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uniform solid sphere has a mass of 1.765 kg and a radius of 0.854 m.a. Find the torque required to bring the sphere from rest to an angular velocity of 317 rad/s, clockwise, in 15.5 s.b. What magnitude force applied tangentially at the equator would provide the needed torque

Sagot :

Nuhulawal20idn

Answer:

a) the torque required is  10.53 N-m

b) The magnitude force applied tangentially is 12.33 N

Explanation:

Given the data in the question;

mass m = 1.765 kg

radius r = 0.854 m

first we calculate the moment of inertia;

[tex]I[/tex] = [tex]\frac{2}{5}[/tex]mr²

we substitute

[tex]I[/tex] = [tex]\frac{2}{5}[/tex] × 1.765 × (0.854)²

[tex]I[/tex] = 0.514897 kg.m²

a)

Find the torque required to bring the sphere from rest to an angular velocity of 317 rad/s, clockwise, in 15.5 s

ω[tex]_{initial[/tex] = 0

ω[tex]_{final[/tex] = 317 rad/s

t = 15.5 s

we know that; ω[tex]_{final[/tex] = ω[tex]_{initial[/tex] + ∝t

so we substitute

317 = 0 + ∝(15.5)

∝ = 317 / 15.5

∝ = 20.4514 rad/s²

so

ζ = [tex]I[/tex] × ∝

we substitute

ζ = 0.514897 × 20.4514

ζ = 10.53 N-m

Therefore, the torque required is  10.53 N-m

b)

What magnitude force applied tangentially at the equator would provide the needed torque.

ζ = F × r

we substitute

10.53  = F × 0.854

F = 10.53 / 0.854

F = 12.33 N

Therefore, magnitude force applied tangentially is 12.33 N

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