Respuesta :
a weight of mass 1.09 kg is suspended by a string wrapped around a pulley wheel, which consists of a solid disk of mass 4.22 kg and radius 1.04 m. the system is released from rest. vertical distance does the hanging mass move in 3.0 seconds is 18.27 m
distance can be calculate as follows:
Suspended mass, m = 1.09 kg
Pulley mass, M=4.22 kg
pulley radius, r = 1.04 m
now,
Let's put some tension on the "T" string
For this,
vertical net force
mg - T = ma …………(1)
Where,
g is the gravitational acceleration
a is the acceleration of the suspended mass.
Pulley torque = Iα
I is the moment of inertia of the pulley
α is the angular acceleration
Pulley torque is due to string movement
therefore,
Torque = T x r
Also
α = a/r
and I = (Mr²/2) (for circular discs)
Substituting the values of the above relationship for torque, we get
T × r = (Mr²/2) × (a/r)
T = (Ma)/2 …………(2)
from 1 and 2
mg - [(Ma)/2] = ra
mg= a(M + r)
2
(1.09x9.8) = a( 4.22 + 1.04)
2
a= 4.06
now we know that
s= ut+1/2 at²
where s is the distance traveled
u is the initial velocity = 0 (in this case)
t is time = 3 seconds
So if you replace the value
s= (0x3)+ 1/2 4.06 (3)²
s = 18.27 m
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