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Newton’s Second Law: Net Force Causes Acceleration

Newtons Second Law of Motion: Net Force Causes Acceleration

Newton’s Second Law of Motion: (Fnet = ma)

A net force on an object cause it to accelerate in the direction of that net force.  Force is a vector, having magnitude and a direction.

Learning Targets

  • I understand what force is
  • I can determine net force
  • I can draw a force diagram
  • I can solve (Fnet = ma) problems
  • I can solve problems with (Fnet = ma) and acceleration equations combined

What is a force?

  • A force is any push or pull
push or pull force

The Unit of Force is the Newton

Mass

  • The kilogram (kg) is the unit of mass in physics
  • This is a measure of the matter in an object

Acceleration

  • Meters per second squared (m/s2) is the unit of acceleration
  • This is a measure of how much faster an object will move every second in a direction

Force

  • A Newton (N) is derived from kilograms times meters per second squared (kg ∙ m/s2)
  • One Newton is the force required to accelerate one kilogram of mass by one meter per second squared
Deriving a Newton

Deriving a Newton

Acceleration is Directly Related to Net Force

Acceleration is directly related to force

  • When force goes up acceleration goes up
  • Notice that acceleration doubles when force doubles

Acceleration is inversely related to mass

  • When mass goes up acceleration goes down
  • Notice that doubling mass halves acceleration
Force Inversely Related to Mass And Directly to Acceleration

Force Diagram

  • A force diagram is a list of all the forces represented by arrows on an object
  • Both pushes and pulls are drawn from the center of the object outward
forces on a pushed box

Force Diagram Example

  • This person is applying a force (FA)
  • Friction (Ff) is pushing back on the box
  • Weight (FW) is pushing down
  • Normal force (FN)is pushing up
Force Diagram

Free Body Diagram Example

  • Like a force diagram showing forces on an object
  • But the object is represented by a dot
Free Body Diagram

Weight and Normal Force

  • Weight (FW) force of earth attracting the object
  • Normal force (FN) the force of the a surface pushing back against weight
  • Without Normal force pushing back up an object would accelerate at 10 m/s2 to the ground

Notice in the animation, when a normal force is present from either the surface of the table or ground, the object stays in static equilibrium.  There is no net force since normal force opposes the weight of the object.

Weight and Normal Force

What is a net force?

  • The overall force causes by one or many forces
  • An object will accelerate when there is a nonzero net force
Net Force From Three Forces

Q1: What is the magnitude of net force when a person pushes a box with 1N of force to the west?

1N

Net force From One Force

Q2: What is the magnitude of net force when two people push a box with 1N of force to the west?

            2N

Net Force From Two Forces

Q3: What is the magnitude of net force when one person pushes a box with 1N of force to the west and another one with 1N of force east?

Zero Net Force

 

Q4: What is the magnitude of net force when one person pushes a box with 1N of force to the west and another one with 1N of force north?

Since this question asks for magnitude you do not have to provide a direction.  Draw the vectors head to tail and solve for the hypotenuse.

        4   

Net Force From Two Forces at a Right Angle

Q5: What is the net force when one person pushes a box with 1N of force to the west, another one pushes with 1N of force to the north, and a third pushes with 1N of force 30° South of East?

First break down the 1N 30° South of East into its south and east components

5a

Now find the total X-axis and total Y-axis force when the three vectors are combined.

5b

Now draw the components head to tail and solve for the resultant.  Since this question does not ask for only magnitude, you have to provide the entire vector answer.

5c

Net Force From Three Forces

Q6: What is the net force in the diagram?net force question

           40 N left

Force and Acceleration Equation Variables

NameVariableUnitUnit Abbreviation
ForceFNewtonN
Massmkilogramkg
Initial Velocity or Initial Speedvimeters per secondm/s
Final Velocity or Final Speedvfmeters per secondm/s
Timetsecondss
Accelerationameters per second squaredm/s2
Displacement or DistanceXmetersm

Problems Involving Newtons Second Law: Force and the One Dimensional Motion Equation

Problems involving the net force equation (Fnet = ma) often tie into one dimensional motion problems.  Notice in the picture to the right that you may have force and mass to solve for acceleration.  Later you may use this to find the final velocity or another unknown seen in the left side of the picture.

You may also have to start with the equations on the left.  Later you may use those to find a mass or net force causing that acceleration.

Making a givens list will help you determine how to proceed in a problem.

Newton's Second Law F = ma to Accelerated Motion Equations

Fnet Questions:

Q7: What is the force required to accelerate a 10 kg object by 3 m/s2?

F = ?

m = 10

a = 3

Fnet = ma

Fnet = (10)(3)

Fnet = 30 N

Q8: What is the force required to accelerate a 50 kg object by 3m/s2?

