Answer:
1. Kinetic Energy = 0.0161 Joules
2. Height = 0.0137m
Explanation:
Given
Length of Rod, l = 0.64m
Mass, m = 120g = 0.12kg
Angular speed, w = 1.40 rad/s
a.
Calculating the Rod's kinetic energy
This is calculated by
Kinetic Energy = ½Iw²
Where I = rotational inertia of the rod about an axis.
This is calculated as follows;
I = Icm + mh²
I = ImL² + m(L/2)²
I = 1/12 * 0.12 * 0.64² + 0.12 * (0.64/2)²
I = 0.016384 kgm²
By substituton
KE = ½Iw² becomes
KE = ½ * 0.016384 * 1.40²
KE = 0.01605632J
KE = 0.0161 Joules
2. Using the total conservation of momentum;
K + U = Kf + V
Where K = Initial Kinetic Energy of the rod at lowest point.
U = Initial gravitational potential energy of the rod at lowest point
Kf = Final Kinetic Energy of the rod at maximum height = 0 J
V = Final gravitational potential energy of the rod at maximum height
So, K + U = Kf + V become
K + U = 0 + V
K + U = V
K = V - U = mgh
substitute 0.01605632J for K
0.01605632J = mgh
h = 0.01605632J/mg
h = 0.01605632J/(0.12 * 9.8)
h = 0.013653333333333
h = 0.0137m
