Honors Pre-Calculus Sec. 8.5 Applications with Vectors.

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Presentation transcript:

Honors Pre-Calculus Sec. 8.5 Applications with Vectors

A common application of vectors is in modeling a system of forces acting on an object. Every force has direction and magnitude, therefore each can be represented by a vector. The sum of all forces acting on an object is called the ________________. Some examples of quantities that are represented as vectors by physicists are __________, _________, and _________. Example 1: Lenny Montana was a former world heavyweight wrestling champion and actor. Suppose that Lenny and a tag team wrestling partner are each pulling horizontally and at a right angle to each other on the arms of a wrestling opponent. Lenny exerts a force of 180 pounds due north while his partner exerts a force of 125 pounds due east. A) Draw a labeled diagram that represents the forces. velocity weight gravity In all your problems, use an accurate ___________ to help check answers and to prevent any errors.drawing resultant force

B) Determine the resultant force exerted on the opponent. C) Determine the angle the resultant force makes with the east-west axis. The resultant force on the opponent was about 219 lbs. Use Rt. Triangle Trig.

Example 2: Justin works for a package delivery service. Suppose that he is pushing a cart full of packages weighing 125 pounds up a ramp 10 feet long at an incline of 20 o. Find the work done by gravity as the cart moves the length of the ramp. Assume that friction is not a factor Apply the formula for determining work done by gravity. Work done by gravity is negative when an object is lifted or raised. As the cart moves the length of the ramp, work done by gravity is ft. per lb.

Example 3: Dr. Masucci is hanging a sign for his medical practice. The sign is held by two support bars as shown in the figure. If the bars make a 60 o angle with each other and the sign weighs 100 pounds, what are the magnitudes of the forces exerted by the sign on each support bar? Sometimes there is no motion when several forces are at work on an object. This situation, when forces balance one another, is called ______________. Recall that an object is in equilibrium if the resultant force on it is _________. equilibrium zero ** Remember equal vectors have the same magnitude and direction. Force exerted on Bar 2 is about 115 lbs. Force exerted on Bar 1 Is about 58 lbs.

Example 4: A large TV screen inside a restaurant is supported equally on each of its sides by two cables suspended from the ceiling of the restaurant. The cables form a 100 o angle with each other. If the screen weighs 800 pounds, what is the force exerted by each of the cables on the screen? TV 800 lb. x lb. Take these vectors and draw them tip-to-tail. Since the two cables support the picture equally, they are congruent and the triangle is isosceles. x lb. 800 lb. We can use Law of Sines to find the force exerted on the cables. The force exerted on both cables is about 622 lb.