## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

$v = 6.26~m/s$
We can find the work that gravity does on the block. $W_g = mg~d~cos(180^{\circ})$ $W_g = (1.02~kg)(9.80~m/s^2)(2.00~m)~cos(180^{\circ})$ $W_g = -20.0~J$ We can find the work done by tension. $W_T = T~d$ $W_T = (20~N)(2.00~m)$ $W_T = 40.0~J$ We can use the work energy theorem to find the kinetic energy of the block as it reaches 2.00 m. $KE_f = KE_0 + W_g+W_T$ $KE_f = 0 - 20.0~J+40.0~J$ $KE_f = 20.0~J$ We can find the speed of the block. $KE_f = 20.0~J$ $\frac{1}{2}mv^2 = 20.0~J$ $v^2 = \frac{(2)(20.0~J)}{m}$ $v = \sqrt{\frac{(2)(20.0~J)}{m}}$ $v = \sqrt{\frac{(2)(20.0~J)}{1.02~kg}}$ $v = 6.26~m/s$