Name:______Section: ______Date: ____/____/______

Notes: Newton’s Second Law of Motion

“During the years 1665 and 1666, Isaac Newton developed three laws that describe all of the states of motion—rest, constant motion, and accelerated motion. In addition, these three laws explain how forces cause all of the states of motion.” (Prentice Hall Science)

Review

  • Acceleration is a change in ______.
  • Speeding Up. (including going from rest to moving)
  • Slowing Down. (including going from moving to stopped)
  • Changing Direction.
  • Objects with more mass have more ______.
  • It is more difficult to change the motion of an object that has more ______. Therefore it is more difficult to change the motion of an object that has more mass.
  • To accelerate an object, you must exert an unbalanced ______on the object.
  • When the forces on an object are ______, the object is either at rest or moving at constant velocity.
  • When the forces on an object are ______, the object is accelerating.

An Example: Grocery Shopping

  • First, you come across a stationary grocery cart. If you push on the grocery cart, it will begin to move. The cart is ______.
  • If you push harder on the cart, it will accelerate ______.
  • The greater the force, the ______the acceleration.
  • If the grocery cart is filled with groceries, you will have to push ______to have the same acceleration as when it is empty.
  • A filled grocery cart has more ______, and therefore more ______.

Newton’s Second Law Conceptually

  • For a given object, more net force produces more acceleration.
  • For a given amount of force, more massive objects experience less acceleration.

Back to Grocery Shopping

  • Use the second law of motion to explain the following observations.
  • Twins Katy and Kelly have a grocery cart race. Each is able to exert the same amount of force on a grocery cart. Katy pushes a loaded grocery cart; Kelly pushes an empty grocery cart. Kelly wins the race. Why?
  • Kelly and her little brother Kevin have a grocery cart race. Both carts are empty. Kelly is able to exert more force than her little brother. Kelly wins the race. Why?
  • Katy and her little brother Kevin have another grocery cart race. This time Katy's cart is loaded and Kevin’s cart is empty. They tie. Why?

Newton’s Second Law of Motion: The Equation

Newton’s Second Law of Motion explains how force, mass, and acceleration are related.

  • It is extremely important to note that the “F” in Newton’s Second Law really stands for “Net Force” even if we don’t always say it.

Sample Problem / How much force is needed to accelerate a 1400-kg car at 2 m/s2.
Solution
Step 1 / Write your knowns / F =?
m = 1400 kg
a = 2 m/s2
Step 2 / Write the formula /
Step 3 / Substitute given numbers /
Step 4 / Solve and write the final answer with units! / (this is the same as 2800 kg-m/s2)

Note that the units work out since 1 Newton is defined to be 1 kilogram • meter/second2

Problem 1 / How much force is needed to accelerate a 10-kg box at 5 m/s2.
Solution
Step 1 / Write your knowns / F =
m =
a =
Step 2 / Write the formula /
Step 3 / Substitute given numbers /
Step 4 / Solve and write the final answer with units! /
Problem 2 / What is the force on a 1000-kg elevator that is freely falling at 10 m/s2.
Solution
Step 1 / Write your knowns / F =
m =
a =
Step 2 / Write the formula /

Step 3 / Substitute given numbers
Step 4 / Solve and write the final answer with units! /

Other forms of the equation:

  • Like the speed equation, we can re-write Newton’s Second Law in three forms.

Applications

  • Johnny exerts a force of 4N to the left on a box. Susie exerts a force of 10N to the right on the same box. The box has a mass of 2kg.
  • What is the net force on the box? ______
  • Which direction will the box accelerate? ______
  • What is the box’s acceleration? SHOW YOUR WORK.
  • If you push horizontally on your book with a force of 1N to make the book slide at a constant velocity, how much is the force of friction on the book? Explain.
  • You are sitting at rest in your chair. What is the net force acting on you? Use Newton’s Second Law to explain.

Newton’s Three Laws of Motion—Summary:

  • Newton’s 1st Law: Forces are necessary to change the motion of an object.
  • Newton’s 2nd Law: Force, mass and acceleration are related through

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