In the figure below, the hanging object has a mass of m_1 = 0.430 kg; the slidin
ID: 1449998 • Letter: I
Question
In the figure below, the hanging object has a mass of m_1 = 0.430 kg; the sliding block has a mass of m_2 = 0.880 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R_1 = 0.020 0 m, and an outer radius of R_2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is mu_k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of V_i = 0.820 m/s toward the pulley when it passes a reference point on the table. Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. Find the angular speed of the pulley at the same moment.Explanation / Answer
from the conservation of enrgy
1/2 ( m1+ m2) ( vf^2- vi^2) + 1/2 ( 1/2 M ( R1^2 + R2^2)( wf^2 - wi^2) = m1gh - uk m2 g
solving
vf = sqrt vi^2 + m1gh- um2g/0.5( m1+ m2) _ 0.5 M( 1+ ( R1/R2)^2
= sqrt (0.82)^2 + 0.430( 9.8) ( 0.7 ) - 0.250 (0.88) (9.8)/0.5 ( 0.430+ 0.880) + 0.5 (0.350 ( 1+ (0.02/0.03)^2
=sqrt (0.82)^2 + 0.430( 9.8) ( 0.7 ) - 0.250 (0.88) (9.8)/0.907
=sqrt (0.82)^2 +0.875
=1.2439 m/s
(b)
wf = v/R2 = 1.2439 m/s/0.03 =41.46 rad/s