Answer:
2.84 m/s
Explanation:
At the top position of the circular trajectory, the normal reaction is zero:
N = 0
So it means that the only force that is providing the centripetal force is the gravitational force (the weight of the bucket). Therefore we have:

where
m is the mass of the water bucket
g = 9.8 m/s^2 is the acceleration of gravity
v is the speed of the bucket
r = 0.824 m is the radius of the circle
Solving for v,

Answer:
longitudinal engineering strain = 624.16
true strain is 6.44
Explanation:
given data
diameter d1 = 0.5 mm
diameter d2 = 25 mm
to find out
longitudinal engineering and true strains
solution
we know both the volume is same
so
volume 1 = volume 2
A×L(1) = A×L(2)
( π/4 × d1² )×L(1) = ( π/4 × d2² )×L(2)
( π/4 × 0.5² )×L(1) = ( π/4 × 25² )×L(2)
0.1963 ×L(1) = 122.71 ×L(2)
L(1) / L(2) = 122.71 / 0.1963 = 625.16
and we know longitudinal engineering strain is
longitudinal engineering strain = L(1) / L(2) - 1
longitudinal engineering strain = 625.16 - 1
longitudinal engineering strain = 624.16
and
true strain is
true strain = ln ( L(1) / L(2))
true strain = ln ( 625.16)
true strain is 6.44
Answer:
α = -π/3 rad/s²
θ = 1.5π rad ≈ 4.71 rad
θ = 0.75 rev
Explanation:
30 rev/min (2π rad/rev) / (60 s/min) = π rad/s
α = (ωf - ωi) / t = (0 - π) / 3 = -π/3 rad/s²
θ = ½αt² = ½(π/3)3² = 1.5π rad ≈ 4.71 rad
θ = 1.5π rad / 2π rad/rev = 0.75 rev
First let's convert everything into SI units.
The length of the blade is 3 inches. Keeping in mind that 1 inc=0.025 m, we have

The angular speed is 600 revolutions per minute. Keeping in mind that

and

, the angular speed becomes

And so, the linear velocity of the edge of the blade is equal to