Newton’s Laws
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
For each object, draw a free-body diagram with only the real forces on it, choose axes, and write ΣF = ma along each axis. Forces between two objects always come in equal and opposite third-law pairs.
1. One equation per object
2. A routine that works
1. Draw a free-body diagram for each object. Never draw “ma” as a force.
2. Pick a positive direction that follows the motion (around the pulley, if there is one).
3. Write ΣF = ma for each object, then solve the equations together.
Shortcut: treat connected objects as one system. Internal forces like T cancel: a = (net external force) ÷ (total mass). Then go back to one object to find T.
3. Example, then try it
A 50 kg student stands on a scale in an elevator accelerating downward at 2.0 m/s². What does the scale read?
Taking up as +: N − mg = m(−2.0), so N = 50(10 − 2.0) = 400 N. The scale reads less than the true weight, 500 N.
In the figure below, a 4.0 kg block on a frictionless table is tied over a pulley to a hanging 1.0 kg block. Find the acceleration and the tension. Then repeat with μk = 0.10 between the table block and the table.
System: a = m2g ÷ (m1 + m2) = 10 ÷ 5.0 = 2.0 m/s².
Tension (table block): T = (4.0)(2.0) = 8.0 N. Check the hanging block: 10 − 8.0 = (1.0)(2.0) ✓.
With friction: f = (0.10)(40) = 4.0 N, so a = (10 − 4.0) ÷ 5.0 = 1.2 m/s².
New tension: T − 4.0 = (4.0)(1.2), so T = 8.8 N. Check: 10 − 8.8 = (1.0)(1.2) ✓.
Answer: 2.0 m/s² and 8.0 N; with friction, 1.2 m/s² and 8.8 N.
4. Common mistakes
Earth pulls a falling book downward. What is the third-law partner of that force?
Third-law pairs involve the same two objects. If Earth pulls the book down, the book pulls Earth up with an equal force.
Ready to practice?
4 questions on Newton’s Laws, each with a hint and an explanation for every wrong answer.