Question

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 block’sspeed 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

E_Tot = KE + U

KE = (1/2) m v²

U = m g h

E_{Tot, A} = 0 + (5 kg)(9.8 m/s²)(5 m) = 245J

E_Tot = 245 J = constant

E_{Tot, B} = (1/2)(5 kg)(v_B²) + (5kg)(9.8 m/s²)(3.2 m) = E_Tot = 245 J

(1/2)(5 kg)(v_B²) + 156.8 J = 245 J

(1/2)(5 kg)(v_B²) = 245 J - 156.8 J = 88.2J

v_B² = (35.38)(J/kg)

v_B² =(35.38)(m²/s²)

v_B = 5.9 m/s

speed at point C

E_{Tot, C} = (1/2)(5 kg)(v_C²) + (5kg)(9.8 m/s²)(2.0 m) = E_Tot = 245 J

(1/2)(5 kg)(v_C²) + 98 J = 245 J

(1/2)(5 kg)(v_C²) = 245 J - 98 J =147 J

v_C² = 147 J / 2.5 kg

v_C² = (147/2.5)(J/kg)

v_C² = (58.8)(J/kg)

v_C = 7.7 m/s

b.)

W_AC = m g h

W_AC = (5 kg) ( 9.8 m/s²) (5.0 m - 2.0m)

W_AC = (5 kg) ( 9.8 m/s²) (3.0 m)

W_AC = 147 J