Unlock access to content

Select one option:

Free of charge

Unlock the chapter "Viscous and Air Resistance Forces"

Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »

Subscribe to OpenProf If you do not get a better grade, you get your money back!

Unlock access to all problems solutions.
Available from 8.25 £ / month.

Continue »

Solved problems for the chapter:

Viscous and Air Resistance Forces

View the theory »

Viscosity

View the theory »

Introduction to Force

1. What is force?

2. How do we know that a force is acting on a body?

2.1. Effects of forces

3. Name, symbol and unit of force

4. Properties of force

5. Drawing forces

6. Contact force or field force

7. Surface and volume distributed forces

7.1. Area-distributed or surface forces

7.2. Volume-distributed or body forces

8. Measuring forces

9. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:viscous_and_air_resistance_forces/5135/

Example 1.

A car drives at a speed of 61 km/h to a 1 mm thick layer of water on the road and slips. We call this slip, aquaplaning. The contact area between the water and the tires of the car is . Calculate the force with which the layer of water acts on the car. The coefficient of water viscosity is .

Example 2.

A plate with a surface area is slowly dragged along the surface of an unknown liquid. The depth of the fluid is and the plate is moving at a speed of . What is the viscosity of this unknown liquid if the plate is pulled by a force ? Which liquid is it?

An iron ball with a radius of 2 mm falls uniformly in oil. The rate of fall is 2 mm/s. During the fall, the linear law of resistance applies. What is the viscosity of the oil? The densities of iron and oil are and respectively.

A piston moves in a cylinder so that there is a 0.1 mm layer of oil between the piston and the cylinder. The surface of the cylinder jacket is . What is the longitudinal force required for the piston to move at a speed of 20 cm/s? The coefficient of viscosity of the oil is .

Which of the cases described below requires quadratic law of resistance and which requires linear law of resistance?

A bullet fired from a gun travels through the air at a speed of . Its diameter is , the air density is , and the air viscosity is .
A sphere of diameter of moves through honey at a speed of . The density of honey is and its viscosity is .
A soccer ball flies through the air at a speed of . Its radius is .
A cube with a side length of sinks sideways to the bottom of a lake at a speed of . The viscosity of water is .

An engine drives a ship at a constant speed with a force of 4 kN.

What is the force of water resistance?
Does the engine power depend on the weight of the cargo on the ship? Explain why.

A skydiver, who is falling vertically through the air, opens his parachute. Which row describes the velocity of the skydiver immediately after he opens his parachute?

	direction of velocity	magnitude of velocity
A	downwards	decreases
B	downwards	increases
C	upwards	decreases
D	upwards	increases

The graph shows how quantity P varies with quantity Q for a body falling vertically downwards in a uniform gravitational field with air resistance.

Which pair of quantities could be represented by P and Q?

	P	Q
A	acceleration	force of air resistance
B	acceleration	time
C	velocity	force of air resistance
D	velocity	time

A submarine descends vertically at constant velocity. The three forces acting on the submarine are viscous drag, upthrust and weight. Which relationship between their magnitudes is correct?

weight < drag
weight = drag
weight < upthrust
weight > upthrust

10.

A snowflake and a raindrop are in still air. They both fall from rest at the same time and from the same height, far above the ground. The snowflake and raindrop contain the same mass of water. Assume that there is no evaporation or melting. Also assume that, for a given speed, the drag force acting on the snowflake is greater than the drag force acting on the raindrop.

Which statement about the snowflake and raindrop is correct?

The raindrop takes more time than the snowflake to reach terminal velocity.
The raindrop takes more time than the snowflake to reach the ground.
They reach the same terminal velocity.
They take the same amount of time to reach the ground.

11.

A ship of mass is approaching a harbor with speed . By using reverse thrust it can maintain a constant total stopping force of . How long will it take to stop?

12.

A rocket of mass sits on a launch pad on the Earth’s surface. The rocket motors provide an upward force of on the rocket. What is the initial acceleration of the rocket?

13.

An air bubble in a tank of water is rising with terminal (constant) velocity. The forces acting on the bubble are , and , as shown.

The upthrust on the bubble is . Which statement about the forces is correct?

is the viscous force on the bubble, is the weight of the bubble and .
is the viscous force on the bubble, is the weight of the bubble and .
is the weight of the bubble, is the viscous force on the bubble and .
is the weight of the bubble, is the viscous force on the bubble and .

14.

Two balls of identical shape and size but different masses are falling through the same liquid. The sum of the drag force and upthrust acting on each ball is equal to its weight. Which statement about the two balls is correct?

The heavier ball has a larger acceleration than the lighter ball.
The heavier ball has a smaller deceleration than the lighter ball.
The heavier ball is falling at the same speed as the lighter ball.
The heavier ball is falling at a larger speed than the lighter ball.

15.

The resultant force on a raindrop of mass falling with velocity is given by the equation

Where is a constant and is the acceleration of free fall.

What is the velocity of the raindrop when it reaches a constant (terminal) velocity?

16.

A ball of mass is thrown vertically into the air. When the ball has speed , the air resistance acting on the ball is . What is the magnitude of the acceleration of the ball when its speed is as it rises and as it falls?

	acceleration when ball is rising	acceleration when ball is falling
A
B
C
D

17.

A snowflake is falling from the sky on a still day. Its weight acts vertically downwards and air resistance acts vertically upwards. As the snowflake falls, air resistance increases until it is equal to the weight and there is no resultant force acting on the snowflake.

When the forces become equal, which statement is correct?

The snowflake accelerates.
The snowflake decelerates.
The snowflake is stationary.
The snowflake moves at a constant velocity.

18.

The drag force acting on a sphere moving through a fluid is given by the expression

where is a constant, is the density of the fluid and is the speed of the sphere.

A ball of weight falls vertically from rest in air. The drag force acting on the ball is given by the expression above. The ball reaches a constant (terminal) speed of . Assume that the upthrust acting on the ball is negligible and that the density of the air is uniform. For the instant when the ball is travelling at a speed of , determine

the drag force on the ball,
the acceleration of the ball.

19.

A ball falls through a liquid at a constant speed. It is acted upon by three forces: an upthrust, a drag-force and its weight. Which statement is correct?

The drag-force increases with increasing depth.
The drag-force is equal to the sum of the upthrust and weight.
The upthrust is constant with increasing depth.
The weight is greater than the sum of the drag-force and the upthrust.

20.

A solid sphere falls at constant (terminal) velocity in a liquid. The three forces acting on the sphere are shown in the diagram.

How are the three forces related?

21.

A body falling in a uniform gravitational field encounters air resistance. The air resistance increases until terminal velocity is reached. Which factor does not affect its terminal velocity?

the density of the air
the height from which the body falls
the mass of the body
the shape of the body