Consider three objects at the top of an incline with = 12 and a height of 1.3 m:
ID: 1514633 • Letter: C
Question
Consider three objects at the top of an incline with = 12 and a height of 1.3 m: a sphere (I = 2 5mr2), a cylindrical shell (I = mr2), and a solid cylinder (I = 1 2mr2). Each object has a mass of 2 kg and a radius of 9 cm, and each is released from rest, then allowed to roll without slipping down the incline to the bottom.
A. What are the final velocity of each of the three objects at bottom of incline? what's the total transitional kinetic energy. What's the total rotational energy?
B. What's the time it takes each object to reach bottom of incline?
Explanation / Answer
Ans :- =12 h= 1.3m M= 2kg r = 9cm
for sphere
MEi = MEf
Mgh + KEi = KEf + PEf
2*9.8*1.3 = ½*I*w^2 + ½*m*V^2
25.48 = ½*2/5*mr^2( v^2/r^2) + ½*mv^2
= 1/5*mv^2 + ½*mv^2 = 0.7mv^2
V= sqrt (25.48/0.7m) = 4.27m/s
All have same velocity
KEtrans = ½*m*v^2 = ½*2*4.27^2 =18.23J
Total KEtrans = 3*18.23 =54.69J
Total rotational energy = 1/2*Iw^2 =1/2 (2/5mr^2+mr^2+1/2mr^2)v^2/r^2
= ½(2/5*2 + 2 +1/2*2)18.23 = 34.64J
B]h 1.3m, vi = 0,vf = 4.27m/s, a=9.8 t=?
V= vi + at
4.27 = 9.8t
t = 0.44s