Physics Forces in Equilibrium Practice

Practice Exercises Exercise 1: While moving out of her dorm room, Bridget carries a 120-N box to her car, holding it in both arms. a) How much force must be exerted by each of her arms to support the box? b) How will this force change if Bridget holds the box with only one arm? a) Each arm holds half the weight or 60 N. b) The force will be twice as great, or the full 120 N. Exercise 2: Answer: a. 60 N Answer: b. 120 N A flower pot weighing 42.0 N is hung above a window by three ropes, each making an angle of 15.0° with the vertical, as shown. What is the tension in each rope supporting the flower pot? 1 of 42.0 N, or 14.0 N. 3 (14.0 N)/cos 15.0°  14.5 N Each rope supports Answer: Exercise 3: 14.5 N Luke Skywalker must swing Princess Leia across a large chasm in order to escape the Storm Troopers. If Luke and Leia’s combined weight is 1450 N, calculate the tension in the rope just before Luke and Leia start their swing, when the pair makes an angle of 30.0° with the vertical. F  w/cos   1450 N/cos 30.0°  1670 N Answer: 1670 N Exercise 4: The ACE towing company tows a disabled 10,500 N automobile off the road at a constant speed. If the tow line makes an angle of 10.0° with the vertical as shown, what is the tension in the line supporting the car? F  w/cos   10,500 N/cos 10.0°  10,600 N Answer: Exercise 5: 10,600 N Yvette hangs a 24-N bird feeder in the middle of a rope tied between two trees. The feeder creates a tension of 480 N in each side of the the rope. a) If the two trees are 4.0 m apart, how much will the rope sag in the center? b) If a bird lands on the feeder, will this have any effect on the tension in the rope? Explain. a) sin   Fy/F  (12 N)/(480 N)   1.43° Shared equally by either side of the rope. dy  (2.0 m)tan 1.43°  0.050 m b) The tension in each side of the rope will be greater to support the bird’s weight. Answer: a. 0.050 m Answer: b. tension will be greater Additional Exercises A-1: To make extra money during the summer, Mr. Garber, a 660-N physics teacher, paints the outside of houses while sitting on a 40.-N plank suspended by two vertical cables. What is the tension in each of the two cables? A-2: Erma receives a 50.0-N package in the mail tied with a string that goes around each side of the box, as shown. If Erma lifts the box by the string in the center so that each piece of string makes an angle of 45.0° with the vertical, what is the tension in each piece of string? A-3: While camping in Denali National Park in Alaska, a wise camper hangs his pack of food from a rope tied between two trees, to keep the food away from the bears. If the 50.-N bag of food hangs from the center of a rope that is 3.0 m long, and the rope sags 6.0 cm in the middle, what is the tension in the rope? A-4: In the figure, a 12,400-N wrecking ball is pulled back with a horizontal force of 5480 N before being swung against the side of a building. a) What angle does the wrecking ball make with the vertical when it is pulled back? b) What is the tension in the ball’s supporting cable when it is at this angle? A-5: The amazing Gambini walks across a 30.0-m-long tightrope high above a 3-ring circus. If the 750.-N Gambini pushes the tightrope down 15.0 cm in the center, find the tension in the tightrope. Challenge Exercises for Further Study B-1: Malcolm, the 200.-N monkey, hangs from a jungle vine, as shown. a) What is the tension in the segment of vine labeled AB? b) What is the tension in the segment of the vine labeled BC? B-2: Blythe lies in a hospital bed with her foot in traction, as shown. How much tension will the traction device exert on her foot? B-3: After pulling his car off to the side of the road during a rainstorm, Travis is dismayed to find that the car has become stuck in the mud. Travis ties one end of a rope to the front of the car and the other end to a tree 12.00 m away as shown. a) If Travis can exert a force of 610 N on the rope, moving it 1.00 m in the direction shown, how much force will the rope exert on the car? b) Why is this method better than simply tying a rope to the front of the car and pulling the car straight out?