Topicmdb64d16a974403ef_1528449000663_0Topic

Newton's 2nd law

Levelmdb64d16a974403ef_1528449084556_0Level

Second

Core curriculummdb64d16a974403ef_1528449076687_0Core curriculum

I. The use of physical concepts and quantities to describe phenomena and to indicate their examples in the surrounding reality.

II. Motion and forces. The student:

15) uses the concept of mass as a measure of inertia of bodies; analyses the behaviour of bodies based on the second Newton’s law and applies to the calculation the relationship between force and mass and acceleration.

Timingmdb64d16a974403ef_1528449068082_0Timing

45 minutes

General learning objectivesmdb64d16a974403ef_1528449523725_0General learning objectives

Understanding the content of the second Newton’s law.

Key competencesmdb64d16a974403ef_1528449552113_0Key competences

1. Identifying the type of motion based on the acting forces.

2. Calculation of the accelerationaccelerationacceleration of the body based on the second Newton’s law.

Operational (detailed) goalsmdb64d16a974403ef_1528450430307_0Operational (detailed) goals

The student:

- gives the content of the second Newton’s lawsecond Newton’s lawsecond Newton’s law,

- calculates the acceleration of the body based on the second Newton’s law.

Methodsmdb64d16a974403ef_1528449534267_0Methods

1. Student exercises.

2. Experiments.

Forms of workmdb64d16a974403ef_1528449514617_0Forms of work

1. Individual and group work.

2. Work with the whole class.

Lesson stages

Introductionmdb64d16a974403ef_1528450127855_0Introduction

Task 1

a) Provide the definition and unit of acceleration.
b) Provide the definition of uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion.
c) What conditions must be met for the body to remain at rest?
d) What condition must be fulfilled by forces acting on the body so that it moves in uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion?

Answer:mdb64d16a974403ef_1527752263647_0Answer:

a) Acceleration is a vector physical quantity equal to the change of body speed per unit of time. The unit of acceleration in the SI system is $\left[\frac{m}{s^2}\right]$.
b) Uniformly accelerated motion is a motion that takes place in a straight line (the trajectory is a straight line) and in each unit of time the speed increases by the same value (the acceleration is constant).
c) The body remains at rest if the sum of forces acting on this body is equal to zero and the speed of the body relative to the selected reference frame is 0 $\frac{m}{s^{}}$.
d) The body moves in uniform rectilinear motion if any forces doesn't act or sum of all forces acting on this body is equal to zero. In this case we are talking about inertial reference frame that is, such in which the forces don't act on the body, they balance out.

Proceduremdb64d16a974403ef_1528446435040_0Procedure

Experiment:

Research problem:

What motion will the body move under the influence of external, unbalanced forceunbalanced forceunbalanced force?

Hypothesis:

The action of unbalanced force on the body causes a change in its speed, or giving it a specific accelerationaccelerationacceleration. This acceleration can be constant, and thus body motion - uniformly accelerated.

Requisites:

1. a cart with a weight of approx. 200 g,
2. tape measure,
3. stopwatch,
4. a table with a length of approx. 2 m,
5. paper tape,
6. marker for marking,
7. pulley,
8. weight of 5 g - 10 g,
9. durable thread.

Instruction:

1. Build the system according to the drawing below.
2. Attach the paper tape to the table.
3. Place the cart at the beginning of the table.

[Illustration 1]

4. Turn on the stopwatch, release the weight.
5. At equal time intervals, mark the distance travelled.
6. Measure the length of the marked segments on the tape.
7. Record the results in the table.

[Table 1]

Conclusion:

The average speed increases.

The ratio of the change of speed of a moving body to the time when this change occurred within the limits of measurement errors is constant.

It follows that the action on the body of a constant, unbalanced external forceexternal forceexternal force causes the body to move with constant accelerationaccelerationacceleration, i.e. it moves in a uniformly accelerated motion.

[Slideshow]

Task 2

Provide conclusions that you could draw after seeing the drawings below.

Conclusions:

1. The mass of the entire system has not changed.
2. Under the influence of the applied force, the body system moved in a uniformly accelerated motion.
3. If the force increases, the acceleration of the system increases. This means that the acceleration value is directly proportional to the value of the acting force.

The second Newton's law:

If a constant unbalanced forceunbalanced forceunbalanced force acts on the body, the body moves in a uniformly variable motion with an acceleration directly proportional to the applied force and dependent on the body mass. If body weight is greater the acceleration of the body is lesser. This means that the mass is inversely proportional to the acting unbalanced force.

