Tension Physics Example 5

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Example 5

hard
A 4 kg4 \text{ kg} mass hangs from a rope over a frictionless pulley, connected to a 6 kg6 \text{ kg} mass on the other side. What is the tension in the rope and the acceleration of the system? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Solution

  1. 1
    Net force on the system: Fnet=(m2−m1)g=(6−4)×9.8=19.6 NF_{\text{net}} = (m_2 - m_1)g = (6 - 4) \times 9.8 = 19.6 \text{ N}.
  2. 2
    Acceleration: a=Fnetm1+m2=19.610=1.96 m/s2a = \frac{F_{\text{net}}}{m_1 + m_2} = \frac{19.6}{10} = 1.96 \text{ m/s}^2.
  3. 3
    Tension (from the lighter mass): T=m1(g+a)=4(9.8+1.96)=4×11.76=47.04 NT = m_1(g + a) = 4(9.8 + 1.96) = 4 \times 11.76 = 47.04 \text{ N}.

Answer

a=1.96 m/s2,T=47.04 Na = 1.96 \text{ m/s}^2, \quad T = 47.04 \text{ N}
In an Atwood machine, the heavier mass accelerates downward while the lighter one accelerates upward. The tension is the same throughout the rope and falls between the two weights.

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 4 medium

Two blocks ([formula] and [formula]) are connected by a rope on a frictionless table. A [formula] fo

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