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Resultant Force in One Dimension
Force
:An external influence that acts on a body to change its shape or its state of motion
Forces in nature are divided into two types
Some forces cannot occur without contact with the body
And some forces do not need to touch the body to occur
Identify which are contact forces and which are field forces
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\[..............\]
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Click here to show solution
Free-body diagrams of forces acting on the body
When solving force problems, for simplicity we should draw the forces acting on the body by drawing an arrow from the center of the body representing the force, with length proportional to the force magnitude and direction matching the force direction
Acquire the skill
A force of
40 N eastward acts on the cube in the picture
First determine the scale
10 N = 1 cm
Resultant force in one dimension
Resultant means sum of forces
Case 1: Forces in the same direction (angle between forces is zero)
The resultant is the sum of the forces in the same direction
\[F_ {net} = F_1 + F_2 = 6 + 3 = 9 N\] east
Case 2: Forces in opposite directions (angle between forces is 180 degrees)
The resultant is the difference between the forces in the direction of the larger force
\[F _{net} = F_1 - F_2 = 60 - 20 = 40 N\] east
The resultant force acting on the body equals
Click here to show solution
In this simulation, calculate the resultant of two forces in one dimension
Acceleration and Force
When a constant force acts on a body, the body will start moving if the force is unbalanced
The body moves with increasing velocity and has constant acceleration
If the force magnitude increases, the body's acceleration increases, represented by the slope of the (velocity-time) graph
Through the simulation, increase the force and each time observe the slope of the graph and note how acceleration increases
Newton's Second Law
Newton's second law states: If a force acts on a body and the body is capable of motion, it produces an acceleration directly proportional to the force and inversely proportional to the body's mass;
meaning that as force increases, acceleration increases,
and as mass increases, acceleration decreases,
and is expressed mathematically as:
\[F=m.a \]
In this simulation, in the first stage we will study the relationship between acceleration and force (with constant mass)
In the second stage, we will study the relationship between acceleration and mass (with constant force)
In this stage, keep the tension force constant and change the car's mass by entering the mass value for the car and its load in the icon
Conduct the experiment and each time increase the system mass without adding to the hanging mass, recording each time the system mass and acceleration
And plot the graph between acceleration and mass
Example 1)"
Arrange the accelerations of the cars from smallest to largest
Click here to show solution
Newton's First Law: Inertia
Newton's first law states: An object at rest stays at rest unless acted upon by an external force
, and an object in motion continues in a straight line at constant velocity unless acted upon by an external force that changes its direction, meaning objects cannot start moving, stop, or change direction on their own but require an external force to cause this change. This property of massive objects to resist changes in their state of motion is called inertia.
Example 1) Traffic administration advises drivers and passengers to wear seat belts while the car is moving. Explain why.
Click here to show solution
Equilibrium
We say an object is in equilibrium
when the net force acting on it is zero
\[\sum F_X=0\;\;\;\;\;\sum F_Y=0\]
In this case, the object may be at rest
\[v=0 \;\;\;\;\;\; a=0\]
or moving at constant velocity
\[v=constan\;\;\;\;\;\;a=0\]
Weight and Normal Force
There is a common mistake in not distinguishing between weight and mass
Mass: The amount of matter in a body (despite the difficulty in defining what matter is)
Weight
:The force exerted on a body by gravity
Mass does not change with location but weight changes according to the gravitational field
The weight of an object is given by the relation
\[W=F_g=m.g\]
\[N=Kg.\frac{m}{S^2}\]
Mass and Weight on this World's Surface
In this simulation, observe how weight changes with location while mass remains constant
When you hang an object on a spring, there is a tension force equal to the object's weight
Click on the planet first
( Reset ) then click on
then on the upward arrow
Apparent Weight
Apparent weight is the non-real weight that appears due to the body's accelerated motion and exists on a scale or object hanging from a spring
Consider the positive direction always as the direction of motion
If the elevator is moving upward
\[F_N - F_g = m .a\]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
If the elevator is moving downward
\[ F_g - F_N = m . a \]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
In this simulation there are two elevators, one moving up and one moving down
Elevator Motion and Apparent Weight
Weight is defined as the gravitational pull force on a body. An object's weight on Earth is the gravitational pull of Earth on the object. Similarly, an object's weight on the Moon is the gravitational pull exerted by the Moon on the object.
