Tip-to-tail vector addition:
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- Bethanie Holt
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1 Tip-to-tail vector addition: Consider the following five force vectors. Sketch the following and draw the resultant (R). Do not draw a scaled vector diagram; merely make a sketch. Label each vector. Clearly label the resultant (R). A + C + D B + E + D 1
2 Billie Budten and Mia Neezhirt are having an intense argument at the lunch table. They are adding two force vectors together to determine the resultant force. The magnitude of the two forces are 3 N and 4 N. Billie is arguing that the sum of the two forces is 7 N. Mia argues that the two forces add together to equal 5 N. Who is right? Explain. Refresher problem: A car is driven 125 km due west, then 65 km due south. What is the magnitude of its isplacement? Solve graphically and mathematically. 2
3 To solve for unknown parts of right triangles: What if the triangle does NOT have a right angle? Find the magnitude of the sum of a 15-km displacement and a 25-km displacement when the angle between them is 90 o and when the angle between them is 135 o. step 1. DRAW your vectors! 3
4 Vectors that are not parallel to the x- or y- axis can be broken down into components: As the 60-Newton tension force acts upward and rightward on Fido at an angle of 40 degrees, the components of this force can be determined using trigonometric functions. 4
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6 Vector components can be added in any order: 20 m, 45 deg m, 300 deg m, 210 deg. SCALE: 1 cm = 5 m A pack of five Arctic wolves are exerting five different forces upon the carcass of a 500-kg dead polar bear. A top view showing the magnitude and direction of each of the five individual forces is shown in the diagram. Find the net force and the direction of acceleration. 6
7 Once you determine the net force, in this case we can find the acceleration of the polar bear carcass: A 400-N force is exerted at a 60-degree angle (a direction of 300 degrees) to move a railroad car eastward along a railroad track. Find the magnitude of the component vectors of this force. 7
8 Try the following three practice problems. 8
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14 Jerome and Michael, linebackers for South s varsity football team, delivered a big hit to the halfback in last weekend s game. Striking the halfback simultaneously from different directions with the following forces: F Jerome = 1230 N at 53 F Michael = 1450 at 107 Determine the resultant force applied by Jerome and Michael to the halfback. (The directions of the two forces are stated as counterclockwise angles of rotation with East.) 14
15 Mom and Dad have tied a rope to Matthew s sled and are momentarily pulling him through the snow. Dad is pulling with force A and Mom with force B. A: 54 N at 65 north of east B: 130 N at 22 south of east a. Determine the resultant force of A and B. b. Determine the acceleration that these forces would create for a 39- kg sled and child (assuming negligible friction). Jerome and Michael, linebackers for South s varsity football team, delivered a big hit to the halfback in last weekend s game. Striking the halfback simultaneously from different directions with the following forces: F Jerome = 1230 N at 53 F Michael = 1450 at 107 Determine the resultant force applied by Jerome and Michael to the halfback. (The directions of the two forces are stated as counterclockwise angles of rotation with East.) 15
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18 Forces on an inclined plane 18
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21 The two diagrams below depict the free-body diagram for a 1000-kg roller coaster on the first drop of two different roller coaster rides. Use the above principles of vector resolution to determine the net force and acceleration of the roller coaster cars. Assume a negligible affect of friction and air resistance. 21
22 Ben Laborin exerts a force on an 86-kg crate of books to push it up the ramp of the loading dock at a constant speed of 24 cm/s. The ramp makes an angle of 12 with the horizontal. The coefficient of friction between the crate and the ramp is Assuming that Ben is pushing parallel to the inclined plane, determine the force with which he is pushing. 22
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