Question

A meter stick has a mass of 0.21 kg and balances at its center. When a small chain is suspended from one end, the balance point moves 14.0 cm toward the end with the chain. Determine the mass of the chain.

Answer 1

0.082 kg

Step-by-step explanation:

The center of the meter stick = 50 cm.

When a small chain is place at one end, the balance point is moved 14 cm towards the end with the chain.

The new balance point = 50-14 = 36 cm

Using the principle of moment,

Sum of clockwise moment = sum of anti clockwise moment.

W(36-0) = W'(50-36).................. Equation 1

Where W = weight of the chain, W' = weight of the meter stick

36W = 14W'

make W the subject of the equation

W = 14W'/36.......................... Equation 2

Given: W' = m'g, where m' = mass of the meter stick, m' = 0.21 kg

W' = 0.21(9.8) = 2.058 N

Substitute into equation 2

W = 14(2.058)/36

W = 0.8 N

But

W = mg,

Where m = mass of the chain.

m = W/g

m = 0.8/9.8

m = 0.082 kg.

Hence the mass of the chain = 0.082 kg

Answer 2

The mass is
`M_n = 0.047kg`

Step-by-step explanation:

From the question we are told that

The mass of the meter stick is
`M_c = 0.21kg`

The distance by which the balance point moves
`d = 14.0 \ cm`

Before the movement of the balance point was at the middle of the meter stick i.e at the 50 cm mark

Mathematically the weight of the meter stick would be

`W = M_c g`

where g is acceleration due to gravity with a value of
`9.8m/s^2`

`W = 0.12 * 9.8`

`=1.176N`

Now when the small chain is suspended from one end and the system reach equilibrium the net torque is zero and this implies that

The moment of force of the meter stick = moment of force of the necklace

`W * 14 = W_n * (50 - 14)`

Where
`W_n` is the weight of the necklace

Substituting values and making
`W_n` the subject we have

`W_n = (1.176*14)/(36)`

`=0.457N`

Mathematically the weight of the chain is

`W_n = M_n * g`

Substituting values and making
`M_n` the subject

`M_n = (W_n)/(g)`

`=(0.457)/(9.8)`

`M_n = 0.047kg`