Everything Science Grade 11

12.3 CHAPTER 12. FORCE,MOMENTUM AND IMPULSE

Example 19: Normal Forces 3

QUESTION

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

accelerating downwardsat 2 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)(−2m· s−^2 )

=− 200 N

= 200 N down

Step 5 : Determine the normalforce, FN

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

Fr = Fg+ FN

−200N =−980N + FN

FN = 780N upwards

Step 6 : Quote the final answer

The normal force is 780N upwards. It balancesthe gravitational force down-

wards just enough so that the man only accelerates downwards at 2 m·s−^2. The

reading on the scale is 780 N.