1.
X, Y and Z are the weights of three objects
suspended by pulleys as shown.
Assuming the pulleys in this system are frictionless
and weightless and that Z= 12 N, what are the
values of X and Y?
24°
50°
Х
Y
Z
Answers
Answer:
The weight of the object X is approximately 3.262 N (Acting downwards)
The weight of the object Y is approximately 8.733 N (Acting downwards)
Explanation:
The question can be answered based on the principle of equilibrium of forces
The given parameters are;
The weight of Z = 12 N (Acting downwards)
The weight of the pulleys = Negligible
From the diagram;
The tension in the in the string attached to object Z = The weight of object Z = 12 N
The tension in the in the string attached to object X = The weight of the object X
The tension in the in the string attached to object Y = The weight of the object Y
Given that the forces are in equilibrium, we have;
The sum of vertical forces acting at a point, [tex]\Sigma F_y[/tex] = 0
Therefore;
[tex]T_{1y} + T_{2y} + T_{3y} = 0[/tex]
[tex]T_{1y} = -( T_{2y} + T_{3y} )[/tex]
Where;
[tex]T_{1y}[/tex] = The weight of object Z = 12 N
[tex]T_{1y}[/tex] = 12 N
[tex]T_{2y}[/tex] = The vertical component of tension, T₂ = T₂ × sin(24°)
∴ [tex]T_{2y}[/tex] = T₂ × sin(156°)
Similarly;
[tex]T_{3y}[/tex] = T₃ × sin(50°)
From [tex]T_{1y} = -( T_{2y} + T_{3y} )[/tex], and [tex]T_{1y}[/tex] = 12 N, we have;
12 N = -(T₂ × sin(156°) + T₃ × sin(50°))...(1)
Given that the forces are in equilibrium, we also have that the sum of vertical forces acting at a point, ∑Fₓ = 0
Therefore at point B, we have;
T₁ₓ + T₂ₓ + T₃ₓ = 0
The tension force, T₁, only has a vertical component, therefore;
∴ T₁ₓ = 0
∴ T₂ₓ + T₃ₓ = 0
T₂ₓ = -T₃ₓ
T₂ₓ = T₂ × cos(156°)
T₃ₓ = T₃ × cos(50°)
From T₂ₓ = -T₃ₓ, we have;
T₂ × cos(156°) = - T₃ × cos(50°)...(2)
Making T₃ the subject of equation (1) and (2) gives;
Making T₃ the subject of equation in equation (1), we get;
12 = -(T₂ × sin(156°) + T₃ × sin(50°))
∴ T₃ = (-12 - T₂ × sin(156°))/(sin(50°))
Making T₃ the subject of equation in equation (2), we get;
T₂ × cos(156°) = - T₃ × cos(50°)
∴ T₃ = T₂ × cos(156°)/(-cos(50°))
Equating both values of T₃ gives;
(-12 - T₂ × sin(156°))/(sin(50°)) = T₂ × cos(156°)/(-cos(50°))
-12/(sin(50°)) = T₂ × cos(156°)/(-cos(50°)) + T₂ × sin(156°)/(sin(50°))
∴ T₂ = -12/(sin(50°))/((cos(156°)/(-cos(50°)) + sin(156°)/(sin(50°))) ≈ -8.02429905283
∴ T₂ ≈ -8.02 N
From T₃ = T₂ × cos(156°)/(-cos(50°)), we have;
T₃ = -8.02× cos(156°)/(-cos(50°)) = -11.3982199717
∴ T₃ ≈ -11.4 N
The weight of the object X = -T₂ × sin(156°)
∴ The weight of the object X ≈ -(-8.02 × sin(156°)) = 3.262 N
The weight of the object X ≈ 3.262 N (Acting downwards)
The weight of the object Y = -(T₃ × sin(50°))
∴ The weight of the object Y = -(-11.4 × sin(50°)) ≈ 8.733 N
The weight of the object Y ≈ 8.733 N (Acting downwards)
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Answer:
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Answer:
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Answers
Answer:
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Explanation:
From the question,
If two forces act at right angle to each other, Their result force can be calculated using Pythagoras theorem.
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The water level at the beach changes on a regular basis. What is the primary force that causes these changes in water levels?
Answers
Explanation:
The water level at the beach changes on regular basis because of high and low tides in the sea. The high tide and low tide in the sea is because of moons gravitational force on Earth. The tide are low or high depends upon the differences in how much the moon's gravity pulls on different parts of Earth. Places where pull is less experience low tide whereas places where pull is more experience high tide.
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Answer:
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Answers
Answer:
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Answers
Answer:
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Explanation:
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Answer:
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Explanation:
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Answer: five
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Explanation:
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Explanation:
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Answer:
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Explanation:
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Answers
Answer:
Option D is correct answer of this question
Explanation:
=> Because in it sound is going from one
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The planets move around the stars in different orbits .which planet will have the shortest of revolution (year)?
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Answer:
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Answer:
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Explanation:
Answer:
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Explanation:
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Answers
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Answers
Answer:
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Answer:
A & B
Explanation:
He used 2 peach basket and a soccer ball
Guys I need help on this
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Answer:
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Answer:
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Answers
Explanation:
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Answer:
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will mark as brainliest . pls help
Answers
Answer:
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circuit breaker is useful when you do something with your domestic electric circuit..
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to generate the neutrons that are needed to break the nuclei
to overcome the repulsion between the protons in the nuclei that join
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to keep the uranium fuel separate from the control rods
Answers
Explanation:
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Answer:
bBBBB
Explanation:
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Answers
Answer:
El resorte se comprime 0.38 m.
Explanation:
La distancia de compresión del resorte se puede calcular por conservación de la energía:
[tex] \Sigma E_{i} = \Sigma E_{f} [/tex]
[tex] E_{p} = E_{e} [/tex]
[tex] mgh = \frac{1}{2}kx^{2} [/tex] (1)
En donde:
[tex]E_{i}[/tex] y [tex]E_{f}[/tex]: son las energías inciales y finales
[tex] E_{p}[/tex]: es la energía potencial gravitacional
[tex]E_{e}[/tex]: es la energía potencial elástica
m: es la masa = 1.50 kg
g: es la gravedad = 9.81 m/s²
h: es la altura
k: es la constante de fuerza = 320 N/m
x: es la distancia de compresión
Dado que el objeto está 1.20 m sobre el resorte, entonces h es:
[tex] h = 1.20 + x [/tex] (2)
Entonces, introduciendo la ecuación (2) en (1) y resolviendo para x tenemos:
[tex] \frac{1}{2}kx^{2} - xmg - 1.20mg = 0 [/tex]
[tex] 160x^{2} - 14.72x - 17.66 = 0 [/tex]
Resolviendo la ecuación cuadrática anterior tenemos:
x₁ = -0.29 y x₂ = 0.38
Tomando el valor positivo entonces, el resorte se comprime 0.38 metros.
Espero que te sea de utilidad!
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Answers
Answer:
Explanation:
weight ( w ) = 100 N
mass (m) = ?
WE know
g = 10 m/s²
w = m * g
or
m = w / g
m = 100 / 10
m = 10 kg
hope it will help :)
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Ad
p
d
Ap
Answers
change in position of an object we use the
symbol ∆×\ delta×∆×for displacement, where ∆. means
"change" ∆ vector quantity with units of distances start
text ,d,I,s,t,a,n,c,e , end text.