Question

The catapult shown below is used to lay siege to your neighbor's cubicle. You fire 1-g peanut M&Ms at their desk until they surrender. The catapult arm moves from horizontal to 30° in 0.1 s, when it hits the crossbar and releases the projectile. Assume air resistance is negligible and the arm velocity is constant until it hits the crossbar. If the M&M lands on their desk 3 meters away in 1 s, determine: A. The velocity of the projectile as it leaves the bucket. B. The angular velocity of the bucket at the end of the arm just before it hits the crossbar. C. The force on the M&M as the arm hits the crossbar. (Hint: at of the bucket = a of the projectile.) D. The torsional spring constant of the bands in N.m/deg. E. The energy of the M&M just before impact on the desk. F. The velocity of the M&M after impact with the desk. Assume a coefficient of restitution of 0.8. 7 120 mm

Please show all work and steps. Any help will be appreciated and thank you for your time!

Answer 1

A. Let the angulars acceleration bed and final angular velocity of the catapault is w, and Aftersch final velocity of projectile is v. 30, 0-1. 2+ [here, O=30°, t=0:18 - x = 1 + (0.12 10oT rad/s2 Agaim, -Cubon, Co-1)) mode = lot sadla 3 arm is Now the length of the cata pault 120cm or o.l2m. So velocity of the projectile as it leaves the bucket is- v=wer (whe here 830.12m] -Korg x(0-12.) Jamie Va 12.6 m/s B. As done in the previous past, the angular velocity of the bucket at the end of the just before it hits the cross bar is w=loa radis wa 10:47 rad/s Droo 3

them c. If the moment of imertia of the Me Mis I and force om Mo M is f Id=F [r= 120mm] -> ?=[m=19 = 1000kg] Femra 1 X 120-X1007 [x= 100k mad 13 looo looo F ñ0.0126N constant D. We know, t= -KO [K-torsionals spring here I = Ic=m8? (E-) (x=20 2.me 72 =K=200022 Putting the values m, t=0.18 m=1 1000 bo kg i k= 1000 X120 1000 (1000 N.m/nad (0.112 2.88x103 n.com load E: Acerning air resistance is negligible, Carn conclude that energy is conserved at the time of flight. So, energy of the M&M before it leaves the catapault is K.E. = 2 Iw2

Po (104) [w= 10kpadle] = tooo (1206) (193)2 J KE 2 7.9810-45 so, energy of the M&M just before it ground is 79x16"J. F. Let the velocity of the M8 Mafter, it hits the desk is v. Them re= coefficient of hits the Love 7.9x104 restitution Exooo =x uz = 0.8 1000 7.9810 -4 7.9 m/s v z 1mls
Note:plzzz don't give dislike...plzzz comment if you have any problem i will try to solve your problem....plzzz give thumbs up i am in need......