TP 8.35

Given:

m = 1.90 kg

F = 4.60 N

Find: W_nc, U,  K,  E

at d = 0.00 m (or y = 1.80 m)

W_nc= F Dx cos(q) = (4.60 N)(0 m)cos(180^o) = 0 J

U = m g y = (1.90 kg)(9.81 m/s²)(1.80 m) = 33.5502 J =  33.6 J

K   = 1/2 mv² = 0 J (since v = 0 m/s)

E = K + U = 0 J + 33.5502 J = 33.6 J

at d = 0.500 m (or y = 1.30 m)

W_nc= F Dx cos(q) = (4.60 N)(0.500 m)cos(180^o) = -  2.30 J

U = m g y = (1.90 kg)(9.81 m/s²)(1.30 m) = 24.2307 J = 24.2 J

W_nc= (K_f + U_f) - (K_i + U_i)

K_f = W_nc- U_f + (K_i+ U_i)

K_f = (-2.30 J)- (24.2307 J) + (0 J+ 33.5502 J) = 7.0195 J = 7.02 J

E = K + U = 7.0195 J + 24.2307 J = 31.202 = 31.2 J

at d = 1.00 m (or y = 0.800 m)

W_nc= F Dx cos(q) = (4.60 N)(1.00 m)cos(180^o) = -  4.60 J

U = m g y = (1.90 kg)(9.81 m/s²)(0.800 m) = 14.9112 J =  14.9 J

W_nc= (K_f + U_f) - (K_i + U_i)

K_f = W_nc- U_f + (K_i+ U_i)

K_f = (- 4.60 J) - (14.9112 J) + (0 J+ 33.5502 J) = 14.039 J = 14.0 J

E = K + U = 14.039 J + 14.9112 J = 28.9502 J =  29.0 J