Quiz 1.2

In the lab, a student is given a glass beaker filled with water with an ice cube of mass m and volume Vc floating in it. The downward force of gravity on the ice cube has magnitude Fg . The student pushes down on the ice cube with a force of magnitude FP so that the cube is totally submerged. The water then exerts an upward buoyant force on the ice cube of magnitude FB . Which of the following is an expression for the magnitude of the acceleration of the ice cube when it is released?

(FB−Fg)/m

A sphere is moving vertically in a liquid. The free-body diagram shows the magnitudes and directions of the forces exerted on the sphere at a particular instant. What is the magnitude of the sphere's acceleration and the direction of the sphere's motion?

0.7m/s^2 - Downward Direction

A 1.0m by 2.0m by 3.0m rectangular block has a uniform density of 600kg/m3and is completely submerged and held stationary in a deep pool of water. The water exerts an upward buoyant force on the block of 6×104N . The block is released and, after rising a short distance toward the surface, experiences a drag force of 2×104N. The magnitude of the acceleration of the block at this instant is most nearly

1.31m/s2

A small submarine is underwater and moving horizontally at the same constant speed as the northward current in a straight, level section of a river. It releases a sensor that will float in the water. If resistance is negligible, what is the shape of the path followed by the sensor?

A parabolic path toward the north and curving upward

The small dots in the figure represent the molecules of a solid object, and the dashed lines represent the molecular bonds between them. The large dots represent the molecules of a liquid in which the object floats. Which of the following best describes the force that explains the interaction of the object and the liquid?

An electrical force that repels the electrons of the object's molecules from the electrons of the liquid's molecules

A sphere with density ρs and volume V is submerged in a fluid with density ρf , which exerts a buoyant force of magnitude ρfVg on the sphere. Immediately after being released from rest, the sphere moves upward with an acceleration of magnitude a . Which of the following changes would result in an acceleration with greater magnitude immediately after release?

Increasing the density of the fluid

A solid cube is submerged in a container of water of density ρw . The cube has mass M , volume Vc , and density ρw2 . The water exerts an upward buoyant force on the cube of magnitude ρwVcg . Which of the diagrams is the best representation of the forces exerted by the water on the cube?

Pressure on top of the box is less then the pressure on the bottom of the box. The sides cancel each other out, so they are equal.

A solid cube is submerged in a container of water of density ρw . The cube has mass M , volume Vc , and density ρw2 . The water exerts an upward buoyant force on the cube of magnitude ρwVcg . A solid sphere with unknown mass and twice the volume of the cube is submerged and then released. The sphere is observed to have the same acceleration immediately after release as the original cube. Which of the following claims can be made about the density of the sphere?

The density of the sphere must be the same as that of the cube because in order to have the same acceleration, the sphere's mass must be twice the mass of the cube.

A block is submerged in a container of water and remains at rest with the only forces exerted on it being gravity and forces exerted by the water. The force exerted by the water on the bottom of the block is greater than the force exerted by the water on the top of the block. Which of the following is an explanation of the microscopic cause of the difference in the forces?

The molecules of water hitting the bottom of the block have a greater average speed than those hitting the top of the block, and thus they exert a greater force.

Four cubes with equal volumes are at rest in a container of water, as shown in the figure. A student claims that cube D is experiencing a greater number of water molecule collisions per second with its bottom surface than the other cubes. Which of the following indicates whether or not the student is correct and provides evidence?

The student is correct, because the bottom surface of cube DD is deepest, which means the pressure is greatest.

Two metal cylinders of equal density and volume are submerged in water and remain at rest with their top surfaces at the same height, as shown. Cylinder A has a smaller height and a larger cross-sectional area than cylinder B. Which of the following explains why the force exerted on the top of cylinder A is greater than the force exerted on the top of cylinder B?

The water molecules striking the top surface of cylinder AA have the same average speed as the water molecules striking the top surface of cylinder BB, but more water molecules strike the top surface of cylinder AA than the top surface of cylinder BB.

A solid cube is submerged in a container of water of density ρw . The cube has mass M , volume Vc , and density ρw2 . The water exerts an upward buoyant force on the cube of magnitude ρwVcg . The cube is released and allowed to rise. What is the magnitude of the acceleration of the cube immediately after release?

g

A sphere of metal is placed in a liquid. The sphere sinks with an acceleration less than g due to the vertical buoyant force FB exerted by the liquid and the gravitational force Fg on the sphere. Which of the following best represents these two forces?

the sphere has a downward acceleration less than g, the buoyant force must be opposite the gravitational force, and downward force of gravity must be greater than the upward buoyant force.

In the lab, a student is given a glass beaker filled with water with an ice cube of mass m and volume Vc floating in it. The ice cube displaces a volume Vd of water as it floats. The density of the water is ρw , and the density of the ice is ρi . The water exerts an upward buoyant force of magnitude ρwVdg on the ice cube. Which of the following is equal to the magnitude of the force that the ice cube exerts on the water?

ρw Vd g