19 5.4 Applications
- Rocket propulsion: burning gas of large mass is expelled backwards (downwards) at high speed; the reaction on the rocket is a thrust forward (upwards). A rocket needs no air to push against, so it works in space.
- Recoil of a gun: the gun pushes the bullet forward; the bullet pushes the gun backward with an equal force, but the gun's much larger mass gives it a very small acceleration.
- Swimming/walking: a swimmer pushes the water back, the water pushes him forward; when walking your foot pushes the ground backward and the ground pushes you forward.
- Space: an astronaut who throws an object in one direction moves in the opposite direction. This suggests how a spacecraft can change its direction outside the atmosphere: by ejecting gas in the direction opposite to the desired change.
✍️ Worked examples
Example 1.
- Two skaters stand on smooth ice.
- Skater A (60 kg) pushes skater B (40 kg) with a force of 120 N.
- Then B pushes A with 120 N in the opposite direction (third law).
- aB = 120/40 = 3 m/s²; aA = 120/60 = 2 m/s², in opposite directions. The lighter skater accelerates more, although the forces are equal.
Example 2.
- A hammer hits a nail with 400 N.
- The nail pushes back on the hammer with 400 N in the opposite direction.
- The nail moves in because it has little resistance; the hammer slows down because of the force of the nail.
Example 3. A 0.02 kg bullet leaves a 4 kg rifle with an acceleration of 5000 m/s² during the shot. Force on the bullet = 0.02 × 5000 = 100 N. Force on the rifle = 100 N backward; its acceleration = 100/4 = 25 m/s² backward (so a firm grip is needed).
Example 4.
- Which statement is wrong?
- "The weight of a book and the upward force of the table on it are an action-reaction pair." They act on the same object (the book) and are balanced, so they are not an action–reaction pair; the third-law pair of the table's force on the book is the force of the book on the table.