Everything Science Grade 11

CHAPTER 12. FORCE,MOMENTUM AND IMPULSE 12.3

Example 20: Normal Forces 4

QUESTION

A man with a mass of100 kg stands on a scale (measuring newtons)inside a lift that is

accelerating upwards at4 m·s−^2. What is the reading onthe scale?

SOLUTION

Step 1 : Identify what information is given and what isasked for

We are given the mass of the man and his resultant acceleration - this isjust the

acceleration of the lift. We know the gravitationalacceleration also acts onhim.

Step 2 : Decide which equationto use to solve the problem

Once again we can useNewton’s laws. We know that the sum of all theforces

must equal the resultantforce, Fr.

Fr= Fg+ FN

Step 3 : Determine the force due to gravity, Fg

Fg = mg

= (100kg)(9,8m· s−^2 )

= 980 kg· m· s−^2

= 980N downwards

Step 4 : Determine the resultant force, Fr

The resultant force can be calculated by applyingNewton’s Second Law:

Fr = ma

Fr = (100kg)(4m· s−^2 )

= 400 N upwards

Step 5 : Determine the normalforce, FN

The sum of all the vertical forces is equal to theresultant force, therefore

Fr = Fg+ FN

400N =−980N + FN

FN = 1380N upwards

Step 6 : Quote the final answer

The normal force is 1380 N upwards. It balances the gravitational forcedown-

wards and then in addition applies sufficient force to accelerate the manupwards

at 4m·s−^2. The reading on the scale is 1380 N.