Section 2.3: Tension
This section covers tension in ropes, strings, and cables, and how to analyze forces when objects are connected by a rope or pulley system.
Key Points:
- Tension is a pulling force along the length of a string, rope, or cable.
- Tension is the same throughout an ideal (massless, frictionless) rope.
- Draw free-body diagrams including tension forces acting on each object.
- Use Newton's Second Law to relate tensions to acceleration.
Example 1
Two blocks, m1 = 5 kg and m2 = 10 kg, connected by a massless rope on a frictionless surface. Find the tension in the rope if blocks accelerate together.
Total mass: m1 + m2 = 15 kg
Assume applied force F = 30 N on m2 → acceleration a = F/(m1+m2) = 30/15 = 2 m/s²
Tension: T = m1 * a = 5*2 = 10 N
Example 2
Block of mass 8 kg hanging from a rope over a frictionless pulley. Find tension if it is accelerating downward at 2 m/s².
Weight: W = mg = 8*9.8 = 78.4 N
Tension: T = W – ma = 78.4 – 8*2 = 78.4 – 16 = 62.4 N
Practice Problems
- Two blocks, m1 = 6 kg and m2 = 4 kg, connected by rope on frictionless surface. Applied force 20 N on m2. Find acceleration and tension.
- Block of 10 kg suspended from ceiling by rope. Find tension when at rest and if accelerated upward at 3 m/s².
- Three blocks connected in a line on horizontal frictionless surface, pulled by 60 N. Find tension in each rope.
- Block of 5 kg hanging from rope over pulley, with 2 kg block on other side. Find tension and acceleration.
- A 12 kg block on frictionless incline, connected to hanging 4 kg block via pulley. Find tension and acceleration.