1) Blocks A (mass 3.50 kg ) and B (mass 10.50 kg ) move on a frictionless, horiz

Question

1) Blocks A (mass 3.50kg ) and B (mass 10.50kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 7.00m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of A.

a) Find the velocity of A.

b) Find the velocity of B.

2) An airplane propeller is rotating at 1950rpm .

a) When the propeller were turning at 22.0rad/s , what is the period (in seconds) of this propeller?

3) A flywheel with a radius of 0.260m starts from rest and accelerates with a constant angular acceleration of 0.550rad/s2 .

a) Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0?.

b) Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 120?.

4) Standing sound waves are produced in a pipe that is 1.80m long.

a) If the pipe is closed at the left end and open at the right end , determine the locations along the pipe (measured from the left end) of the displacement nodes for the fundamental frequency.

b) If the pipe is closed at the left end and open at the right end , determine the locations along the pipe (measured from the left end) of the displacement nodes for the first overtone.

Explanation / Answer

mass of A, M1=3.5kg

mass of B, M2=10.5kg

initial velocity of A, U1=7m/s

initial velocity of B, U2=0m/s

final Velocity of A, V1={[(M1-M2)*U1]+[2*M2*U2]}/(M1+M2)

                                     ={[(3.5-10.5)*7]+[2*10.5*0]}/(3.5+10.5)

                                     ={[-49]+[0]}/11

                                     =(-4.45)m/s

-ve sign indicates -ve x axis direction

final velocity of B, V2= +4.45m/s that is in +ve x axis direction

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