Answer: thickness h = 0.014cm
Question: In the manufacturing of computer chips, cylinders of silicon are cut into thin wafers that are 3.30 inches in diameter and have a mass of 1.50 g of silicon. How thick (mm) is each wafer if silicon has a density of 2.33 g/cm 3 ? (The volume of a cylinder is V=πr 2 h )
Explanation:
The volume of a cylinder is
Volume V = πr^2h ....1
The density of a material is
Density D = mass m / volume V
D = m/V ....2
Since m and D are given, we can make V the subject of formula.
V = m/D ....3
From equation 1, we need to derive the thickness h of the cylindrical silicon.
h = V/πr^2 .....4
Substituting equation 3 into 4
h = (m/D)/πr^2 .....5
Given.
mass m = 1.50g
density D = 2.33g/cm^3
radius r = diameter/2 = 3.00in/2 = 7.62/2 cm = 3.81cm
Substituting the given values into the equation
h = (1.5/2.33)/(π ×3.81^2)
thickness h = 0.014cm
Answer:
(a) 1058.4 J
(b) -10584 J
Explanation:
Parameters given:
Mass of astronaut, m = 72 kg
Distance moved by astronaut, d = 15 m
(a) WORK DONE BY FORCE FROM THE HELICOPTER
Work done is given as the product of Force applied to a body and the distance moved by the body:
W = F * d
The force from the helicopter is given as:
F = m * a
where a = acceleration of the astronaut due to the helicopter
Therefore, the work done is given as:
W = m * a * d
W = 72 * g/10 * 15
W = 
W = 1058.4 J
(b) WORK DONE BY FORCE OF GRAVITY
W = F * d
The force of gravity is given as:
F = -m * g
where g = acceleration due to gravity
The negative sign is due to the fact that the astronaut moves in an opposite direction (upwards) to the force of gravity (Gravity acts downwards)
Therefore, the work done is given as:
W = -m * g * d
W = -72 * 9.8 * 15
W = -10584 J