Water current at a speed of hits an object of surface area of at right angles. When water hits the object, its speed drops to zero. With what force does the flow of the water current act on the object? Water density is .

Example 2.

Gases emitted by a jet engine at a mass flow rate of 4 and speed of 6 falls on a wall and bounces off it at the same speed. The angle of incidence and the angle of reflection are with respect to the vertical. How much force does the wall exert on the gases?

The jet engine of an aircraft emits 24 kg of gas per second at a speed of . What is the thrust force on the aircraft?

A firefighter stands on a skateboard and holds in his hands a hose connected to a water tank. He doesn’t move at first but after opening the valve on the pipe, the water starts to flow out at a constant rate of . The mass flow rate of the water is .

How far does the firefighter move in 6 seconds if the total mass of the skateboard and firefighter is 80 kg? Friction is ignored.
What is the distance travelled if a valve is connected to the pipe to reduce the cross-section of the jet in a ratio of 3 : 2?

A flyboard draws water from the sea and directs it into two jets. The jets are oriented so that a person can float in the air on the board. The pump ejects of water per second, and the total weight of the board and the person on it is 130 kg. At what speed does water come out in the form of jets? The density of sea water is .

A stationary trolley with mass is pushed through a distance of in 20 seconds. How much force is applied on the trolley?

A car with a mass of drives on a flat road at a speed of . How much braking force do we need to stop it after traveling a distance of ?

An elevator with a mass of starts to rise with an acceleration of . What is the force in the elevator rope? What will be the force in the rope if the elevator descends with the same acceleration?

Two bodies are suspended via a rope on an attached pulley. The first body has a mass of 0.1 kg and the second 0.3 kg. The bodies are first held with the hand and then released. With what acceleration are they moving? What is the force on both sides of the rope?

10.

A body slides on a rough surface and stops at a distance of . The coefficient of friction between the body and the base is . What is the initial velocity of the body?

11.

A body slides at a speed of on a smooth horizontal surface. What is the distance covered after a coefficient of friction of 0.2 occurs between the body and the ground?

12.

A rocket model with a mass of is launched vertically upwards with an initial velocity of . It reaches its maximum height in . With what average force does air resistance impede the rocket?

13.

A stationary elevator with a mass of rises through a height of in . How much force does the elevator rise with?

14.

The position of a body in a plane is described by the equations:

In this case, is the time in seconds, and and are the positions of the body in the coordinate system in metres. The coordinate is the altitude. What's the magnitude of the forces and acting on the body with weight ?

15.

Two bodies with masses and lying on a horizontal smooth surface are connected by a light rope. The rope breaks at a force greater than . Two forces and begin to act on the bodies in opposite directions as shown in the figure below. The constant , and is the time in seconds.

Body on a horizontal smooth surface .

Obtain an equation that shows the change in the acceleration of the bodies with time.
What is the force in the rope after from the start of the forces?
How long does it take for the rope to break?

16.

A small ring with a mass of can slide frictionlessly along a wire which is twisted into a semicircular loop with radius as shown in the figure below. The semicircular loop is rotated around an axis at an angular velocity .

Figure 1: Rotating semicircular loop with ring

Draw the external forces on the ring when the ring is at the height of with respect to the lowest position, and name the forces.
Find the relationship between the angular velocity and the height .
At what angular velocity is the ring at the height of ?
What is the resultant force acting on the ring?
What force does the semicircular loop exert on the ring?
Explain whether it is possible for the ring to fall off the rotating loop!

17.

A brick slips from the top of a roof as shown in the figure below. The roof is long and is inclined at an angle to the horizontal. The height of the outer wall of the house is and the coefficient of friction between the brick and the roof is .

Brick on the roof

What external forces act on the brick? Draw the forces and name them.
With what acceleration does the brick slide on the roof?
With what speed does the brick slide off the roof?
How long does it take the brick to fall to the ground after slipping off the roof?
Where does the brick fall to the ground?
With what speed and at what angle with respect to the horizontal does the brick fall to the ground?

18.

A car is driven into a sharp bend in a horizontal road. The radius of the bend is , and the coefficient of friction between the tires and the ground is .

Driving a car in a bend .

