Answer:
Rotational kinetic energy = 0.099 J
Translational kinetic energy = 200 J
The moment of inertia of a solid sphere is .
Explanation:
Rotational kinetic energy is given by
where <em>I</em> is the moment of inertia and <em>ω</em> is the angular speed.
For a solid sphere,
where <em>m</em> is its mass and <em>r</em> is its radius.
From the question,
<em>ω</em> = 49 rad/s
<em>m</em> = 0.15 kg
<em>r</em> = 3.7 cm = 0.037 m
Translational kinetic energy is given by
where <em>v</em> is the linear speed.
The two wires carry current in opposite directions: this means that if we see them from above, the magnetic field generated by one wire is clock-wise, while the magnetic field generated by the other wire is anti-clockwise. Therefore, if we take a point midway between the two wires, the resultant magnetic field at this point is just the sum of the two magnetic fields, since they act in the same direction.
Therefore, we should calculate the magnetic field generated by each wire and then calculate their sum. We are located at a distance r=0.10 m from each wire.
The magnetic field generated by wire 1 is:
The magnetic field generated by wire 2 is:
And so, the resultant magnetic field at the point midway between the two wires is
Answer:
the magnitude of the average contact force exerted on the leg is 3466.98 N
Explanation:
Given the data in the question;
Initial velocity of hand v₀ = 5.25 m/s
final velocity of hand v = 0 m/s
time interval t = 2.65 ms = 0.00265 s
mass of hand m = 1.75 kg
We calculate force on the hand F
using equation for impulse in momentum
F × t = m( v - v₀ )
we substitute
F × 0.00265 = 1.75( 0 - 5.25 )
F × 0.00265 = 1.75( - 5.25 )
F × 0.00265 = -9.1875
F = -9.1875 / 0.00265
F = -3466.98 N
Next we determine force on the leg F
Using Newton's third law of motion
for every action, there is an equal opposite reaction;
so, F = - F
we substitute
F = - ( -3466.98 N )
F = 3466.98 N
Therefore, the magnitude of the average contact force exerted on the leg is 3466.98 N
Given:
Height of tank = 8 ft
and we need to pump fuel weighing 52 lb/ to a height of 13 ft above the tank top
Solution:
Total height = 8+13 =21 ft
pumping dist = 21 - y
Area of cross-section = = =16
Now,
Work done required =
=
= 832)
= 113152 = 355477 ft-lb
Therefore work required to pump the fuel is 355477 ft-lb
Answer:
a) P = 44850 N
b)
Explanation:
Given:
Cross-section area of the specimen, A = 130 mm² = 0.00013 m²
stress, σ = 345 MPa = 345 × 10⁶ Pa
Modulus of elasticity, E = 103 GPa = 103 × 10⁹ Pa
Initial length, L = 76 mm = 0.076 m
a) The stress is given as:
on substituting the values, we get
or
Load, P = 44850 N
Hence<u> the maximum load that can be applied is 44850 N = 44.85 KN</u>
b)The deformation () due to an axial load is given as:
on substituting the values, we get
or