The drawing shows two identical systems of objects; each consists of the same th

Question

The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m1 = 9.7 kg, m2 = 6.7 kg, and m3 = 7.5 kg. The magnitude of the force is F = 491 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.60 s?

Explanation / Answer

Given that
m1=9.7 kg m2=6.7 kg m3 = 7.5 kg The magnitude of force, F = 491 N ---------------------------------------------------------------------------------
(a)
   The moment of inertia of each system will be
For system A    I = m1 r12+ m2r22 + m3r32
     = (9.7 kg) (r1)2 + (6.7 kg) (r2)2 + (7.5 kg) (r3)2
     = ......... kg.m2( you dont provide the values of r1, r2 and r3. If we know them we can solve it)
For system B       I = m1 r12+ m2r22 + m3r32
     = (9.7 kg) (r1)2 + (6.7 kg) (r2)2 + (7.5 kg) (r3)2
     = ......... kg.m2( you dont provide the values of r1, r2 and r3. If we know them we can solve it) -------------------------------------------------------------------------------------
(b)
  we have a relation betweeb torque and force as torque = force * distance
    = F l
For system A the torque will be
    = - F l
      = - (446 N) (l)         ( here also we dont know the value of l )
      = ....... N.m
For system B the torque will be
    = F l
      = (446 N) (l)         ( here also we dont know the value of l )
      = ....... N.m For system A the torque will be
    = - F l
      = - (446 N) (l)         ( here also we dont know the value of l )
      = ....... N.m
For system B the torque will be
    = F l
      = (446 N) (l)         ( here also we dont know the value of l )
      = ....... N.m -------------------------------------------------------------------------------------------- (c) The equation for the angular velocity is given by     = o + t
We can write the angular acceleration as        = I        = /I
since the both systems are starts from rest, The initial angular velocity o = 0 rad/s final angular velocity are after t = 5.60 s can be calculated as
For system A      = o + (/I) t      = (/I) t         = ........ rad/s      = (/I) t For system B      = o + (/I) t
        = ........ rad/s          (IF WE KNOW THE VALUES WE CAN EASILY EVALUATE THE REQUIRED VALUES)      = o + (/I) t
        = ........ rad/s          (IF WE KNOW THE VALUES WE CAN EASILY EVALUATE THE REQUIRED VALUES)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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