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Unable to solve rotation KE problem using torque

  • Thread starter Zynoakib
  • Start date
1. The problem statement, all variables and given/known data
A war-wolf or trebuchet is a device used during the Middle
Ages to throw rocks at castles and now sometimes
used to fling large vegetables and pianos as a sport. Model it
as a stiff rod of negligible mass, 3.00 m long, joining
particles of mass m1 = 0.120 kg and m2= 60.0 kg at its
ends. It can turn on a frictionless, horizontal axle perpendicular
to the rod and 14.0 cm from the large-mass
particle. The operator releases the trebuchet from rest
in a horizontal orientation. Find the maximum
speed that the small-mass object attains.

2. Relevant equations


3. The attempt at a solution
I could get the answer using rotational KE concept but when do the same thing with torque, I cannot get the answer.

Net torque = (60)(9.8)(0.14) - (0.12)(9.8)(2.86) = 78.96 Nm

Find the moment of inertia of the system

Center of mass of the system: [(0.12)(0) + (60)(3)]/ 60.12 = 2.994 m

Moment of inertia at CM
(0.12)(2.994)^2 + (60)(3 - 2.944)^2 = 1.078 kgm^2

Moment of inertia = Moment of inertia at CM + MD^2 = 1.078 + (60 + 0.12)(2.994 - 2.86)^2 = 2.158 kgm^2

Net torque = moment of inertia x angular acceleration
78.96 = 2.158 x acceleration
acceleration = 36.6 rads^-2

s = 1.57 rad, a = 36.6, u = 0, v = ?
v = 10.7 rad/s = 30.66 m/s, which is wrong

Is that because the downward force by weight is not constant during the rotation, so that the torque and the angular acceleration I calculated will become wrong as they way I calculated it seems to treat everything to be constant during the rotation

Thanks!
 

ehild

Homework Helper
15,316
1,740
No, the torque is not constant during the motion. How do you calculate the torque?
 

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