Map sapling learning Two different balls are rolled (without slipping) toward a
ID: 1468250 • Letter: M
Question
Map sapling learning Two different balls are rolled (without slipping) toward a common finish line. Their angular speeds are shown to the right. The first ball, which has a radius of 0.0688 m, is rolling along a conveyor belt which is moving at 1.69 m/s and starts out 8.87 m from the finish line. The second ball has a radius of 0.0488 m and is rolling along the stationary floor. If the second ball starts out 5.54 m from the finish line, how long does each ball take to reach the finish line? 21.2 rad/s Number #1 | 12.82 15.3 rad/s Number #2 | | 7.42 What angular speed would the losing ball have needed to cross the finish line at the same time as the winning ball? Number 36.15 rad/ sExplanation / Answer
let,
speed of the belt Vb=1.69 m/sec
angular speed of ball 1 is, w1=21.2 rad/sec
radius of the ball 1 is, r1=0.0688 m
distance between starting point of ball 1 and finish line is d1=8.87 m
angular speed of ball 2 is, w2=15.3 rad/sec
radius of the ball 1 is, r2=0.0488 m
distance between starting point of ball 2 and finish line is d2=5.54 m
a)
relative speed Vr=V_ball1+Vb
relative speed Vr=(r1*w1)+Vb
time taken to reach the finish line by ball 1 is,
t1=d1/Vr
t1=d1/((r1*w1)+Vb)
t1=8.87/((0.0688*21.2)+1.69)
t1=2.82 sec
b)
time taken to reach the finish line by ball 2 is,
t2=d2/Vr
t2=d2/((r2*w2)+Vb)
t2=5.54/((0.0488*15.3)+0)
t2=7.42 sec
c)
ball 2 need angular speed w=d2/(t1*r2)
w=5.54/(2.82*0.0488)
W=40.26 rad/sec