Weight is usually measured by placing the object on a stationary scale. In this case, the scale exerts a normal force equal to the gravitational force; meaning what is actually measured is the value of this normal force.
If an object is placed on a scale, the normal force is the supporting force. If an object is hung from a spring, the supporting force is the tension force
Apparent weight is the non-real weight that appears due to the body's accelerated motion and exists on a scale or hung from a spring
When placing an object on a scale and applying Newton's second law, considering the positive direction as the direction of motion
If the elevator is moving upward
\[FN - Fg = m .a \]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
If the elevator is moving downward
\[ Fg - FN = m . a \]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
\[3\star \star\]
A girl with a mass of 60 kg stands on a bathroom scale placed on the floor of an elevator moving upward with an acceleration of
2 m / S2
Then the girl's apparent weight is
g= 10 m / S2
Click here to show solution
Choose the correct answer
\[4\star \star\]
A man with a mass of 80 kg stands on a bathroom scale placed on the floor of an elevator moving downward with an acceleration of
2 m / S2
Then the man's apparent weight is
g= 10 m / S2
Click here to show solution
Choose the correct answer
Drag Force
When we let an object fall freely with air resistance, at the start of the fall there is only one force - the object's weight. As the object's speed increases, air resistance appears opposing the motion and increases with speed according to the relation
\[F_d = - K 𝜗 = - \frac{1}{2} .𝜌 .A . C_d . 𝜗 \]
𝜌( fluid density )
A ( cross-sectional area of the object )
Cd (drag coefficient - dimensionless )
𝜗 ( object's velocity )
As the object's speed increases, air resistance increases until it equals the object's weight, at which point we say the object has reached terminal velocity and moves at constant speed
Newton's Third Law
For every action there is an equal and opposite reaction
(Forces in nature come in pairs)
You cannot find the resultant of action and reaction because action acts on one body and reaction acts on another body
Applications of Newton's Laws
Motion of an object on a horizontal surface
Resultant Force in One Dimension |
Forces in nature are divided into two types
Some forces cannot occur without contact with the body
And some forces do not need to touch the body to occur
A force of
40 N eastward acts on the cube in the picture The resultant force acting on the body equals A girl with a mass of 60 kg stands on a bathroom scale placed on the floor of an elevator moving upward with an acceleration of Choose the correct answer A man with a mass of 80 kg stands on a bathroom scale placed on the floor of an elevator moving downward with an acceleration of Choose the correct answer
Drag Force
Newton's Third Law
Identify which are contact forces and which are field forces
Click here to show solution
Free-body diagrams of forces acting on the body
When solving force problems, for simplicity we should draw the forces acting on the body by drawing an arrow from the center of the body representing the force, with length proportional to the force magnitude and direction matching the force direction
Acquire the skill
First determine the scale
10 N = 1 cm
Resultant force in one dimension
Resultant means sum of forces
Case 1: Forces in the same direction (angle between forces is zero)
The resultant is the sum of the forces in the same direction
\[F_ {net} = F_1 + F_2 = 6 + 3 = 9 N\] east
Case 2: Forces in opposite directions (angle between forces is 180 degrees)
The resultant is the difference between the forces in the direction of the larger force
\[F _{net} = F_1 - F_2 = 60 - 20 = 40 N\] east
Click here to show solution
In this simulation, calculate the resultant of two forces in one dimension
Acceleration and Force
When a constant force acts on a body, the body will start moving if the force is unbalanced
The body moves with increasing velocity and has constant acceleration
If the force magnitude increases, the body's acceleration increases, represented by the slope of the (velocity-time) graph
Through the simulation, increase the force and each time observe the slope of the graph and note how acceleration increases
Newton's Second Law
Newton's second law states: If a force acts on a body and the body is capable of motion, it produces an acceleration directly proportional to the force and inversely proportional to the body's mass;
meaning that as force increases, acceleration increases,
and as mass increases, acceleration decreases,
and is expressed mathematically as:
\[F=m.a \]
In this simulation, in the first stage we will study the relationship between acceleration and force (with constant mass)
In the second stage, we will study the relationship between acceleration and mass (with constant force)
In this stage, keep the tension force constant and change the car's mass by entering the mass value for the car and its load in the icon
Conduct the experiment and each time increase the system mass without adding to the hanging mass, recording each time the system mass and acceleration
And plot the graph between acceleration and mass
Example 1)"
Arrange the accelerations of the cars from smallest to largest
Click here to show solution
Newton's First Law: Inertia
Newton's first law states: An object at rest stays at rest unless acted upon by an external force
, and an object in motion continues in a straight line at constant velocity unless acted upon by an external force that changes its direction, meaning objects cannot start moving, stop, or change direction on their own but require an external force to cause this change. This property of massive objects to resist changes in their state of motion is called inertia.
