of the cube is increased.
  • DThe pressure exerted on the base of the cube, its vertical sides, and its lid is increased.
  • EThe pressure exerted on the base of the cube and its vertical sides is increased.

Q2:

A bag attached to an intravenous drip holds saline solution that has a density of 2,160 kg/m3. The bag is 15 cm in height and full to the top. The solution flows from the drip through a hole of area 0.785 cm2 and passes through the tube into a cannula that has an opening of area 0.0225 cm2.

What is the magnitude of the force exerted by the saline solution at the hole at the base of the drip bag? Give your answer to two decimal places.

What is the magnitude of the force exerted by the saline solution at the cannula? Give your answer to three decimal places.

Q3:

A solid object falls through water of density 1,000 kg/m3. At the instant that the top of the object is 25 cm below the water’s surface, the water exerts a pressure on the top, bottom, and side of the object, as shown in the diagram.

Find π‘ƒοŠ§.

Find π‘ƒοŠ¨.

Find π‘ƒοŠ©.

Q4:

A tall and thin water container has holes in its side at different heights above the ground, as shown in the diagram. Water leaks from the holes in the container and only the leak from hole 𝐴 is shown. The leaks from the different holes travel different distances sideways from the water container. From which hole would the water travel farthest away from the container?

  • AHole 𝐡
  • BHole 𝐢
  • CHole 𝐴
  • DHole 𝐷

Q5:

A container that is 1.2 m under the sea, near the shore, is full of water of density 1,020 kg/m3. The container is suspended above the sea bed on a pole. The container is 3.5 m in height. Water can enter and leave the container through three holes in its walls and one hole in its base, as shown in the diagram. Water pressure is increased gradually at one of the holes in the walls until the pressure there is 7,500 Pa.

Is the pressure π‘ƒοŠ§ greater than, less than, or equal to 7,500 Pa?

  • AGreater than 7,500 Pa
  • BEqual to 7,500 Pa
  • CLess than 7,500 Pa

Is the pressure π‘ƒοŠ¨ greater than, less than, or equal to 7,500 Pa?

  • AEqual to 7,500 Pa
  • BGreater than 7,500 Pa
  • CLess than 7,500 Pa

Is the pressure π‘ƒοŠ© greater than, less than, or equal to 7,500 Pa?

  • AEqual to 7,500 Pa
  • BLess than 7,500 Pa
  • CGreater than 7,500 Pa

Q6:

Water in a container is pushed horizontally by a movable wall of the container, as shown in the diagram. The movable wall has sides of length 𝐿=0.25m and 𝐿=0.75m. Within the water in the container is a square metal sheet with sides of length 0.125 m. The sheet is supported by a pole so that all of its downward-facing surface is in contact with the liquid apart from a small area that the pole fits through. The water pushes the sheet when the container’s movable wall is moved. The force applied to the movable wall is equal to the force applied to the water by the wall.

What is the magnitude of the force due to the motion of the movable wall that pushes upward on the downward-facing surface of the metal sheet? Ignore the area of the hole where the pole passes through the sheet.

What is the magnitude of the force due to the motion of the movable wall that pushes downward on the upward-facing surface of the metal sheet? Ignore the area of the hole where the pole passes through the sheet.

Q7:

Water in a container is pushed horizontally by a movable wall of the container, as shown in the diagram. Inside the water-filled part of the container is a square metal sheet with sides of length 0.25 m. The base of the sheet is attached to the floor of the container, keeping the sheet vertically oriented. The water pushes the sheet when the container’s movable wall is moved. The movable wall has sides of lengths 𝐿=0.25m and 𝐿=0.75m. The force applied to the movable wall is equal to the force applied to the water by the wall.

What is the magnitude of the force that pushes the surface of the metal sheet that faces the movable wall?

What is the magnitude of the force that pushes the surface of the metal sheet that faces away from the movable wall?

  • A25 N
  • B100 N
  • C75 N
  • D400 N
  • E50 N

Q8:

A hydraulic pump has a thin shaft with an area of 0.15 m2 and a thick shaft with an area of 1.2 m2, as shown in the diagram. At the tops of the shafts are pistons that can be pushed. A force ||=85F N is applied to the piston in the thin shaft and the pressure of the hydraulic fluid applies a force F to the piston in the thick shaft. Find the magnitude of F.

Q9:

A curved object that is underwater moves a distance 𝐷 toward a larger object of the same shape, as shown in the diagram. All the water that the smaller object displaces due to its motion impacts the entire curved surface of the larger object that is facing the smaller object. The area of the smaller object that displaces water is 0.25 m2, and the area of the larger object that the displaced water impacts is 1.5 m2. The larger object moves a distance 𝑑 due to the force of the water that impacts it. What is the ratio of 𝑑 to 𝐷?

Q10:

A thin, rectangular-prism-shaped piston has sides 0.01 m and 0.015 m in length. The piston is pushed a horizontal distance of 0.25 m along a tube attached to a larger water tank, as shown in the diagram. The tube has the same cross section as the piston. The water tank is a rectangular prism with a cross section that has sides of lengths 0.05 m and 0.075 m. Floating on top of the water in the tank is a thin, wooden, rectangular-prism-shaped plank that has the same cross section as the water tank. Assume that the friction between the piston and the tube and that between the plank and the tank is negligible.

What is the distance 𝑑 that the plank rises?

The work done on the piston to move it is 5 J. What is the average force applied to the plank?

