A lift of mass M is suspended from a cable - AQA - A-Level Physics - Question 15 - 2019 - Paper 1

To find the tension T in the cable, we start by applying Newton's second law. The forces acting on the lift include the tension T acting upwards and the weight of the lift Mg acting downwards, along with the frictional force F also acting downwards.

1. Identify the forces:

   • Weight of the lift: ( Mg )
   • Frictional force: ( F )
   • Tension in the cable: ( T )

2. Apply Newton's second law: Since the lift is descending with an acceleration ( α ), we can express this as:

   [ M g - T - F = M (-α) ] Since the net force is downward (due to the acceleration), the equation rearranges to:

   [ T = M g - F + M α ]

   or, alternatively,

   [ T = M (g - α) - F ]

3. Conclusion: After rearranging, we find that the correct answer for the tension in the cable is:

   [ T = M (g - α) - F ]

From the multiple-choice options given, the correct equation corresponds to option D.