Two masses are being pulled up a 30.0 degree incline by a force F parallel to the incline. The acceleration down the incline is 1.00 m/s² and the velocity is down the incline. The force is applied to a 200 kg mass and a string connects the 200 kg mass to a 150 kg mass. The coefficient of kinetic friction is 0.200. The force F is A) 771 N. B) 875 N. C) 1,050 N. D) 1,960 N. E) 2,330 N.

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Quizplus · Accepted Answer

The force of gravity pulling the masses down the incline is:$$F_g = (200 kg + 150 kg)(9.8 m/s^2)sin30.0^\circ = 2,940 N$$The force of friction opposing the motion is:$$F_f = (200 kg + 150 kg)(9.8 m/s^2)(0.200)cos30.0^\circ = 588 N$$The net force acting on the masses is:$$F_net = F - F_g - F_f$$$$F_net = F - 2,940 N - 588 N$$$$F_net = F - 3,528 N$$The acceleration of the masses is:$$a = \frac{F_net}{m}$$$$a = \frac{F - 3,528 N}{200 kg + 150 kg}$$$$a = \frac{F - 3,528 N}{350 kg}$$$$1.00 m/s^2 = \frac{F - 3,528 N}{350 kg}$$$$F = 3,528 N + 350 kg(1.00 m/s^2)$$$$F = 3,528 N + 350 N$$$$F = 3,878 N$$

Two Masses Are Being Pulled Up a 30