Tension Physics Example 4

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Example 4

medium
Two blocks (3 kg3 \text{ kg} and 5 kg5 \text{ kg}) are connected by a rope on a frictionless table. A 24 N24 \text{ N} force pulls the 5 kg5 \text{ kg} block. What is the tension in the connecting rope?

Solution

  1. 1
    Total system acceleration: a=Fm1+m2=243+5=3 m/s2a = \frac{F}{m_1 + m_2} = \frac{24}{3 + 5} = 3 \text{ m/s}^2.
  2. 2
    The tension accelerates only the 3 kg3 \text{ kg} block: T=m1⋅a=3×3=9 NT = m_1 \cdot a = 3 \times 3 = 9 \text{ N}

Answer

T=9 NT = 9 \text{ N}
In a system of connected objects, the tension in the connecting rope only needs to accelerate the trailing mass. The tension is less than the applied force because it does not need to accelerate the entire system.

About Tension

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

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More Tension Examples

Example 1 easy

A [formula] lamp hangs from a single vertical rope. What is the tension in the rope? Use [formula].

Example 2 medium

A [formula] block is pulled upward by a rope with an acceleration of [formula]. What is the tension

Example 3 medium

A 5 kg mass hangs from a rope. Find the tension in the rope. (Use [formula] m/su00b2)

Example 5 hard

A [formula] mass hangs from a rope over a frictionless pulley, connected to a [formula] mass on the

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