Newton’s 3rd Law of Motion

Statement of Newton’s 3rd Law Forces come in pairs. Whenever one object exerts a force on a second object, the second object exerts a force on the first object that is equal in MAGNITUDE but opposite in DIRECTION Often referred to as “For every action, there is an equal and opposite reaction.”

Thoughts on the 3rd Law An unbalanced force is required for an object to go into motion (Newton’s 1st Law), but if all forces are equal and opposite, aren’t all forces balanced? -- In other words, why can objects move? Answer: The forces act on different objects. -- “action” force acts on object #1 -- “reaction” force acts on object #2 Therefore, even though the forces are equal and opposite, they do not act on the same object and are not balanced

Example of Forces From Newton’s 3rd Law v1 v2 m1 m2 a1 a2 F21 F12 F12 = F21 m1a1 = m2a2 If the two objects have the same mass they will experience equal accelerations in opposite directions

Real-Life 3rd Law Example Questions v1 v2 In a head-on collision: Which truck will experience the greatest force? Which truck will experience the greatest change in velocity? Which truck will experience the greatest acceleration? Which truck would you rather be in during the collision? They will experience equal but opposite forces Click The less massive truck with a greater change in velocity Click The less massive truck will experience the greater acceleration Click It would be safer to be in the dump truck because it would have a much smaller acceleration. You wouldn’t feel as much ‘jarring’ Click

3rd Law Example Another example of equal force but different masses can be seen in a cannon firing a cannonball

How Rockets Work Newton’s 3rd Law helps to explain how rockets work and why balloons fly around the room when they are not tied closed How is this rocket lifting off? How does a rocket work in space?

The hot gas exerts a forward force on the rocket, propelling it forward, the rocket exerts an opposite force on the gas molecules pushing them out the back of the rocket

Momentum Newton’s 3rd Law also can explain conservation of momentum. Momentum – the quantity of motion that an object has because of its mass and velocity Within a system, momentum can NEVER be lost or gained. It is always conserved.

Momentum = mass x velocity Calculating Momentum Momentum can be calculated using the following formula: Momentum = mass x velocity So that we don’t confuse the m for mass with momentum, we use the letter p to represent momentum. Therefore, our equation is: p = m x v The units for momentum are kilogram-meters per second, or kg m/s Since velocity has a direction, so does momentum, it is a vector quantity

Conservation of Momentum The Law of Conservation of Momentum States: The total momentum of a group of object does not change unless outside forces (usually friction) act upon the objects

Examples of Momentum A slow-moving elephant and a bullet fired out of a gun may have similar momentums - The elephant has a small velocity, but its mass is very large - The bullet has a small mass but it has a very large velocity

Momentum Practice Problems What is the momentum of a 100-gram baseball that is traveling at 225 m/s? 2. What is the velocity of an 85-kg jogger traveling with a momentum of 500 kg m/s? m = 100 g = .1 kg v = 225 m/s p = ? p = m x v = .1 kg x 225 m/s 22.5 kg m/s m = 85 kg p = 500 kg m/s v = ? v = p / m = 500 kg m/s / 85 kg 5.88 m/s

Challenging Practice Problem A 3,000-kg car traveling at 20 m/s crashes head-on into a 2,500-kg car traveling at 40 m/s. After the collision, the 3,000-kg car has a velocity of 15 m/s. What is the velocity of the 2,500-kg car, assuming there is no friction?