Answer:
Explanation:
The problem is related to rotational motion . So we shall find out rotational kinetic energy .
K E = 1/2 x I ω²
ω is the final angular velocity
Moment of inertial of the disk
I ₁ = 1/2 m r²
= .5 x 165 x 2.93²
= 708.25 kgm²
Moment of inertial of the person
I₂ = mr²
= 62.5 x 2.93²
= 536.55 kgm²
ω₂ = v / R
= 3.11 / 2.93 rad /s
At the time of jumping , law of conservation of angular momentum will apply
I₁ ω₁ + I₂ω₂ = (I₁ + I₂)ω
708.25 x0.691 + 536.55 x ( 3.11 / 2.93 ) = ( 708.25 + 536.55 ) ω
ω = 0 .85 rad/ s
K E = 1/2 x I ω²
= .5 x ( 708.25 + 536.55 ) ( .85 )²
449.68 J
Yes..............................
We will find the mass from
mass = density x volume
We are told the density and must find the volume from the dimensions given
the volume of the washer will be the area x thickness (remembering to convert all measurements to meters)
if the washer had no hole, its area would be pi (0.0225m)^2 (remember to convert to meters and to use radius)
the area of the hole is pi(0.00625m)^2
so the area of the washer is pi[(0.0225m)^2 - (0.00625m)^2] = 1.5x10^-3 m
the volume of the washer is 1.5x10^-3 m x 1.5x10^-3 m = 2.25x10^-6 m^3 (the thickness of the washer is 1.5 mm = 1.5x10^-3m)
thus, the mass of the washer = 8598kg/m^3 x 2.25x10^-6m^3 = 0.0189kg = 18.9 grams
The solution for this problem:
Given:
f1 = 0.89 Hz
f2 = 0.63 Hz
Δm = m2 - m1 = 0.603 kg
The frequency of mass-spring oscillation is:
f = (1/2π)√(k/m)
k = m(2πf)²
Then we know that k is constant for both trials, we have:
k = k
m1(2πf1)² = m2(2πf2)²
m1 = m2(f2/f1)²
m1 = (m1+Δm)(f2/f1)²
m1 = Δm/((f1/f2)²-1)
m 1 = 0.603/
(0.89/0.63)^2 – 1
= 0.609 kg or 0.61kg or 610 g
You're right, Answer C
The dust and gas accumulate to form a solar nebula, which later on creates the star and the planets.