Draw the external forces on the car and name them.
What does the maximum speed of a car depend on when driving safely through a bend in a horizontal road?
What is the maximum speed with which the car can drive safely around the bend?
On normal road traffic, only the right half of the road should be used. Based on the equation obtained in part b above, explain on which side of the bend the car can drive at a higher speed.

19.

A ball of mass 100 g is suspended on a long rope of length 1 m. The ball is moved away so that it is inclined at an angle to the vertical and then released.

Setting up the experiment .

How high is the ball raised relative to its lowest position?
What is the velocity of the ball as it passes through the lowest position?
Draw the external forces on the ball in its lowest position and name them.
Determine the magnitude of external forces on the ball in its lowest position.

20.

A ball of mass is tied to a light rope. The ball is rotated uniformly at a frequency in a horizontal circle of radius as shown in the figure below.

Rotating pendulum

Draw the external forces on the ball and name them.
What is the tension force of the rope?
What is the length of the rope?

21.

Two bodies of the same mass are attached to the ends of a light and inextensible rope, which is passed over a pulley. A smaller body of a mass is attached to the body on the right side of the rope. The mass of the rope and the pulley and the friction in the pulley are neglected.

Weights on a string .

Draw the forces on the body on the left and on the system of bodies on the right side of the rope and name them.
With what acceleration does the whole system start to move?
What is the tension force in the rope?
Calculate the force with which the body of mass acts on the body of mass .

22.

Smooth straight grooves are attached to an upright circular plate with radius . Groove 1 is vertical and groove 2 is at an angle with respect to groove 1 as shown in the figure below.

Figure 1: Round plate with grooves.

A ball is dropped down groove 1 and then down groove 2. In which case does the ball leave the plate first?

23.

A body with a mass of rolls up a circular slope as shown in the figure below. The velocity at point is equal to half the initial speed at point A. The circular slope is very smooth and has radius .

Figure 1: Body on a circular slope

Write an equation that relates the initial velocity to the angle .
Calculate the initial velocity of the body.
Calculate the force with which the slope acts on the body when it is at an angle ?
How high does the body reach?
What is the range of the body?

24.

A body with mass and tied to a long rope is rotated uniformly in a vertical plane at a speed of . The rotating body is observed in three positions at angles , and to the horizontal as shown in figure 1 below.

Figure 1: Rotating body

Draw the external forces on the body in position 1 and name them.
Calculate the tension force in the rope in all three positions.
Calculate and record in a table, the tension force in the rope when the body is at the positions at the multiple of angles from to .
Draw the graph of the tension force in the rope against the angle .

25.

A body of mass is placed on a rotating plate at a distance from the axis of rotation of the plate as shown in the figure below. The plate rotates at a frequency , and the body has not yet slipped off the plate.

Figure 1: Body on a rotating plate

Draw the external forces acting on the body.
Calculate the angular velocity of rotation of the plate.
Calculate the resultant force on the body.
What is the coefficient of friction between the body and the plate in the radial direction?

26.

Two logs with masses and that are connected by a rope that is passed over a light pulley lie on a slope as shown in figure 1 below:

Figure 1: Connected logs on slopes

The slopes are inclined at angles and to the horizontal. The coefficient of friction between the logs and the slope is . The log with mass is held above the second log with mass and both are released at some point.

What is the distance the logs will have to travel for them to be at the same height?
What is the acceleration of the logs?
How long does it take the logs to be at the same height after they start moving?
What is the speed of the logs at that time?

27.

Logs of masses and are connected by a rope which is passed over a light pulley as shown in figure 1 below.

Figure 1: Connected logs on slopes .

The angles of the inclined planes with respect to the horizontal are and . The log with mass is lower than the log with mass . After the logs move for 3 seconds, they are both at the same height. The coefficient of friction between the logs and the plane is . What is the ratio of the mass to that of ?

28.

With the help of Newton's second law, explain the following phenomena:

We are standing in a bus when it suddenly starts. Why can we lose our balance? In which direction can we fall if we face the direction of travel? How do we prevent this?
A weight is hanging on a rope attached to the ceiling of a car. In which direction will it deviate during acceleration and in which direction during braking?
We are sitting in a car. We have a container of water in our hands. We observe the water level. How do we know when a car is accelerating, braking, or driving steadily?
We lower a 15 kg sand container uniformly with a rope. How much force do we feel in our hands? Do we feel more or less force while dropping the container on the ground?
Explain how the seat belt works during a sudden stop. What does the force with which the belt acts on the driver when it stops depend on?
When a plane accelerates along the runway we feel it sticking us to the backrest. Explain the phenomenon.

