(a)(i) What peculiar property does the effort has in all classes of levers?
(ii) A meter rule of weight 1.0N is supported horizontally on two knife edges each placed 10.0cm from its ends. If the weight of 1.5N is placed at its mid-point, calculate the reaction at the supports.
(b)(i) State the law of floatation.
(ii) Find the fraction of the cork that partially immersed when a piece of cork of density 0.25 g/cm3 and a mass of 20 g floats in water.
SECTION 01
(a)(i) What peculiar property does the effort has in all classes of levers?
Force creates efforts for different types of levers
-In class 1 of levers effort situated at the end after pivot at the middle
-In class 2 of levers effort situated at the end after load at the middle
-In class 3 of levers effort situated at the middle of load and pivot
(ii) A meter rule of weight 1.0 N is supported horizontally on two knife edges each placed 10.0 cm from its ends. If the weight of 1.5 N is placed at its mid-point, calculate the reaction at the supports.
Data and Reasoning:
Weight of the ruler = 1N (assumed to be located at the center of ruler)
Force located at the center = 1.5N
Distance near the edges = 0.1m
At equilibrium, sum of clockwise moments = sum of counter clockwise moment, hence 0.4R1 = 0.4R2 … (i)
At equilibrium, sum of upward forces = sum of downward forces, hence R1 + R2 = 2.5 … (ii)
Solving two equations, R1 = 1.25N and R2 = 1.25N
SECTION 02
(b)(i) State the law of floatation.
"Floating object displace its own weight on fluid it floats."
(ii) Find the fraction of the cork that partially immersed when a piece of cork of density 0.25 g/cm 3 and a mass of 20 g floats in water.
Data and solution:
Fraction of cork immersed corresponds to volume of liquid displaced
Volume displaced corresponds to up-thrust from water
For floating objects, up-thrust, U = weight of an object, W (application of Law of floatation)
So, Up-thrust (U) = Mass x gravity = 0.020Kg x10N/Kg = 0.2 N
Also, Up-thrust (U) = Weight of fluid displaced (Wd) = 0.2N of water (application of Archimedes principle)
- What is volume of water with weight of 0.2N?
- Weight = Mass x acceleration due to gravity and Mass = Density x Volume
- Weight = Density x Volume x acceleration due to gravity = ρvg
- V = Weight / (Density x Acceleration due to gravity) = 0.2N/(1000Kg/m^{3 }x 10N/Kg) = 0.00002m^{3 }= 20cm^{3} of water
- Since volume of water displaced is equal volume of cork under water, so volume of cork under water = 20 cm^{3 }
But the question ask for fraction, so what is the total volume?
- Volume = m/ρ = 20g / 0.25gcm^{3} = 80cm^{3}
- So fraction = 20cm^{3}/ 80cm^{3} = ¼ Ans.
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