In this worksheet, we will practice comparing friction and drag forces and finding the terminal velocity resulting from variable drag forces acting on an object.

**Q1: **

A ball bearing of mass 150 g is dropped into a tube filled with oil. The ball bearing hits the oil’s surface with a vertically downward velocity of 1.5 m/s and after falling through the oil for 1.5 s, the ball bearing’s velocity becomes 6.3 m/s. What vertically upward average drag force does the oil apply to the ball bearing?

**Q2: **

The shapes (A), (B), (C), (D), and (E) shown in the diagram are the shapes of the surfaces of objects that move through a fluid. The front of each object has the shape shown. All the objects move at the same speed through the same fluid. Which object has the largest drag force acting on it?

- A(B)
- B(A)
- C(C)
- D(D)
- E(E)

**Q3: **

A wheel falls off an airplane that is flying horizontally. The vertically downward speed of the wheel changes with time as shown in the diagram.

How much time after the wheel detaches from the airplane does the upward force applied by the air on the wheel equal the weight of the wheel?

What is the magnitude of the upward force applied by the air on the wheel at the instant that the wheel detaches from the airplane?

At what time would the net force on the wheel be equal to the wheel’s weight?

Is the acceleration of the wheel increasing, decreasing, or constant in the first two seconds after the wheel detaches from the airplane?

- ADecreasing
- BIncreasing
- CConstant

Is the acceleration of the wheel increasing, decreasing, or constant between 4 and 6 seconds after the wheel detaches from the airplane?

- ADecreasing
- BIncreasing
- CConstant

Is the velocity of the wheel increasing, decreasing, or constant between 2 and 4 seconds after the wheel detaches from the airplane?

- AConstant
- BDecreasing
- CIncreasing

Is the velocity of the wheel increasing, decreasing, or constant between 6 and 8 seconds after the wheel detaches from the airplane?

- AIncreasing
- BConstant
- CDecreasing

**Q4: **

The graph shows the change in velocity of an object over time as the object is subject to a constant force and to a drag force acting in the opposite direction to the constant force. Which of the points , , , , and most correctly shows the time at which the object starts to move at its terminal velocity?

- APoint
- BPoint
- CPoint
- DPoint
- EPoint

**Q5: **

A spear from a speargun is fired horizontally underwater. The spear’s mass is 250 g and it is fired with an initial horizontal velocity of 16 m/s. The spear travels a distance of 10 m horizontally before its horizontal speed becomes zero. What horizontal average force does the water apply on the spear in the direction of its motion before the spear’s horizontal velocity becomes zero?

**Q7: **

A bird flies horizontally at a constant speed of 15 m/s, beating its wings to push the air back. The force applied by the bird’s wings is 3.5 N. How much drag force acts on the bird?

**Q8: **

Which of the following statements about drag and upthrust is not correct?

- AThe direction of drag is the direction opposite to an object’s motion. The direction of upthrust is opposite to an object’s weight.
- BThe magnitude of the drag force always depends on the velocity at which an object moves through a fluid. Upthrust is independent of an object’s velocity.
- CUpthrust depends on an object’s density. Drag is independent of an object’s density.
- DUpthrust depends on a fluid’s density. Drag is independent of a fluid’s density.

**Q9: **

A ball is rolled down a slope. At the base of the slope, there is a length of track that can be covered with various different choices of surface material, A, B, C, and D. The average speed at which the ball moves along the track is shown in the table.

Surface Material | A | B | C | D |
---|---|---|---|---|

Average Speed (m/s) | 0.25 | 0.33 | 0.16 | 0.52 |

Which surface material produces the least friction force on the ball? Assume that the drag on the ball from the air is negligible.

- AB
- BA
- CC
- DD

**Q10: **

Which of the following statements about drag and friction is not correct?

- AThe drag force on an object moving through a fluid always acts in the opposite direction to the direction in which the object is moving.
- BThe magnitude of the drag force always depends on the velocity at which an object moves through a fluid.
- CA drag force is not produced by the contact between two solid surfaces that move at different velocities from each other.
- DThe magnitude of a friction force between two surfaces that are in contact must be zero if both surfaces have the same velocity as each other.

**Q11: **

An object with a mass of
135 kg
moves through a gas at an initial velocity of
2.5 m/s.
The surface of the object that faces the oncoming gas is square, as shown in the diagram. The gas has a density of
0.75 kg/m^{3}.

What is the momentum of the object before it has displaced any gas?

What volume of gas is displaced in one second by the object?

What mass of gas is displaced in one second by the object?

What momentum is given to the gas in one second, assuming that the object moves at 2.5 m/s for the whole of the second?

What would the velocity of the object be after moving through the gas for one second if the object lost the same amount of momentum as would be gained by the gas had the object maintained a constant velocity of 2.5 m/s through the gas?

**Q12: **

A metal bead has a cross-sectional surface area of 0.001 m^{2}.
The bead starts at rest and falls a distance of 5 cm through a fluid with a
density of kg/m^{3}.

What total mass of fluid does the bead displace as it falls through 5 cm?

If the acceleration of the bead as it falls is 8.2 m/s^{2},
how much average force does the bead exert on the fluid that it displaces?

**Q13: **

Which of the graphs (a), (b), (c), and (d) most correctly shows how the velocity of an object changes with time if the object is subject to a constant force while moving through a fluid that exerts a drag force on it, bringing it to its terminal velocity?

- A(c)
- B(a)
- C(d)
- D(b)