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

To determine the tension in the cable, we begin by analyzing the forces acting on the lift. The forces include:

1. Weight of the lift (W): The gravitational force acting downward is given by: $W = Mg$ where M is the mass of the lift and g is the acceleration due to gravity.

2. Frictional force (F): This force acts upward, opposing the motion of the descending lift.

3. Net force (F_net): According to Newton's second law, the net force acting on the lift can be represented as: $F_{net} = Ma$ where a is the downward acceleration of the lift.

Now, since the lift is descending, we can express the net force as the difference between the weight and the forces acting against it (friction and tension in the cable):

$Mg - T - F = Ma$

Rearranging this equation to solve for the tension T yields:

$T = Mg - Ma - F$

This can be further simplified to: $T = M(g - a) - F$.

Thus, the correct answer is:

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