Question

Help me with the following problem

Answer 1

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

Change in kinetic energy of the particle

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

Apply principle of conservation of energy

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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