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 up 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 tension in the string is A) 840 N. B) 980 N. C) 1,140 N. D) 1,530 N. E) 2,660 N.

Question

Quizplus · Accepted Answer

The tension in the string is equal to the force applied to the 200 kg mass minus the force of friction on the 200 kg mass. The force of friction is equal to the coefficient of kinetic friction times the normal force on the 200 kg mass. The normal force is equal to the weight of the 200 kg mass minus the component of the force applied to the 200 kg mass that is perpendicular to the incline. The component of the force applied to the 200 kg mass that is perpendicular to the incline is equal to the force applied to the 200 kg mass times the sine of the angle of the incline. Therefore, the tension in the string is equal to:$$T = F - f = F - \mu_k(mg - F\sin	heta)$$$$T = 2000 N - 0.200(200 kg)(9.8 m/s^2 - 2000 N\sin30.0^\circ)$$$$T = 840 N$$

Two Masses Are Being Pulled Up a 30