Consider three force vectors F1 with magnitude 51 N and direction 150◦ , F2 with magnitude 36 N and direction −41◦ , and F3 with magnitude 11 N and direction 110◦ . All direction angles θ are measured from the positive x axis: counter-clockwise for θ > 0 and clockwise for θ < 0.

a. What is the magnitude of the resultant vector F~ = F1 + F2 + F3?
b. What is the direction of the net force vector F?

Apendulum has a mass of 1.5 kg and starts at a height of 0.4 m. if it is released from rest, how fast is it going when it reaches the lowest point of its path? acceleration due to gravity is g = 9.8 m/s2. a. 2.8 m/s b. 0 m/s c. 5.9 m/s d. 4.3 m/s

Aproduction line at v. j. sugumaran's machine shop has three stations. the first station can process a unit in 7 minutes. the second station has two identical machines, each of which can process a unit in 16 minutes (each unit only needs to be processed on one of the two machines). the third station can process a unit in 10 minutes. ▼ is the bottleneck station, with a bottleneck time of nothing minutes per unit (enter your response as a whole number).

16. a brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 n on him. the mass of the losing player plus equipment is 90.0 kg, and he is accelerating at 1.20m/s2 size 12{1 "." "20"" m/s" rsup { size 8{2} } } {} backward. (a) what is the force of friction between the losing player’s feet and the grass? (b) what force does the winning player exert on the ground to move forward if his mass plus equipment is 110 kg? (c) draw a sketch of the situation showing the system of interest used to solve each part. for this situation, draw a free-body diagram and write the net force equation.