Q11:

The ratio between the cross section of the large piston to that of the small piston of a hydraulic lift is 3. By how much should the pressure acting on the large piston increase to maintain the two pistons at the same horizontal level if the pressure acting on the small piston increased by Δ𝑃?

  • AΔ𝑃
  • BΔ𝑃3
  • C2Δ𝑃
  • D3Δ𝑃

Q12:

The figure shows connected tubes with a horizontal base. If water is poured gradually, the height of the water in the branches A, B, and C at equilibrium is .

  • Aβ„Ž=β„Ž=β„ŽABC
  • Bβ„Ž>β„Ž>β„ŽBCA
  • Cβ„Ž=β„Ž<β„ŽBAC
  • Dβ„Ž<β„Ž<β„ŽBCA

Q13:

A force 𝐹 acts on the small piston of a hydraulic press so it moves downwards a distance of 300 cm. The ratio between the areas of the pistons of a hydraulic press is 150. Calculate the upward distance moved by the large piston.

  • A75 cm
  • B6 cm
  • C150 cm
  • D3 cm

Q14:

The areas of the pistons of a hydraulic press are 15 cm2 and 50 cm2. When a weight is placed on the small piston, the big piston moves 3 cm upwards, so the small piston moves a distance of cm downwards.

  • A7.5
  • B1.1
  • C10
  • D0.9

Q15:

The areas of the two branches of a U-shaped tube are 7 cm2 and 3 cm2. A suitable amount of water is poured in the tube, then some amount of oil is poured in the wide branch, so the level of water inside is lowered by 12 cm. If the densities of water and oil are 1β€Žβ€‰β€Ž000 kg/m3 and 881 kg/m3, respectively, then the mass of the displaced water is .

  • A0.04 kg
  • B0.03 kg
  • C0.06 kg
  • D0.08 kg

Q16:

The given figure shows a glass container of height 42 cm, completely filled with water. If the pressure due to water on point 𝐴 is 𝑃 and that at the base of the container is 3𝑃, then height β„Ž from the base of the container to point 𝐴 is equal to .

  • A14 cm
  • B28 cm
  • C37 cm
  • D21 cm

Q17:

A frictionless piston is used to trap an amount of air in a U-shaped tube containing mercury. The tube has an open branch and a closed one, as shown in the figure. If the piston has a mass of 5 kg and a cross-sectional area of 3Γ—10οŠͺ m2 and the trapped air has a pressure of 1.4Γ—10 Pa, then the height, β„Ž, of mercury indicated in the figure is . Take Hg density = 13,600 kg/m3, atmospheric pressure = 10 Pa, and 𝑔=10/ms.

  • A100 cm
  • B72 cm
  • C68 cm
  • D93 cm

Q18:

In the figure below, a hydraulic press is used to lift up a mass 𝑀 a distance of 1 cm. If the efficiency of the press is 90% and the work exerted on the smaller piston is 800 J, calculate the maximum mass which can be lifted by the press, given that the acceleration due to gravity is 10 m/s2.

  • A8,889 kg
  • B72 kg
  • C7,200 kg
  • D8,000 kg

Q19:

Some oil is poured into a U-shaped tube which is initially containing mercury, as shown in the figure. What is the value of β„Ž? Take 𝜌Hg = 13,600 kg/m3 and 𝜌=520/oilkgm.

  • A37.7 cm
  • B6.5 cm
  • C24.8 cm
  • D41.4 cm

Q20:

A U-shaped tube has an amount of water that fills 10 cm of the tube which is 20 cm in height. The tube has unequal cross-sectional areas with a ratio of 1∢2. Some oil with a density of 750 kg/m3 is poured into the smaller end. If the oil moves to the edge of the tube and the liquids are balanced, then the height of the oil above the water is . Take 𝜌=1,000/wkgm.

  • A10 cm
  • B20 cm
  • C19 cm
  • D5 cm

Q21:

A hydraulic press has a large piston of area 2.8 m2 and a small piston of area 0.025 m2. An object of weight π‘Š lies on the large piston. If a force of 65 N acts vertically downwards on the small piston, calculate π‘Š which makes the two pistons balanced in one horizontal plane.

  • A7,280 N
  • B8,270 N
  • C6,950 N
  • D8,600 N

Q22:

Two cars, A and B, are held by the two pistons of a hydraulic press at the same horizontal level. Car A weighs 3,400 N, and car B weighs 2,850 N. Calculate the ratio between the area of the piston car A is sitting on and the area of the piston car B is sitting on.

  • A0.5
  • B1.2
  • C1
  • D0.8

Q23:

The figure shows a hydraulic press system which is made of one small piston and 3 large pistons. If the cross-sectional area of the small piston is 12.5 cm2 and the cross-sectional area of each of the large pistons is 130 cm2, calculate the resultant force on each of the large pistons if a force of 220 N acts on the small piston.

  • A4,234 N
  • B2,288 N
  • C762.67 N
  • D6,864 N

Q24:

In the figure, a force F is applied on the smaller piston of a hydraulic lift which has an area of 15 cm2 to lift up a car of mass 2,300 kg a distance of 2.5 m. The car is held by the other piston which has an area of 2.5 m2. Calculate the force F, given that the density of the oil is 870 kg/m3 and the acceleration due to gravity is 10 m/s2.

  • A46 N
  • B4.4Γ—10 N
  • C4.6Γ—10 N
  • D4.4Γ—10 N

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