Can someone please work out how to solve both of these problems 14. An 10 kg obj
ID: 1732010 • Letter: C
Question
Can someone please work out how to solve both of these problems
14. An 10 kg object in flight splits apart at the top of its path into 5 kg and 5 kg masses. They strike the ground at X2 = 4 m and X3 = 8 m. The center of mass will land at a value of X closest to (in meters) a. 4 b. 6 c. 8 d. 12 15. A disk (I MR2 and a sphere of equal mass and radius (Is 2MRS)roll without slipping down a ramp from a height H. Let Vo and Vs be the velocity of the disk and sphere respectively at the bottom of the ramp. Which statement below is true: a. V> Vs because less energy goes into the rotational kinetic energy of the disk bVs> V because less energy goes into the rotational kinetic energy of the sphere c. Vo-Vs: the speed is independent of any rotational properties d. Vo Vs each object must share the rotational and translational energies equallyExplanation / Answer
The center of mass of the 10kg object will be exactly at the center of both the 5kg pieces. So the center of mass will land at a value of x closest to b. 6
Potential energy of both the disc and the sphere are same when they are at the top of the ramp as their masses are same. So at the bottom of the ramp, their kinetic energy will be same as that of each other. Kinetic energy of the disc is 0.5*m*vd^2+0.5*mr^2/2*vd^2/r^2= m*vd^2. Similarly kinetic energy of the sphere is 0.5*m*vs^2+0.5*2mr^2/5*vs^2/r^2= 0.7m*vs^2. so, m*vd^2= 0.7*m*vs^2. so, vd= 0.8366*vs . Also the rotational kinetic energy of the sphere is less as shown above. so, b. VS>VD, because less energy goes into the rotational kinetic energy of the sphere.