A block of aluminum that has dimensions 2.07 cm by 2.55 cm by 5.00 cm is suspended from a spring scale. The density of aluminum is 2702 kg/m^3.
(a) What is the weight of the block?
0.699 N
(b) What is the scale reading when the block is submerged in oil with a density of 817 kg/m^3?
Please help I don't know how to do part b; Thanks.
mg = ρ•V •g =
=(2.07•2.55•5) •10^-6•2702•9.8 = 0.699 N
buoyancy force Mg
mg - Mg =
=ρ•V •g – ρ1•V•g = (ρ – ρ1) •V•g =
=(2702 – 817) •(2.07•2.55•5) •10^-6•9.8 = 0.48 N.
To solve part b, we need to calculate the buoyant force acting on the block when it is submerged in oil. The buoyant force is the upward force exerted by a fluid on an object immersed in it and it is equal to the weight of the fluid displaced by the object.
To calculate the buoyant force, we need to determine the volume of the block that is submerged in the oil.
Step 1: Calculate the volume of the block:
Volume = Length x Width x Height
Given:
Length = 2.07 cm = 0.0207 m
Width = 2.55 cm = 0.0255 m
Height = 5.00 cm = 0.0500 m
Volume = 0.0207 m x 0.0255 m x 0.0500 m
Volume = 2.65 x 10^-5 m^3
Step 2: Calculate the weight of the block:
Weight = Density x Volume x Acceleration due to gravity
Given:
Density of aluminum = 2702 kg/m^3
Acceleration due to gravity = 9.8 m/s^2
Weight = 2702 kg/m^3 x 2.65 x 10^-5 m^3 x 9.8 m/s^2
Weight = 0.0721 N
Step 3: Calculate the buoyant force:
Buoyant force = Weight of fluid displaced
Given:
Density of oil = 817 kg/m^3
Buoyant force = Density of oil x Volume x Acceleration due to gravity
Buoyant force = 817 kg/m^3 x 2.65 x 10^-5 m^3 x 9.8 m/s^2
Buoyant force = 0.0219 N
Step 4: Calculate the scale reading:
The scale reading is equal to the weight of the block minus the buoyant force.
Scale reading = Weight - Buoyant force
Scale reading = 0.0721 N - 0.0219 N
Scale reading = 0.0502 N
Therefore, the scale reading when the block is submerged in oil with a density of 817 kg/m^3 is 0.0502 N.