A blockof mass m = 5.00 kg is released from point A and slides on thefrictionless track shown in Figure P8.6. Determine (a) the blockâsspeed at points B and C and (b) the net work done by thegravitational force on the block as it moves from point A to pointC.
Am I correct?? If not please provide detail.
a.)
Speed at point B
ETot = KE + U
KE = (1/2) m v2
U = m g h
ETot, A = 0 + (5 kg)(9.8 m/s2)(5 m) = 245J
ETot = 245 J = constant
ETot, B = (1/2)(5 kg)(vB2) + (5kg)(9.8 m/s2)(3.2 m) = ETot = 245 J
(1/2)(5 kg)(vB2) + 156.8 J = 245 J
(1/2)(5 kg)(vB2) = 245 J - 156.8 J = 88.2J
vB2 = (35.38)(J/kg)
vB2 =(35.38)(m2/s2)
vB = 5.9 m/s
speed at point C
ETot, C = (1/2)(5 kg)(vC2) + (5kg)(9.8 m/s2)(2.0 m) = ETot = 245 J
(1/2)(5 kg)(vC2) + 98 J = 245 J
(1/2)(5 kg)(vC2) = 245 J - 98 J =147 J
vC2 = 147 J / 2.5 kg
vC2 = (147/2.5)(J/kg)
vC2 = (58.8)(J/kg)
vC = 7.7 m/s
b.)
WAC = m g h
WAC = (5 kg) ( 9.8 m/s2) (5.0 m - 2.0m)
WAC = (5 kg) ( 9.8 m/s2) (3.0 m)
WAC = 147 J