The magnitudes of the forces that the ropes must exert on the knot connecting are :
- F₁ = 118 N
- F₂ = 89.21 N
- F₃ = 57.28 N
<u>Given data :</u>
Mass ( M ) = 12 kg
∅₂ = 63°
∅₃ = 45°
<h3>Determine the magnitudes of the forces exerted by the ropes on the connecting knot</h3><h3 />
a) Force exerted by the first rope = weight of rope
∴ F₁ = mg
= 12 * 9.81 ≈ 118 kg
<u>b) Force exerted by the second rope </u>
applying equilibrium condition of force in the vertical direction
F₂ sin∅₂ + F₃ sin∅₃ - mg = 0 ---- ( 1 )
where: F₃ = ( F₂ cos∅₂ / cos∅₃ ) --- ( 2 ) applying equilibrium condition of force in the horizontal direction
Back to equation ( 1 )
F₂ = [ ( mg / cos∅₂ ) / tan∅₂ + tan∅₃ ]
= [ ( 118 / cos 63° ) / ( tan 63° + tan 45° ) ]
= 89.21 N
<u />
<u>C ) </u><u>Force </u><u>exerted by the</u><u> third rope </u>
Applying equation ( 2 )
F₃ = ( F₂ cos∅₂ / cos∅₃ )
= ( 89.21 * cos 63 / cos 45 )
= 57.28 N
Hence we can conclude that The magnitudes of the forces that the ropes must exert on the knot connecting are :
F₁ = 118 N, F₂ = 89.21 N, F₃ = 57.28 N
Learn more about static equilibrium : brainly.com/question/2952156
Kinetic energy can be used to develop electric energy which can be used as electricity.
<u>Explanation:</u>
The kinetic energy can be harnessed; much like some hydro power technologies harness water movement. A way to convert this kinetic energy into electric energy is through piezoelectric. By applying a mechanical stress to a piezoelectric crystal or material an electric current will be created and can be harvested.
Kinetic energy is also generated by the human body when it is in motion. Studies have also been done using kinetic energy and then converting it to other types of energy, which is then used to power everything from flashlights to radios and more.
Answer:
1 m = 39.37 in = 39.37/12 ft = 3.28 ft
V = 1145 k/hr = 1145k/hr * 6076 ft/k = 6957020 ft / hr
V = 6957020 ft/hr / 3600 s/hr = 1933 ft/sec
V = 1933 ft/sec / (3.28 ft / m) = 589 m/s
Check:
88 ft/sec = 60 mph
(1145 k/hr * 6076 ft / k) 3600 sec/hr = 1933 ft/sec = 589 m/s
1933 ft/sec / (88 ft/sec) * 60 mph = 1318 mph
Also, 1318 / 1145 = 6076 / 5280 as it should
Answer:
the required value is 
Explanation:
Given that,
mass, m = 1kg
spring constant k = 21N/M
damping force = 

By Newtons second law ,
The diffrential equation of motion with damping is given by

substitute the value of m =1kg, k = 21N/M, and 


suppose the equation of the form
,
and the auxilliary equation is given by

The general solution for the above differential equation is

Derivate with respect to t

(a)
since time is 0 then mass is one meter below
so x(0) = 1
Also it start from rest , that implies , velocity is 0 and time is 0

substitute the initial condition


Solve the above equation to get C₁ and C₂

substitute for C₁ and C₂ in general solution

Thus the required value is 
Answer:
Explanation:
The question is incomplete.
The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 4.5 seconds.
s= sin2(pi)t
Acceleration = d²S/dt²
dS/dt = 2πcos2πt
d²S/dt² = -4π²sin2πt
A(t) = -4π²sin2πt
Next is to find acceleration after 4.5 seconds
A(4.5) = -4π²sin2π(4.5)
A(4.5) = -4π²sin9π
A(4.5) = -4π²sin1620
A(4.5) = -4π²(0)
A(4.5) = 0m/s²