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2 years ago

Help me with the following problem

Physics

1 answer:

timofeeve [1]2 years ago

5 0

The rope will remain taut until the particle makes 79⁰ angle.

<h3>Change in kinetic energy of the particle</h3>

The change in kinetic energy of the particle is calculated as follows;

ΔK.E = K.Ei - K.Ef

Before the particle will achieve the given angular displacement, it will touch two new corners. Total kinetic energy lost = 30%

ΔK.E = 100%K.E - 30%K.E = 70%K.E = 0.7K.E

let the vertical displacement of the particle = h
horizontal length = side of the prism = a
hypotenuse side = length of the pendulum = L

<h3>Apply principle of conservation of energy</h3>

K.E = P.E

0.7K.E = mgh

0.7(¹/₂mv²) = mg(Lsinθ)

0.7(v²) = 2g(Lsinθ)

from third kinematic equation;

v² = u² + 2gh

v² = 0 + 2gh

v² = 2g(a tanθ)

0.7(2g(a tanθ)) = 2g(Lsinθ)

0.7(a tanθ) = Lsinθ

0.7a/L = sinθ/tanθ

0.7a/L = cosθ

(0.7 x 0.8)/(3) = cosθ

0.1867 = cosθ

θ = cos⁻¹(0.1867)

θ = 79⁰

Thus, the rope will remain taut until the particle makes 79⁰ angle.

Learn more about kinetic energy here: brainly.com/question/25959744

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Answer:

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This is illustrated below.

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where

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$v_2 = 3.40 m/s$ is the velocity of the second ball after the collision

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