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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A clay ball (mass = 0.25kg) has a rightward momentum of +1.75 kg∙m/s. A second clay ball (mass = 0.25 kg) has a leftward momentum of -1.75 kg∙m/s. The two collide, stick together, and come to a complete stop after the collision.
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Answers
Answer:
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Explanation:
first we should know the velocity of the 2 balls:
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we have the momentum and the mass of the 2
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Answer:
changing nuclear energy to radiant energy
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What is kinetic energy?Kinetic energy is a type of motion energy (i.e., energy in movement), which is used to perform work.
Conversely, potential energy is a type of energy stored in an object, which can be converted to kinetic energy.Nuclear energy is a type of potential energy because this energy is stored in the atomic nucleus.In conclusion, changing nuclear energy to radiant energy is an example of transforming potential energy into kinetic energy.
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Answer:
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Explanation:
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Answer:
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Answer:
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Answers
Answer:
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Explanation:
Given the following data;
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Answer:
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Answer:
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Answer:
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Answer:
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Answer:
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Explanation:
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Answer:
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Explanation:
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where,
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Now, the equivalent resistance of two springs connected in parallel, as shown in the diagram, will be:
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For a load of 30 N, applying Hooke's Law:
[tex]\Delta x = \frac{F}{k_{eq}}\\\\\Delta x = \frac{30\ N}{500\ N/m}\\\\\Delta x = 0.06\ m = 6\ cm\\[/tex]
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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:
Explanation:
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Answer:
Organic matter
Explanation:
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With time, organic sediments continue to fill the pond and its depth is gradually decreased. A swamp or bog is now formed.
This trend of succession continues until the pond eventually turns into land.