29.

Kelvin keeps a barrel on an inclined plane so that it doesn't roll down. The angle of the slope is and the weight of the barrel is 80 kg. With what force does Kelvin hold on to the barrel?

30.

A car weighing 1500 kg reaches a speed of 24 m/s in 8 s. What is the resultant of the forces acting on the car?

31.

On a 30 kg trolley, a force of 60 N is applied for 6 s. What is the speed of the trolley?

32.

A log weighing 50 kg is dragged on a horizontal surface. The frictional force between the log and the surface is 200 N. What force must be applied on the log for the acceleration to be ?

33.

Two trolleys weighing 40 kg and 60 kg are connected by a drawbar. We pull the heavier trolley with a force of 200 N.

What is the acceleration of the system if we ignore the friction?
How much force does the drawbar apply on the lighter trolley?

34.

A trolley with a mass of 0.9 kg is tied with a rope via a fixed pulley to a weight of 0.1 kg as shown in the figure below.

How fast do the bodies move?
What is the force with which the rope accelerates the trolley?

35.

The weight of a man on Earth is 650 N. What is his mass?

36.

The mass of an object on Earth is 48 kg. What is the mass and weight of the object on the Moon?

The gravitational acceleration on the moon is about one-sixth of that on Earth and the gravitational acceleration on Earth is .

37.

In a car, a passenger weighing 70 kg is fastened with a seat belt. The car is traveling at a speed of 36 km/h when it suddenly stops due to a collision. The time it takes to stop is 0.2 s. How strong is the seat belt holding the passenger?

38.

On an aircraft carrier, a special device called a catapult accelerates a military aircraft to take-off speed. On a 90 m long runway, the aircraft reaches a takeoff speed of 100 m/s. With what force does the catapult act on the aircraft? The mass of the aircraft is 45 t.

39.

The graph of the acceleration of a body with a mass of 5 kg against the time is as shown below. Draw the graph of the force acting on the body against the time.

Acceleration-time graph of the body

40.

Identify the correct and the incorrect statements in the list below:

A body moves with uniform acceleration if the force on the body increases uniformly with time.
A body moves with uniform deceleration if a constant force acts on the body in the opposite direction to its motion.
If the mass of a body is reduced twice at the same force, the acceleration is also reduced twice.
If the force acting on a body is ten times greater, the acceleration is also ten times greater.
If a ship is moving uniformly and in a straight line, a constant force is acting on it.
If a constant force acts on a body in the direction of motion, the body accelerates uniformly. If the force acts in the opposite direction, it decelerates uniformly.
If the force on a body changes over time, the motion is non-uniform.
If a car goes into a corner at a uniform speed, the resultant of the forces acting on the car is zero.
A stone is thrown vertically upwards. When it reaches its maximum height, just before it begins to fall down, it stops for a moment. At this point, the resultant of the forces acting on the stone is zero.

41.

A body weighing 60 kg moves non-uniformly. The figure below is a graph of its velocity against time. Draw the graph of the resultant forces on the body against time.

Time-dependent velocity graph

42.

A mass of 6 kg is pulled with two equally large forces of magnitude 8 N without friction on a smooth surface. Both forces act at an angle with respect to the direction of motion, as shown in the figure below. How much acceleration does the body move with?

43.

A body weighing 600 g is on a slope at an angle of to the horizontal. The force of friction between the body and the slope is 0.5 N.

At what acceleration does the body move?
Use the graphical method to determine the forces on the slope.

Body on the slope

44.

Two masses of 0.5 kg each are suspended on the rope of an attached pulley - each on its own side (Figure A). Are the masses at rest? What is the force of the rope?
We hang an additional weight with a mass of 0.1 kg on the left side (picture B). In which direction is the weight moving? What is the acceleration of the motion?

45.

A log with a mass of 2 kg is dragged on a flat surface with a force of 20 N and at an angle with respect to the horizontal. The log moves with an acceleration of . What is the force of friction between the log and the surface?

