A wad of sticky clay of mass m = 5.0 g and velocity v_1 = 107 m/s is fired at a

Question

A wad of sticky clay of mass m = 5.0 g and velocity v_1 = 107 m/s is fired at a solid cylinder of mass M = 15.0 kg and radius R = 25 cm (Figure P11.37). The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through the center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d = 24 cm, less than R, from the center. Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. rad/s(b) Is mechanical energy conserved in this process? Yes No

Explanation / Answer

Here ,

vi = 107 m/s

m = 0.005 Kg

M = 15 Kg

R = 0.25 m

a) let the angular speed of the system is wf

Using conservation of angular momentum

m * v * d = (I * wf)

0.005 * 107 * 0.24 = (0.5 * 15 * 0.25^2 + 0.005 * 0.25^2) * wf

solving for wf

wf = 0.273 rad/s

the final angular speed is 0.273 rad/s

b)

No, the mechanical energy is not conserved

as the collision is not elastic , the mechanical energy is not conserved

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