Answer :
At h = 4.0
K = 0.5 (0.18) (0)² = 0
U = (0.18) (9.81) (4.0) = 7.06 J
E = K + U
E = 0 + 7.06 = 7.06 K
At h = 3.0
K = 0.5 (0.18) (2)(9.81)(1.0) = 1.76 J
U = U = (0.18) (9.81) (3.0) = 5.30 J
E = 1.76 + 5.30 = 7.06 J
At h = 2.0
K = 0.5 (0.18) (2)(9.81)(2.0) = 3.53 J
U = U = (0.18) (9.81) (2.0) = 3.53 J
E = 3.53 + 3.53 = 7.06 J
K = 0.5 (0.18) (0)² = 0
U = (0.18) (9.81) (4.0) = 7.06 J
E = K + U
E = 0 + 7.06 = 7.06 K
At h = 3.0
K = 0.5 (0.18) (2)(9.81)(1.0) = 1.76 J
U = U = (0.18) (9.81) (3.0) = 5.30 J
E = 1.76 + 5.30 = 7.06 J
At h = 2.0
K = 0.5 (0.18) (2)(9.81)(2.0) = 3.53 J
U = U = (0.18) (9.81) (2.0) = 3.53 J
E = 3.53 + 3.53 = 7.06 J
A) At h=4.0 m
At h=4.0 m, the kinetic energy of the ball is zero, because its velocity is 0, so
[tex]K=\frac{1}{2}mv^2=\frac{1}{2}(0.18 kg)(0)^2=0[/tex]
The gravitational potential energy is instead:
[tex]U=mgh=(0.18 kg)(9.8 m/s^2)(4.0 m)=7.06 J[/tex]
So, the total mechanical energy is
[tex]E=K+U=0+7.06 J=7.06 J[/tex]
B) At h=3.0 m
The gravitational potential energy is now:
[tex]U=mgh=(0.18 kg)(9.8 m/s^2)(3.0 m)=5.29 J[/tex]
Since air resistance is negligible, the total mechanical energy is conserved, so it is still
[tex]E=7.06 J[/tex]
And so we can find the kinetic energy as follows:
[tex]K=E-U=7.06 J-5.29 J=1.77 J[/tex]
C) At h=2.0 m
The gravitational potential energy is now:
[tex]U=mgh=(0.18 kg)(9.8 m/s^2)(2.0 m)=3.53 J[/tex]
Since air resistance is negligible, the total mechanical energy is conserved, so it is still
[tex]E=7.06 J[/tex]
And so we can find the kinetic energy as before:
[tex]K=E-U=7.06 J-3.53 J=3.53 J[/tex]