## Newton's Third Law of Motion: Action Reaction Pairs

### The third law states that an applied force creates an equal and opposite force.

When you push a wall the wall pushes you with equal force but in the opposite direction.

### Newtons Third Law Formula

• F1 = -F2
• Since F=ma it can also be restated as (m1a1)= -(m2a2)
• The subscript one represents the first object and the subscript two represents the second object.

In the picture to the fight the cart will accelerate more to the right while the force is applied since its mass is less.

### Newtons Third Law: Action Reaction Forces are the Same but Accelerations Differ Because of Mass

While Forces are equal the accelerations depend on the objects mass.

In the animation above, it was the acceleration which caused the but to smash  because its mass was so much less than the cars.

Acceleration is directly related to force.  So if one goes up the other does too.  If you push harder the object will accelerate more.

Acceleration is inversely related to mass.  So if one goes up the other goes down.  Pushing a 2000 kg real car will cause much less acceleration than pushing a 0.01 kg toy car.

### Example Problem (Newton's Third Law)

What is the acceleration of a 45 kg boy that jumps off a 2 kg skateboard accelerating the skateboard 12 m/s2 to the right?

We’ll call the boy object 1 so the boy is m1 and his acceleration is a1, the skateboard is m2 and the skateboards acceleration is a2.

Givens

• m1 = 45 kg
• a1 = ?
• m2 = 2 kg
• a2 = +12 m/s2 (+ being right)

Equation and Solution

m1 = -m22

(45)(a1) = -(2)(12)

a1 = -(2)(12)/45

a1 = -0.53 m/s2 or 0.53 m/s2 left

Newton's Laws and The Third Law of Motion Quiz

1 / 8

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

2 / 8

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

3 / 8

Which of Newtons Laws are best represented by this scenario.

If you push on a wall with 50 N of force, the wall pushed on you with 50 N of force

4 / 8

When you are on earth, which of the following is true?

5 / 8

When hitting a baseball you apply 150 N of force with the bat on the ball.  How does the magnitude of force the ball applies to the bat compare?

6 / 8

95kg Joe jumps off a 0.8kg skateboard and accelerates at 1.5 m/s/s right what is the acceleration of the skateboard?

F = ma

a = F/m

Forces on both are equal but if mass is less (its inversely related to acceleration) the acceleration caused by an equal force is more.

7 / 8

When a more massive skater jumps of a less massive skateboard. Which is true of the scenario?

8 / 8

When a bug hits your windshield.  Which of the following are true?