Tension Physics Example 3

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Example 3

medium
A 5 kg mass hangs from a rope. Find the tension in the rope. (Use g=9.8g = 9.8 m/s\u00b2)

Solution

  1. 1
    Draw a free-body diagram: the mass is in static equilibrium, so the net force is zero. Two forces act on it: weight WW downward and tension TT upward.
  2. 2
    Apply Newton's second law for equilibrium (a=0a = 0): T−W=0  ⟹  T=W=mgT - W = 0 \implies T = W = mg
  3. 3
    Substitute the values: T=5 kg×9.8 m/s2=49 NT = 5\,\text{kg} \times 9.8\,\text{m/s}^2 = 49\,\text{N}

Answer

The tension in the rope is T=49 NT = 49\,\text{N}.
When an object hangs motionless from a rope, the tension exactly equals the object's weight. The rope must exert an upward force equal to gravity to keep the object in equilibrium. If the object were accelerating, the tension would differ from the weight.

About Tension

The pulling force transmitted through a rope, string, or cable when it is pulled taut at both ends.

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Example 2 medium

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Example 5 hard

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