question no 6 5) Ou a frictionless surface, a 3 kg block moving at 4m/sto the ri

Question

question no 6

5) Ou a frictionless surface, a 3 kg block moving at 4m/sto the right cllides with an kg block moving to the left at 2m/s. a) If the two blocks stick together, what is the final velocity (magnitude and direction? b) The final K.E. is what fraction of the initial K.E.? b) How much mechanical energy is lost in part (a)? o) lf the two blocks make a completely elastic head-on collision, what are their final velocities? 6) A billiard ball moving at 5,00 imls strikes a stationary ball of the same mass After the collision, the first ball moves at 4.33 m/s and at an angle of 30.0° with respect to the original line of motion. Assuming an elastic collision (and ignoring friction and rotational motion), find the struck ball's velocity A system consists of 3 particles m1=2kg located at (1, 0), m,-2kg at (2,1), m, 3kg at Find the center of mass of the system Bonus: n a ballistic pendulum experiment, suppose that h= 5,00 m,m,-500g, and M-1 00kg. Find (a) the initial speed of the bullet and (b) the loss in mechanical energy due to the collision.

Explanation / Answer

6)

here,

6)

intial speed of billiard ball , u1 = 5 i m/s

the final speed of ball 1, v1 = 4.33 * ( cos(theta) i + sin(theta) j) m/s

v1 = 4.33 * ( cos(30) i + sin(30) j) m/s

v1 = 3.75 i m/s + 2.16 j m/s

let the final speed of ball 2 be v2

using conservation of momentum

m * u1 = m * v1 + m * v2

5 i = 3.75 i + 2.16 j + v2

solving for v2

v2 = 1.25 i m/s + 2.16 j m/s

the magnitude of final velocity , |v2| = sqrt(1.25^2 + 2.16^2)

|v2| = 2.5 m/s

theta = arctan(2.16/1.25) = 60 degree

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