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 𝑃.

Find 𝑃.

Find 𝑃.

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 𝐵
  • BHole 𝐶
  • 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 𝑃 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 𝑃 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 𝑃 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=0.25m and 𝐿=0.75m. 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=0.25m and 𝐿=0.75m. 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 F=85 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?

  • A3
  • B2
  • C6
  • D4
  • E1

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?

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