Mass m_A = 0.500 kg sits on top of mass m_B = 2.00 kg which sits on top of a lon
ID: 1612092 • Letter: M
Question
Mass m_A = 0.500 kg sits on top of mass m_B = 2.00 kg which sits on top of a long shelf that is L = 2.50 m long, and mounted H = 2.80 m off the floor, as shown in Fig-1. m_B is attached to m_c = 10.00 kg by means of a rope which is draped over a massless, frictionless pulley. Take the width of m_A as being negligible, but its height is h_A = 1.00 cm. Initially, it starts with its center of mass a distance d = 30.0 cm from the left end of m_B. The height of m_B is h_B = 8.00 cm, and it starts with its left end at the left end of the shelf. The static and kinetic coefficients of friction between m_A and allother surfaces are given by mu_s_A = 0.260 and mu_k_A = 0.250, respectively. The static and kinetic coefficients of friction between m_B and the shelf are given by mu_s_B = 0.380 and mu_k_B = 0.375, respectively. Where, relative to the left end of the shelf, does m_A ultimately wind up?Explanation / Answer
the frictional force is
f = uk ( mA + mB )
f = 0.375 X 2.5 X 9.8
f = 9.1875
weight is = m g = 98 N
m g - uk ( mA + mB ) - uk m g = m a
98 - 10.425 =12 a
a = 7.3 m/sec2
mA 7.3 - 0.25 XmA X 9.8 = mA
a = 4.851 m/sec2
t = ( 2 d / a )1/2
t = 0.355 sec
d = 1/2 a t2
d = 0.5 X 7.3 X 0.3552
d = 0.46 m