Answer:
a) 567J
b) 283.5J
c)850.5J
Explanation:
The expression for the translational kinetic energy is,
[tex]E_r = \frac{1}{2} mv^2[/tex]
Substitute,
14kg for m
9m/s for v
[tex]E_r = \frac{1}{2} (14) (9)^2\\= 567J[/tex]
The translational kinetic energy of the center of mass is 567J
(B)
The expression for the rotational kinetic energy is,
[tex]E_R = \frac{1}{2} Iw^2[/tex]
The expression for the moment of inertia of the cylinder is,
[tex]I = \frac{1}{2} mr^2[/tex]
The expression for angular velocity is,
[tex]w = \frac{v}{r}[/tex]
substitute
1/2mr² for I
and vr for w
in equation for rotational kinetic energy as follows:
[tex]E_R = (\frac{1}{2}) (\frac{1}{2} mr^2)(\frac{v}{r} )^2[/tex]
[tex]= \frac{mv^2}{4}[/tex]
[tex]E_R = \frac{14 \times 9^2 }{4} \\\\= 283.5J[/tex]
The rotational kinetic energy of the center of mass is 283.5J
(c)
The expression for the total energy is,
[tex]E = E_r + E_R\\\\[/tex]
substitute 567J for E(r) and 283.5J for E(R)
[tex]E = 567J + 283.5\\= 850.5J[/tex]
The total energy of the cylinder is 850.5J
Answer:
a) 567J
b) 283.5J
c) 850.5J
Explanation:
given
Mass of the cylinder, m = 14kg
Speed of mass, v = 9m/s
To determine the Translational Kinetic Energy, we use KE = 1/2mv²
KE(trans) = 1/2 * 14 * 9²
KE(trans) = 567J
To determine the Rotational Kinetic Energy, we use = 1/2Iw²
KE(rot) = 1/2Iw² = 1/2 * 1/2mr² * (v/r) ²
KE(rot) = 1/4 * mv²
KE(rot) = 1/4 * 14 * 9²
KE(rot) = 283.5J
To determine the Total Energy, we sum up both the transnational and rotational energies = KE(trans) + KE(rot)
Total energy = 567J + 283.5J
Total energy = 850.5J
