Newton's Third Law Example

Newton's third law can be illustrated by identifying the pairs of forces which are involved in supporting the blocks on the spring scale.

Presuming that the blocks are supported and at equilibrium, then the net force on the system is zero. All the forces occur in Newton's third law pairs.

Truck Collision

In a head-on collision:
Which truck will experience the greatest change in momentum?
Which truck will experience the greatest force?
Which truck will experience the greatest impulse?
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?

Discussion of the questions

In a head on collision :

I Newton's third law dictates that the forces on the trucks are equal but opposite in direction. Impulse is force multiplied by time, and time of contact is the same for both, so the impulse is the same in magnitude for the two trucks. Change in momentum is equal to impulse, so changes in momenta are equal. With equal change in momentum and smaller mass, the change in velocity is larger for the smaller truck. Since acceleration is change in velocity over change in time, the acceleration is greater for the smaller truck.

Ride in the bigger truck! There are good physical reasons!

In a head-on collision the forces on the two vehicles are constrained to be the same by Newton's third law. But from both Newton's second law and the work-energy principle it becomes evident that it is safer to be in the bigger truck.

The change in velocity of the driver will be the same as the truck in which he/she is riding. A greater change in velocity implies a greater change in kinetic energy and therefore more work done on the driver.

Solid rocket engine

Solid rocket engines are used on air-to-air and air-to-ground missiles, on model rockets, and as boosters for satellite launchers. In a solid rocket, the fuel and oxidizer are mixed together into a solid propellant which is packed into a solid cylinder. A hole through the cylinder serves as a combustion chamber. When the mixture is ignited, combustion takes place on the surface of the propellant. A flame front is generated which burns into the mixture. The combustion produces great amounts of exhaust gas at high temperature and pressure. The amount of exhaust gas that is produced depends on the area of the flame front and engine designers use a variety of hole shapes to control the change in thrust for a particular engine. The hot exhaust gas is passed through a nozzle which accelerates the flow. Thrust is then produced according to Newton's third law of motion.

The amount of thrust produced by the rocket depends on the design of the nozzle. The smallest cross-sectional area of the nozzle is called the throat of the nozzle. The hot exhaust flow is choked at the throat, which means that the Mach number is equal to 1.0 in the throat and the mass flow rate m dot is determined by the throat area. The area ratio from the throat to the exit Ae sets the exit velocity Ve and the exit pressure pe. You can explore the design and operation of a rocket nozzle with the interactive thrust simulator by NASA, which runs on your browser.