F = ?

m = 50

a = 3

Fnet = ma

Fnet = (50)(3)

Fnet = 150 N

Q9: Which of the objects have more inertia and why?  A 10 kg object or 50 kg object

50 kg object, the more mass the more inertia

Q10: A constant forward net force of 1000 N is applied to car with a total mass of 1500 kg.  How much faster will the motorcycle be travelling after 4 seconds?

           10

vf = 2.67 m/s

Q11: How much force is required by the breaks to stop a 1000 kg car moving at 30 m/s in 5 seconds?

           11

F = -6000 N

Q12: What is the final velocity of a 1200 kilogram car starting from rest after 50 meters when 4500 Newton’s of force is applied?

           12

vf = 19.36 m/s

Q13: How fast is a 10 kg box going to be moving from rest after 3 seconds if a 200 N force is applied to the left and a 50 N force is applied to the right?

           13 

vf = 45 m/s

Example Problem (Force Applied at an Angle)

When force is applied at an angle, only the force component in the direction of motion will directly accelerate the object.  The horizontal component, the adjacent side of the triangle to the right, will accelerate the 5 kg mass.

Example: How much would a 5 kg box accelerate when a 75 N force is applied 25° above the horizon on the right side?

75N force 25 degrees up

You would start by finding the adjacent side:

Adj = (cosӨ)(hyp)

Adj = (cos25)(75) = 68 N

Then figure out the acceleration using Fnet=ma:

F = ma

a = F/m

a = 68/5 = 13.6 m/s2 right without friction present

Force at An Angle

Q14. Sara pulls a 45 kilogram wagon with a force of 200 Newtons at a 25° angle to the horizontal from rest. How fast will the wagon be moving after 3 seconds?

           14

vf = 12.09 m/s

Newton's Second Law Quiz

1 / 10

Which of Newton's Laws is most related to a larger object resisting a change of motion more than a less massive one?

Newtons First Law: Law of Inertia.  An object at rest stays at rest and an object in motion stays in motion unless acted upon by an outside force. (More mass more inertia or resistance to change)

Newtons Second Law: Force causes acceleration (F=ma)

Newtons Third Law: All forces are paired, equal and opposite.  When you push on an object with 15 Newtons of force it pushes back on you with 15 Newtons of force.

2 / 10

Which of Newton's Laws is most related to all the forces on an object causing the object to accelerate?

Newtons First Law: Law of Inertia.  An object at rest stays at rest and an object in motion stays in motion unless acted upon by an outside force. (More mass more inertia or resistance to change)

Newtons Second Law: Force causes acceleration (F=ma)

Newtons Third Law: All forces are paired, equal and opposite.  When you push on an object with 15 Newtons of force it pushes back on you with 15 Newtons of force.

3 / 10

Force and acceleration are ______________ related

force to acceleration

4 / 10

Acceleration and mass are ______________ related

mass and acceleration

5 / 10

What is the mass of an object that accelerates at 4 m/s when 20 N of net force is applied?

Mass From Net Force

6 / 10

Net of three forces

What is the net force in the picture above

  • 30 left is -30
  • 15 right is +15
  • 7 right is +7

Add them together and turn the sign back into a direction (-30 + 15 + 7 = -8) 

8 Newtons Left

7 / 10

What is the acceleration on a 5 kg object that has a force of 20 N applied to the right and 5 newtons applied to the left?

Net Force Problem

8 / 10

What is the net force on a 5 kg object that has a force of 20 N applied to the right and 5 newtons applied to the left?

Sum of Forces

9 / 10

Net force causes _____________________.  Pick the best answer

Net force causes an object to accelerate... not just move.  Acceleration always occurs in the same direction as net force.  If you are pushing something to the right with a greater force than friction, and its net force is to the right, it will accelerate to the right.

10 / 10

Which direction does an object accelerate?

Acceleration is always in the direction of the net force.  If you push a box to the right, with an overall or net force to the right, the object will accelerate to the right.

Your score is

0%

Links

  • Continue to the F=ma Practice Problems
  • Back to the Main Forces Page
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Unit 1: One Dimensional Motion
Unit 2: 2D Motion
Unit 3: Newton’s Laws and Force
Unit 4: Universal Gravitation and Circular Motion
Unit 5: Work, Power, Mechanical Advantage, and Simple Machines
Unit 6: Momentum, Impulse, and Conservation of Momentum
Unit 7: Electrostatics
Unit 8: Current and Circuits
Unit 9: Magnetism and Electromagnetism
Unit 10: Intro to Waves
Unit 11: Electromagnetic Waves
Unit 12: Nuclear Physics

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