A Spiral spring of natural length 20.00cm has a scale hanging freely in its lower end. When an object ass 40 g is placed in the pan. its length becomes cm. ...
Question 1 Report
A Spiral spring of natural length 20.00cm has a scale hanging freely in its lower end. When an object ass 40 g is placed in the pan. its length becomes cm. When the object is replaced with another of 60g, the length becomes 22.05cm. Calculate the mass scale pan. [g = 10 ms\(^{-2}\)]
Answer Details
Using Hooke’s law: extension of the spring is proportional to the total mass attached.
For the 40 g mass, the spring length is \(21.80\text{ cm}\), hence extension:
\[ e_1 = 21.80 - 20.00 = 1.80\text{ cm} \] \[ (m + 40)g = 1.80k \qquad \text{... (i)} \]For the 60 g mass, the extension is:
\[ e_2 = 22.05 - 20.00 = 2.05\text{ cm} \] \[ (m + 60)g = 2.05k \qquad \text{... (ii)} \]Dividing equation (i) by equation (ii):
\[ \frac{m+40}{m+60}=\frac{1.80}{2.05} \] \[ 1.80(m+60)=2.05(m+40) \] \[ 1.80m+108=2.05m+82 \] \[ 26=0.25m \] \[ m=104\text{ g} \]Mass of the scale pan \(= 104\text{ g}\).
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