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

To derive the tension in the cable, we start by considering the forces acting on the lift:

1. The weight of the lift acting downward, which is equal to $Mg$, where $g$ is the acceleration due to gravity.
2. The tension $T$ in the cable acting upward.
3. The frictional force $F$ acting upward as well.

Applying Newton's second law, we can express the net force on the lift as:

$F_{net} = M(a_{down}) = Mg - T - F$

Rearranging the equation gives:

$T = Mg - F - Ma$

This can also be rewritten as:

$T = M(g - a) - F$

Thus, the correct answer from the options given is:

D: $T = M(g - a) - F$