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

To find the tension in the cable, we start by analyzing the forces acting on the lift.

1. Forces Acting on the Lift:

   • The gravitational force acting on the lift is given by:

     $F_g = Mg$

     where M is the mass of the lift and g is the acceleration due to gravity.

   • There is also a frictional force, F, acting against the motion of the lift as it descends.

2. Applying Newton's Second Law:

   • According to Newton's second law, the net force acting on the lift can be expressed as:

     $F_{net} = Ma$

     where a is the acceleration of the lift (downward in this case).

3. Identifying the Net Force:

   • The net force is the difference between the gravitational force and the sum of the frictional force because the lift is accelerating downward:

     $F_{net} = F_g - F - T$

   Rearranging gives us:

   $T = Mg - F - Ma$

   Further simplifying this based on the net force gives:

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

4. Conclusion:

   • The correct expression for the tension T in the cable, accounting for gravitational force, friction, and acceleration is summarized as:

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

   Evaluating the options provided in the question confirms that this aligns with option D.