A firehose is wound around a massive, uniform ring with mass M=100 kg and radius

Question

A firehose is wound around a massive, uniform ring with mass M=100 kg and radius r = 0.5 m. The ring acts like a pulley and is mounted on a fixed horizontal axle located on a roof. A stuntman of mass m= 60 kg steps off the roof and clings on the firehose as he drops down the 10-meter high building. Ignore the mass of the firehose and assume no slipping.

(Note: Moment of Inertia Iring = Mr2). Use g = 10 m/s2.

A. Calculate the linear acceleration a of the man, in units of m/s2.

B. What is the angular acceleration of the ring-shaped pulley, in units of rad/sec2 ?

C. Determine the speed v of the man, in units of m/s, just as he lands on the ground

Explanation / Answer

Let T is the tension inthe string.

Let a is the acceleration of the stuntman.

net force acting on stuntman, Fnet = m*g - T

m*a = m*g - T

T = m*g - m*a

net torque acting on the pulley = T*r

we know, Torque = I*alfa

so,

I*alfa = T*r

M*r^2*(a/r) = (m*g - m*a)*r

M*a = m*g - m*a

a*(M + m) = m*g

a = m*g/(M+m)

= 60*10/(100 + 60)

= 3.75 m/s^2 <<<<<<<<<<---------------Answer

B) angular acceleration, alfa = a/r

= 3.75/0.5

= 7.5 rad/s^2 <<<<<<<<<<---------------Answer

c) Aplply, v^2 - u^2 = 2*a*h

v^2 - 0^2 = 2*a*h

v = sqrt(2*a*h)

= sqrt(2*3.75*10)

= 8.7 m/s <<<<<<<<<<---------------Answer

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