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).

• a_B = 120/40 = 3 m/s²; a_A = 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.