A log dragged on a flat horizontal surface

46.

The rocket for supplying the International Space Station has a mass of 240 t with cargo at takeoff. The thrust force of the rocket engines is 3.2 MN. With what acceleration does it rise at takeoff?

47.

A 560 t aircraft has two engines. Each generates a thrust of 600 kN. At what time does the aircraft reach a take-off speed of 300 km/h?

48.

A rope attached to the ceiling hangs a 2 kg weight. A second rope is attached to this weight, on which hangs a 5 kg weight. What are the tension forces on both ropes and where are they directed?

49.

An elevator with a mass of 800 kg rises uniformly with an acceleration of . What is the force of the elevator rope?

50.

A ball weighing 0.3 kg crashes perpendicular to a wall at a speed of and bounces off elastically. The absolute value of the velocity after collision is equal to the absolute value of the velocity before collision. With what impulse did the wall act on the ball?

51.

A ball weighing 0.3 kg hits a wall at a speed of and at an angle with respect to the vertical. It is elastically reflected from the wall so that the reflecting angle is equal to the incident angle. The absolute value of the speed after reflection is equal to the absolute value of the speed before reflection. With what impulse did the wall act on the ball?

52.

A bullet weighing 20 g is fired at a speed of 400 into a stationary wooden log weighing 8 kg and remains in the log. What is the force impulse of the bullet on the log and that of the log on the bullet?

53.

Two skaters are holding a rope in their hands as shown in the picture. The weight of the first skater is 40 kg and the second 60 kg. The first skater pulls the second with a force of 60 N. What are the speeds of both skaters after two seconds of pulling? Friction is ignored.

54.

A skater, standing on skates, throws a heavy medicine bag of mass in the horizontal direction at a speed of relative to the ground. The mass of the skater is .

What is the speed of the skater immediately after throwing the bag?
What is the coefficient of friction between the skates and the ground if the skater moved a distance of after the throw?

55.

A truck, with a mass of 60 t drives on to a ferry at a speed of 2 , brakes evenly and stops after covering a distance of 3 m. What is the force impulse on the rope with which the ferry is attached to the shore?

56.

Are the following statements correct?

If we act on a body with a certain force, the body also acts on us with an equal and opposite force.
Bodies interact only with direct contact.
A body acts on another body with a force F, and the second body on the first with the opposite same force. Since the sum of both forces is zero, the body is at rest or moving evenly and in a straight line.
The law of interaction also applies when a body acts with force on another body and accelerates it.
The earth acts on the Moon with the same force as the Moon on the Earth.

57.

Determine whether the description of Newton's first or third laws applies in the given cases.

A car drives uniformly on a level road. It is acted upon by the force of the engine and, conversely, by the same force of air resistance.
The force of water resistance inhibits the navigation of the ship, and the ship acts with force on the water to cause waves. Both forces are equal and opposite.
Push a trolley on a flat surface with the force of your hands so that it moves uniformly.
A locomotive acts with force F on the train carriages and accelerates them. The wagons operate with the same opposite force on the locomotive.
A body hangs on a string. The sum of the force on the string and the weight of the body is zero, so the body is at rest.
A body hangs on a string. With its weight it acts on the string vertically downwards, and the string with the equal and opposite force on the body.

58.

Identify which of the listed motions below is described by Newton's first law. Justify the answer.

Brock meandering evenly along the snowy slope.
Raindrops falling from the sky at a speed of 8 m/s.
Children on the carousel rotating at a constant speed.
A passenger plane flying on a straight track and at a constant speed over the Atlantic.
A stone falling to the ground from a height of 10 m.

59.

Tom pulls a log with a force of 30 N at an angle of 45 ° with respect to the horizontal. The frictional force between the log and the ground is 21 N, the weight of the log is 40 N, and the ground acts with a force of 19 N on the log. Draw all the forces acting on the log on a scale and determine whether Newton's first law applies to the motion of the log.

60.

A car is driven on a flat road. The force of the engine is constantly opposed by the force of air resistance, which depends on the speed of the vehicle. Consider four cases:

The engine force is equal to the resistance force. The magnitude of each is 0 N.
The engine force is 800 N and the resistance force is 200 N.
The engine force is equal to the resistance force. The magnitude of each is 400 N.
The engine force is 200 N and the resistance force is 400 N.

