Answer:
A) Must be done 19806.62 joules of work.
B) The average power is 1320.44 Watts.
Explanation:
A) First, we're going to use the work-energy theorem that states total work (
) done on an object is equal to the change in its kinetic energy (
):
(1)
So, all we must do is to find the change on kinetic energy. Because we're working with rotational body, we should use the equation
for the kinetic energy so:
(2)
with
the initial angular velocity,
the final angular velocity (is zero because the wheel stops) and I the moment of inertia that for a thin hoop is
, using those on (2)
(3)
By (3) on (1):


B) Average power is work done divided by the time interval:


NOTE: We use the relation
to convert 280 rev/min(rpm) to 29.32 rad/s
Answer:
Because the bullet is smaller and has a sharp/pointy tip.
Explanation:
The bullet kinda puts the majority of kinetic energy in a small are, whereas the gun butt kinda spreads the energy evenly amongst a larger surface. If more explanation is needed add comment.
Answer:
Explanation:
Work in pumping water from the tank is given as
W = ∫ y dF. From a to b
Where dF is the differential weight of the thin layer of liquid in the tank, y is the height of the differential layer
a is the lower limit of the height
b is the upper limit of the height.
We know that, .
F = ρVg
Where F is the weight
ρ is the density of water
V is the volume of water in tank
g is the acceleration due to gravity
Then,
dF = ρg ( Ady)
We know that the density and the acceleration due to gravity is constant, also the base area of the tank is constant, only the height that changes.
Then,
ρg = 62.4 lbs/ft³
Area = L×B = 3 × 9 = 27ft²
dF = ρg ( Ady)
dF = 1684.8dy
The height reduces from 12ft to 0ft
Then,
W = ∫ y dF. From a to b
W = ∫ 1684.8y dy From 0 to 12
W = 1684.8y²/2 from 0 to 12
W = 842.4 [y²] from y = 0 to y = 12
W = 842.4 (12²-0²)
W = 121,305.6 lb-ft
Answer
given,
expression of Kinetic energy of rotating body

ω = 34.0 rad/s
Assuming mass of the particle equal to 13 Kg
and perpendicular distance from the particle to the axis is r = 1.25 m
now,
moment of inertia of particle = ?
from the given expression
..............(1)
we know

v = r ω

putting value in equation (1)



I = 20.3125 kg.m²