Vectors Day 4 Lyzinski Physics

Vectors Problem Packet Homework Solutions (19-23)

In conclusion, the cake will travel South 51.5o West. 19. Two ants at a picnic find a small piece of cake. Each picks up the cake and tries to carry it home. The first ant’s home is at a bearing of [W 15o N] and he pulls with a force of 10 dynes. The second ant’s home is at a bearing of [S 15o W] , and he pulls with a force of 13.5 dynes. What do you predict will happen? In which direction will the cake travel? x-components: 10 dynes 15o -9.66 + (-3.49) = -13.15 dynes 2.59 y-components: 9.66 15o 2.59 + (-13.04) = -10.45 dynes In conclusion, the cake will travel South 51.5o West. 13.5 dynes 13.04 16.8 dynes 51.5o 10.45 3.49 13.15

20. Linda is pulling a sled with a force of 20 pounds and is heading on a bearing of N30E. Elaine begins to pull the sled with a force of 15 pounds on a bearing of N5W. What force is exerted on the sled and in which direction does it go? 32.26 8.69 1.31 10 17.32 14.94 15 lbs 20 lbs 5o 33.4 lbs 15.1o 30o x-components: -1.31 + 10 = 8.69 lbs y-components: 14.94 + 17.32 = 32.26 lbs

+ = 21. Find the resultant of a 120-Newton force North and an 80 Newton force at N45 E. 56.57 120 N + = 185 N 56.57 45o 80 N 176.57 x-components: 0 + 56.57 = 56.57 N 72o 56.57 y-components: 120 + 56.57 = 176.57 N

22. Two water skiers are being pulled by a boat 22. Two water skiers are being pulled by a boat. The first skier exerts a force of 300 pounds North on the boat; the second skier exerts a force of 400 pounds at N75 E. Find the resultant of the two forces. 386.37 = 300 lbs + 103.53 75o 386.37 400 lbs 403.53 558.7 lbs 43.8o x-components: 0 + 386.37 = 386.37 lbs y-components: 300 + 103.53 = 403.53

23. Three brothers are playing at the local playground with a frisbee 23. Three brothers are playing at the local playground with a frisbee. Each grabs it at the same time. Robbie grabs it at the N63 E point and exerts a force of 100 pounds on it. Chip grabs it at the N27 W point and exerts a force of 100 pounds on it. Ernie pulls with 141.4 pounds at the S18 W point. Who gets control of the frisbee? 45.399 100 lbs 141.4 lbs 89.101 89.101 27o 63o 18o 45.399 x-components: -45.399 + 89.101 + (-43.399) = 0 y-components: 89.101 + 45.399 + (-134.479) = 0 134.479 Since both sets of components are zero, NOBODY wins (the frisbee doesn’t even move) 43.695

Vectors Problem’s from Buffa book (pp. 95-96)

Day #4

has balanced forces acting on it zero

375 lb 649.5 lb Notice that for equilibrium problems (where nothing is moving), the components always sum up to zero. 750 lb Fpole W x: y: F + 375 = 0  F = -375 lb or F = 375 lb  649.5 – W = 0  W = 649.5 lb

140.95 N 51.30 N 150 N 140.95 N 51.30 N 70o W x: y: 140.95 – 140.95 = 0  DUH! 51.30 + 51.30 – W = 0  W = 102.6 N

Solve simultaneous equations! T2sin60 T2cos60 T2 T1 T1cos60 T1sin60 x: y: T2sin60 - T1cos60 = 0 T1sin60 + T2cos60 - 50 = 0 50 N Solve simultaneous equations! T2sin60 - T1cos60 = 0  T2 = (T1cos60)/sin60 = .577 T1 T1sin60 + T2cos60 - 50 = 0  T1sin60 + (.577T1)cos60 - 50 = 0 1.155T1- 50 = 0  T1 = 43.3 N T2 = .577T1  T2 = 24.98 N

F = (3 x + 4 y ) N notation F = (3 x + 4 y ) N notation ^ OR Fy = 4N Fx = 3N Fy = 4N

“Day #4 Vectors HW Problems” (from the packet, #’s 24-25) Tonight’s HW “Day #4 Vectors HW Problems” (from the packet, #’s 24-25) Do Buffa, pp. 96-97, problems 17, 30, 44, 45