Which of the cases does Newton's first law describe?

61.

A square-shaped log is dragged across a table so that it moves uniformly and on a straight line. If the applied force is 4 N and the weight of the log is 6 N, draw to scale, all the forces acting on the log.

62.

Karl and John are standing on skateboards. John has a rope tied around his waist, with which Karl pulls him towards himself with a force of 30 N. Karl notices that during the pulling, he also started moving towards Jan. Explain why.

63.

The mass of a rocket filled with fuel is 380 tonnes. The rocket engines develop a thrust of 4.6 MN. Calculate the resultant of the forces acting on the rocket after take-off.

64.

A pan containing water is placed on a cooker. It acts on the cooker plate with a force of 40 N. Name the force and determine its direction and line of action. Draw the force to scale.

65.

A man pulls an 800 kg log vertically upwards with a force of 6 kN. Will he be able to lift it? What is the resultant force of the log on the ground during the lifting?

66.

Joseph holds a bucket of mortar tied to a rope so that the bucket rests. The rope is passed over a pulley attached to the top of the masonry scaffold, as shown in the figure. On Joseph's side, he pulls the rope at an angle of to the vertical. The weight of the bucket with mortar is 20 kg. How much force does Joseph apply on the rope? Does the magnitude of the force depend on the angle at which Joseph pulls the rope?

67.

Victor wants to lift a block of mass 120 kg using a pulley. The pulley has a fixed part with two wheels and a moving part with one wheel. A tow rope is passed through all three wheels, as shown in the figure. He hangs the load on the moving part of the pulley. What force does Victor apply on the free part of the rope to keep the load in the air at rest? The moving part of the pulley has a negligible mass.

68.

A crate of mass 80 kg rests strapped to the rope of a fixed and movable pulley as shown in the figure. With how much force does Vincet have to pull the rope to keep the crate stationary in the air?

69.

A load of mass 40 kg rests a smooth inclined plane of angle to the horizontal. The block is attached to an unknown weight with a rope over a pulley so that it does not slip down the slope - see picture. What is the mass of the unknown weight?

70.

A professor is standing on the stage. His weight is 700 N. With what force does the stage act on the professor?

71.

Zane and Kelvin stand on skateboards and push off with their hands. Kelvin acts on Zane with a force of 40 N. With what force does Zane act on Kelvin? How will they move after the push?

72.

A ball falls to the ground. Describe this using Newton's 3rd law, a pair of equal and opposite forces acting on the ball.

73.

A spring balance hangs from the ceiling. A ball of mass 0.2 kg is hung on it. At the bottom of the ball is another spring balance, through which we act vertically downwards with a force of 4 N. What force does the upper spring balance show?

74.

A lightweight spring balance hangs on a stand with a 2 N weight suspended on it. Determine at least three pairs of forces according to Newton's third law acting on the stand, spring, and weight.

75.

Let us observe the collision of a heavily loaded wagon with an empty wagon stationary on a railway line. When they collide, the loaded wagon acts on the empty wagon with a force of 2 kN.

With what force does the empty wagon act on a loaded one?
After the collision, the wagons bounce. How do we expect them to move after the collision?

76.

A car accelerates on a flat road. The motion of the car is constantly inhibited by the force of air resistance. Describe what applies to air according to Newton's 3rd law.

77.

A log placed on a slope with an inclination of to the ground has a weight of 80 N. With what force does the slope act on the log?

78.

A box is lying on the table. The box is pushed by a finger with a force of 6 N. The box then begins to move. The motion of the box is hindered by a frictional force of 4 N. With what force does the box act on the finger? Does this force depend on the frictional force?

79.

A magnet attracts an iron box with a force of 6 N.

With what force does the box attract the magnet?

80.

A boat sails uniformly over the sea. It is subjected to an engine force of 20 kN.

What is the force of water resistance?
Does the boat also have a force on the water?
How do you know?

81.

On a slope with an inclination of , John holds a barrel with a force of 300 N with his hand. The dynamic component of the force on the slope is 400 N. How will the barrel move? How much force will the barrel exert on John's hand?

82.

Snowflakes fall uniformly at a speed of 2 m/s. The weight of a snowflake is 0.1 g. What forces act on a snowflake and what is their size?