We write the second Newton's law as:

or

where:

a [$\frac{m}{s^2}$] - acceleration, 
F [N] - force, 
m [kg] - body mass.

From the second Newton’s lawsecond Newton’s lawsecond Newton’s law:

- If different forces act on a body of constant mass, the higher the magnitude of the resultant forceresultant forceresultant force, the larger the acceleration of the body.
- If the same force acts successively on bodies with different masses, the smaller the mass of the body, the larger the accelerations of the body.
- If the same forces is applied on bodies with different masses, smaller acceleration is obtained by a body with a larger mass.

The second Newton's law allows us to define a unit of force.

1 N (newton):
- 1 newton is the magnitude of the force that causes acceleration of 1 $\frac{{\displaystyle m}}{s^2}$ of a body with a mass of 1 kg:

Task 3

A body with a constant mass under the influence of a constant unbalanced forceunbalanced forceunbalanced force can move in:

a) uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion,
b) uniformly accelerated motion,
c) uniformly decelerated motion,
d) none of these motions.

To each of the above statements, assign true or false.

Answer:

a) False. 
b) True. 
c) True. 
d) False.

Task 4

A resultant force giving this body an accelerationaccelerationacceleration of 4 $\frac{{\displaystyle m}}{s^2}$ acts on the body with a mass of 10 kg. Calculate the magnitude of the resultant forceresultant forceresultant force.

Analysis

Given:

$m=10kg$

$a=4\frac{m}{s^2}$

Unknown:

$F_w=?$

Solution:

$a=\frac{F}{m}$

$F=m\cdot a$$[kg\cdot \frac{m}{s^2}=1N]$

$F=10kg\cdot 4\frac{m}{s^2}$

$F=40N$

Answer:

The magnitude of the resultant force is 40 N.

Task 5

The friction force acting on the car is 400 N, while the applied force is 1000 N. The mass of the car is 1,5 t. Calculate the acceleration of the car under the action of a constant force.mdb64d16a974403ef_1527752256679_0The friction force acting on the car is 400 N, while the applied force is 1000 N. The mass of the car is 1,5 t. Calculate the acceleration of the car under the action of a constant force.

Analysis

Given:

$m=1,5t=1500kg$

$F_o=400N$

$F_c=1000N$

Unknown:

$F_w=?$

$a=?$

Solution:

$F_w=F_c-F_o$

$F_w=1000N-400N$

$F_w=600N$

$a=\frac{F_w}{m}$

$a=\frac{600N}{1500kg}$

$a=0,4\frac{N}{kg}$

$a=0,4\frac{kg\cdot \frac{m}{s^2}}{kg}$

Answer:

The accelerationaccelerationacceleration is 0,4 $\frac{m}{s^2}$.

Lesson summarymdb64d16a974403ef_1528450119332_0Lesson summary

- In the 17th century, an outstanding physicist and mathematician Sir Isaac Newton formulated three laws of dynamics. A special role in the development of physics was played by the second one: „If a constant unbalanced forceunbalanced forceunbalanced force acts on the body, the body moves in a uniformly variable motion with an acceleration directly proportional to the applied force and dependent (inversely proportional) on the body mass”.

- The second Newton’s law shows that if different forces act on a body with a constant mass, the higher the magnitude of the resultant force, the larger the acceleration of the body. In turn, if the same force acts successively on bodies with different masses, the smaller the mass of the body, the larger the acceleration of the body.

- The second Newton’s lawsecond Newton’s lawsecond Newton’s law is written using the formulas:

where:

a [$\frac{{\displaystyle m}}{s^2}$] - acceleration,
F [N] - force,
m [kg] - body mass.

- The second Newton’s law allows us to define a unit of force - 1 N (newton).
1 newton is the magnitude of the force that causes accelerationaccelerationacceleration of 1 $\frac{{\displaystyle m}}{s^2}$ of a body with a mass of 1 kg.

Selected words and expressions used in the lesson plan

accelerationaccelerationacceleration

external forceexternal forceexternal force

formulaformulaformula

reference framereference framereference frame

resultant forceresultant forceresultant force

second Newton’s lawsecond Newton’s lawsecond Newton’s law

unbalanced forceunbalanced forceunbalanced force

uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion

uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion