Answer to Question #166943 in Physics for Jay

Question

A crate is forced across an horizontal floor by three people, two pulling the crate by massless ropes attached at the same point and one pushing from behind. The person pushing from behind is pushing in the direction of motion (the x direction) with a force of 85 lbs, one of the ropes makes an angle from the x direction of 35° and the other rope makes an angle of 40° from the x direction in the opposite direction from the other rope. Both ropes are completely in the horizontal plane. The mass of the crate is 450 kg and the coefficient of kinetic friction between the crate and the floor is 0.78. The crate is moving at a constant velocity. What are the tension forces in each rope?

Answer 1

$$T_1\sin{35}=T_2\sin{40}\\T_1\cos{35}+T_2\cos{40}+F=\mu mg$$

$$T_1\sin{35}=T_2\sin{40}\\T_1\cos{35}+T_1\sin{35}\frac{\cos{40}}{sin{40}}+F=\mu mg$$

$$\\T_1\cos{35}+T_1\sin{35}\frac{\cos{40}}{sin{40}}+378=(0.78)(450)(9.8)\\T_1=2037.5\ N\\T_2=1818.1\ N$$