Question

Two identical disks are released when 0 = 30°. Each disk has a weight of 15 lbs. Determine 0 after they collide and rebound from each other if the coefficient of restitution is e=0.85. (25 pts.) Hint: The disks just touch one another at @ = 0° - 2 ft -

Answer 1

Let g=9.8 m/s2 la r=1ft = 0.305 metre At initial conditions , 0-300 , Potential energy (PE) = mgl (1-loso) ke kinetic Energy) = I muz At 30° , PE=malli-cosso) KE=0 when = 0° , PE = mall-coso) = 0 KE = I muz According to energy conservation (PEUKE) at 30º = (PE+KE) at oº E ngl(1-cos 30°) = v2 or v² = 2x gl (1-cos300) velocity before collission Guven Coefficient of restitution = 0.85 = KE after collision Let v = velocity after collision So, 0.85= [/2m VR - 1/ 2mv2 = OR (0.85 ) = v12 . 2xgel 1-os 30°) or v2 = (0.85 2 x 2 x gl (1-cos 30°) - 0 VRE before collision

Fig! - Before collision

Fig! After collision.

Now, Let o be the angle when sphere reaches the point after rebound. So, the whole kinetic energy after the collision gets converted into potential energy at the top point So, prviz = saglal-cose) or I-cose = v or cos e = -1/2 291 cose = l-vo age – Putting vi from @ Oh Cos 0 = 1 - (0-85- xxxgx (1-сos 30° Zgod Cos = 1- (0.85) (1-cos300) Coso = 0.9032033542 342. OR A = 25.4176°