A war-wolf or trebuchet is a device used duringthe Middle Ages to throw rocks at

Question

A war-wolf or trebuchet is a device used duringthe Middle Ages to throw rocks at castles and now sometimes used tofling large vegetables and pianos as a sport. A simple trebuchet isshown in the figure. Model it as a stiff rod of negligible mass,2.60 m long, joining particles of mass57.0 kg and 0.120 kg at its ends. It can turn on africtionless, horizontal axle perpendicular to the rod and15.0 cm from the large-mass particle.The rod is released from rest in a horizontal orientation. (a) Find the maximum speed that the0.120 kg object attains.

(b) Select the statements that are true. While the smaller object isgaining speed, it moves with constant acceleration.
The smaller object does notmove with constant tangential acceleration. The trebuchet moves withconstant angular acceleration. The trebuchet maintains constantmomentum. The trebuchet-Earth system hasconstant mechanical energy. (a) Find the maximum speed that the0.120 kg object attains.

(b) Select the statements that are true. While the smaller object isgaining speed, it moves with constant acceleration.
The smaller object does notmove with constant tangential acceleration. The trebuchet moves withconstant angular acceleration. The trebuchet maintains constantmomentum. The trebuchet-Earth system hasconstant mechanical energy. While the smaller object isgaining speed, it moves with constant acceleration.
The smaller object does notmove with constant tangential acceleration. The trebuchet moves withconstant angular acceleration. The trebuchet maintains constantmomentum. The trebuchet-Earth system hasconstant mechanical energy. While the smaller object isgaining speed, it moves with constant acceleration.
The smaller object does notmove with constant tangential acceleration. The trebuchet moves withconstant angular acceleration. The trebuchet maintains constantmomentum. The trebuchet-Earth system hasconstant mechanical energy. While the smaller object isgaining speed, it moves with constant acceleration.
The smaller object does notmove with constant tangential acceleration. The trebuchet moves withconstant angular acceleration. The trebuchet maintains constantmomentum. The trebuchet-Earth system hasconstant mechanical energy. The trebuchet maintains constantmomentum. The trebuchet-Earth system hasconstant mechanical energy.

Explanation / Answer

This problem requires a few steps: . 1. conservation of energy:   K + U   = 0 .    large mass drops 15.0 cm   while smallmass rises   2.45 m .    so   U = Mgh   + mgh   = 57.0* 9.80 * -0.15 + 0.120 * 9.80 * 2.45  =   -80.9088 Joules . This means    K = 80.9088 Joules. . 2. rotational kinetic energy:    all ofthe final kinetic energy is rotational. So we first find the momentof inertia of the system: .          I = Mr2 + mr2 =   57.0 * 0.152 + 0.120*2.452 =    2.0028kg-m2 . Then we use:       rotational KE = (1/2) I 2 .             80.9088 = (1/2) * 2.0028 2 .       =  8.9886 rad/s    is the final rotational speedof the system/ . 3.   relate rotational and linearspeed:    this means that the linear speed of thesmaller mass is .      v = r =   8.9886 * 2.45 =    22.02 m/s .       =  8.9886 rad/s    is the final rotational speedof the system/ . 3.   relate rotational and linearspeed:    this means that the linear speed of thesmaller mass is .      v = r =   8.9886 * 2.45 =    22.02 m/s

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