A nut with a radius of 0.5 cm requires a torque of 2 Nm in order to loosen it. a

Question

A nut with a radius of 0.5 cm requires a torque of 2 Nm in order to loosen it. a) If a person tries to loosen the nut by hand, what force is required? (In that case, the radius at which the force is applied is that of the nut itself.) b) What force is required if the force is applied using a wrench, as shown in the diagram? 10.10 A sphere with a moment of inertia of 0.25 kgm2 is spinning with an angular velocity of 145 rad/s when it begins to slow down. What net torque is required to bring the sphere to a stop as it turns through 7.5 revolutions?

Explanation / Answer

here,

10.9)

radius , r = 0.005 m

torque , t = 2 Nm

a)

force required by the person be f

f*r = t

f*0.005 = 2

f = 400 N

the force required by the person to loosen the nut is 400 N

b)

length of wrench , l = 0.15

let the force required to apply be f

f*0.15 = t

f*0.15 = 2

f = 13.33 N

the force required is 13.33 N

10.10)

moment of inertia , I = 0.25 kg.m^2

w = 145 rad/s

number of revolution , n = 7.5 rev

theta = n*6.28

theta = 47.1 rad

let the accelration be alpha

w^2 - w0^2 = 2*alpha*theta

0 - 145^2 = 2*alpha*47.1

alpha = - 232.2 rad/s^2

the torque required , t = I * alpha

t = - 0.25 * 232.2

t = - 55.8 Nm

the net torque required to bring the sphere to rest is - 55.8 Nm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.