Answer: 1.59 sec
Explanation:
The kinetic energy contained in the rotation of the cylinder is 1/2 m v^2
The kinetic energy of translation is also 1/2 m v^2
so the total energy is m v^2
The force applied is mg sin (theta)
= m x 9.8 x 1/2
= 4.9 m
Now equate
F x d = m v^2
4.9 m x 3.1 = m v^2
v^2 = 4.9 x 3.1
v = sqrt(4.9 x 3.1) = 3.9 m/s
Acceleration.
V^2 = 2 a s
4.9 x 3.1 = 2 x a x 3.1
4.9 = 2 a
a = 2.45 m/s^2
Time
T = v/a
= 3.9/2.45
= 1.59 sec