Example 1) Traffic administration advises drivers and passengers to wear seat belts while the car is moving. Explain why.
Click here to show solution
Equilibrium
We say an object is in equilibrium
when the net force acting on it is zero
\[\sum F_X=0\;\;\;\;\;\sum F_Y=0\]
In this case, the object may be at rest
\[v=0 \;\;\;\;\;\; a=0\]
or moving at constant velocity
\[v=constan\;\;\;\;\;\;a=0\]
Weight and Normal Force
There is a common mistake in not distinguishing between weight and mass
Mass: The amount of matter in a body (despite the difficulty in defining what matter is)
Weight
:The force exerted on a body by gravity
Mass does not change with location but weight changes according to the gravitational field
The weight of an object is given by the relation
\[W=F_g=m.g\]
\[N=Kg.\frac{m}{S^2}\]
Mass and Weight on this World's Surface
In this simulation, observe how weight changes with location while mass remains constant
When you hang an object on a spring, there is a tension force equal to the object's weight
Click on the planet first
( Reset ) then click on
then on the upward arrow
Apparent weight is the non-real weight that appears due to the body's accelerated motion and exists on a scale or object hanging from a spring
Consider the positive direction always as the direction of motion
If the elevator is moving upward
\[F_N - F_g = m .a\]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
If the elevator is moving downward
\[ F_g - F_N = m . a \]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
In this simulation there are two elevators, one moving up and one moving down
Elevator Motion and Apparent Weight
Weight is defined as the gravitational pull force on a body. An object's weight on Earth is the gravitational pull of Earth on the object. Similarly, an object's weight on the Moon is the gravitational pull exerted by the Moon on the object.
Weight is usually measured by placing the object on a stationary scale. In this case, the scale exerts a normal force equal to the gravitational force; meaning what is actually measured is the value of this normal force.
If an object is placed on a scale, the normal force is the supporting force. If an object is hung from a spring, the supporting force is the tension force
Apparent weight is the non-real weight that appears due to the body's accelerated motion and exists on a scale or hung from a spring
When placing an object on a scale and applying Newton's second law, considering the positive direction as the direction of motion
If the elevator is moving upward
\[FN - Fg = m .a \]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
If the elevator is moving downward
\[ Fg - FN = m . a \]
If the body is accelerating then acceleration is positive, and if decelerating then acceleration is negative
2 m / S2
Then the girl's apparent weight is
g= 10 m / S2
Click here to show solution
2 m / S2
Then the man's apparent weight is
g= 10 m / S2
Click here to show solution
When we let an object fall freely with air resistance, at the start of the fall there is only one force - the object's weight. As the object's speed increases, air resistance appears opposing the motion and increases with speed according to the relation
\[F_d = - K 𝜗 = - \frac{1}{2} .𝜌 .A . C_d . 𝜗 \]
𝜌( fluid density )
A ( cross-sectional area of the object )
Cd (drag coefficient - dimensionless )
𝜗 ( object's velocity )
As the object's speed increases, air resistance increases until it equals the object's weight, at which point we say the object has reached terminal velocity and moves at constant speed
For every action there is an equal and opposite reaction
(Forces in nature come in pairs)
You cannot find the resultant of action and reaction because action acts on one body and reaction acts on another body
Applications of Newton's Laws
Motion of an object on a horizontal surface
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