A load of mass 4 kg is lifted vertically upward with an acceleration of 2 m/s². Find the tension in the string — Physics problems | PhysLabo
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Tension during an upward acceleration

Easy 9 grade Mechanics / Newton's Laws

A load of mass $m = 4$ kg is lifted vertically upward with an acceleration of $a = 2$ m/s². Find the tension in the string that the load hangs from. Neglect air resistance; $g = 10$ m/s².

Given
  • $m = 4$ kg
  • $a = 2$ m/s² (up)
  • $g = 10$ m/s²
  • $T = ?$
Visual demonstration
Hints
Hint 1 / 2
With an upward acceleration the tension is greater than the weight: $T = m(g+a)$.
Hint 2 / 2
For comparison: at rest the tension would be $mg = 40$ N.
Solution

The load accelerates upward, so the tension is greater than the weight. By Newton's second law ($T$ upward, $mg$ downward):

$$T - mg = ma \Rightarrow T = m(g + a)$$

$$T = 4 \cdot (10 + 2) = 4 \cdot 12 = 48 \text{ N}$$

Answer

$T = 48$ N