Car A of mass 1800 kg and car B of mass 1700 kg are at rest

Car A of mass 1800 kg and car B of mass 1700 kg are at rest on a flatcar which is also at rest. Cars A and B then accelerate and quickly reach constant speeds relative to the flatcar of 2.55 in/s and 2.50 m/s, respectively, before decelerating to a stop at the opposite end of the flatcar. Knowing that the speed of the flatcar is 0.34 m/s when the cars are moving at constant speeds, determine the mass of the flatcar. Neglect friction and rolling resistance.

Solution

Given that,

m_A = 1800 kg

m_B = 1700 kg

v_A = 2.55 m / s

v_B = 2.50 m / s

v_F = 0.4 m / s

intial values are,

( v_A)₀ = ( v_B )₀ = ( v_F )₀ = 0

intial moment of the systemm

m_A ( v_A)₀ + m_B ( v_B )₀ + m_F ( v_F )₀ = 0

By the horizontal external forces during the time period under consideration

0 = m_A ( v_A )₀ + m_B ( v_B )₀ + m_F ( v_F )₀

m_F = [ m_A ( v_A ) + m_B ( v_B ) ] / v_F---------------------- Eq - 1

from the given relative velocities

v_A/F = v_A - v_F

v_A = v_F + v_A/F

v_A = 0.34 - 2.55 = - 2.21

v_B = v_F + v_B/F

v_B = 0.34 - 2.50

v_B = - 2.16

by substituing the values in Eq - 1 we get

m_F = [ ( 1800 ) ( - 2.21 ) + ( 1700 ) ( - 2.16 ) ] / 0.34

m_F = [ - 3978 + ( - 3672 ) ] / 0.34

m_F = [ - 7650 ] / 0.34

m_F = 22500 kg

m_F = 22.5 Mg