Everything Science Grade 11

12.3 CHAPTER 12. FORCE,MOMENTUM AND IMPULSE

• This is therefore the resultant force acting on the rocket and it makes therocket accelerate
  forwards.

Example 13: Newton II - lifts

QUESTION

A lift, mass 250 kg, is initially at rest on the ground floor of a tall building. Passengers with

an unknown total mass,m, climb into the lift. The lift accelerates upwards at 1,6 m·s−^2. The

cable supporting the liftexerts a constant upward force of 7700 N. Useg = 10 m·s−^2.

1. Draw a labelled force diagram indicating allthe forces acting on thelift while it acceler-
   ates upwards.


2. What is the maximummass, m, of the passengers the lift can carry in order to achieve a
   constant upward acceleration of 1,6 m·s−^2.

SOLUTION

Step 1 : Draw a force diagram.

Downward force of Earthon lift

Upward force of cable onlift

Downward force of

passengers on lift

(10 x m)

(2500 N)

(FC= 7700 N)

Step 2 : Find the mass, m.

Let us look at the lift with its passengers as a unit. The mass of this unit will

be (250 + m) kg andthe force of the Earthpulling downwards (Fg) will be

(250 + m) x 10 m.s−^2. If we apply Newton’sSecond Law to the situation we

get:

Fnet = ma

FC− Fg = ma

7700 − (250 + m)(10) = (250 + m)(1,6)

7700 − 2500 − 10 m = 400 + 1, 6 m

4800 = 11, 6 m

m = 413,79kg