Question

a teacher at a university in England should move a concrete pipe down a hill. What speed does the pipe have at the end of the slope if it is allowed to roll freely (without slipping) = The tube has inner diameter d and outer diameter D. The slope is L long and slopes θ. The pipe is 3 meters long and concrete has a density of 4000 kg / m 3. The tube starts at rest.

d m D 1,4 1,58 20 m O L m 17 o

Answer 1

Step 1 : Height of inclined surtace ah K -=20m b 170 =0 hs lsina (0 h = 20 SIMIT Step 2: INoment of inertia of hollow citalar Section I= 1 m ( 8² + d²) m= mass of body D = 1.58m d = 1.4m Islam (1,58%+1427 I = 0.55705m Step 3: To Determine the speed of Pipe at down we'll » We use conservation of Energy The corem E = ktu E= Total Energy

K= Kinetic Energy Us potential Energy Oven At point I E = otu را - E = mgh At Point 2 E= otk = 12mvern + 1 I w2. Nom = Rw و في Vom R R = j 2 ( 2 Vom Step 4: Equating Equation in and lig I w2 2 2 2 Vom migh = 1 m vomit mgh = 11 m vem + 1 x 0.55705 40.55705 my gha Vem? + 2*0.55705 x Vem? 2 D2

2 9.81% 20 Simi's Vem2 + 2x0.55705 Vem2 (1.58)2 2 57.363 0:9463 Vem Vcm 7.79 mis o