The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, its acceleration is:

The correct answer is option 1) i.e. 4 ms−2 upwards.

CONCEPT:

• The weight associated with a moving lift (W), tension force on the supporting cable (T), and acceleration (a) of the lift can be categorized into 2 cases:

• In case 1, the lift moves up with an acceleration of a.
• In case 2, the lift moves down with an acceleration of a.

CALCULATION:

Given that:

Mass of a lift, m = 2000 kg

Tension in the supporting cable, T = 28000 N

Since the direction of lift motion is not mentioned, let us assume that the lift is moving upwards (case 1).

Sign convention: upward direction +ve, downward direction (-ve)

The weight of lift acting downwards, W = mg = 2000 × 10 = 20000 N          (Assume g = 10 m/s²)

Net force acting on the lift = T - W = 28000 - 20000 = 8000 N

Net force = ma

8000 = 2000 × a

∴ a = 8000/2000 = 4 m/s²

Hence, the lift is moving upwards with an acceleration of 4m/s².

Important Points

• The positive value of acceleration confirms that our assumption was correct i.e. lift is moving up with an acceleration 'a'
• If the acceleration obtained was negative, it indicates that the assumption is wrong i.e. lift is moving downwards with the acceleration 'a'.