5 Displacement and Force in Two Dimensions 3 Forces in Two Dimensions
5 Displacement and Force in Two Dimensions 3 Forces in Two Dimensions 3(F), 4(C), 4(D), 4(E)
MAINIDEA Write the Main Idea for this section.
REVIEW V...
Identify the factors involved in choosing the coordinate system for solving the problem described in Figure 17.
Identify the force described in Figure 17 that has both x- and y-vector components that must be used to solve the problem.
GET IT? Explain why you would choose the x-direction to be parallel to the slope of an inclined plane.
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3 Forces in Two Dimensions (continued) Student Edition, p. 140
TRY IT !
Use with Example Problem 6.
Use this column for scratch work and sketches.
Problem SLIDE Afrin, who has a mass of 35 kg, is going down a slide sloped at 29°. The coefficient of kinetic friction is 0.23. How fast does she slide 1.5 s after starting from rest? 1. ANALYZE AND SKETCH THE PROBLEM KNOWNS
UNKNOWNS
m =
ϕ =
= ?
μk =
vi =
= ?
μk =
= ?
2. SOLVE FOR THE UNKNOWNS Find the angle of Fg from the +x-axis: Add forces in the y-direction to write an equation for FN.
Because vi, a, and t are all known, use the relationship between velocity, acceleration, and time.
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41. MAINIDEA A rope pulls a 63-kg water skier up a 14.0° incline with a tension of 512 N. The coefficient of kinetic friction between the skier and the ramp is 0.27. Find the magnitude and direction of the skier’s acceleration.
42. Forces One way to get a car unstuck is to tie one end of a strong rope to the car and the other end to a tree, then pull the rope at its midpoint at right angles to the rope. Draw a free-body diagram and explain how even a small force on the rope can exert a large force on the car.
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3 Forces in Two Dimensions (continued) 43. Mass A scoreboard is suspended from an arena’s ceiling by ten cables. Six of the cables make an 8.0° angle with the vertical while the other four make a 10.0° angle. The tension in each cable is 1300 N. Find the scoreboard’s mass?
44. Vector Addition What is the sum of three vectors that, when placed tip to tail, form a triangle? If these vectors represent forces on an object, what does this imply about the object? Describe the motion resulting from these three forces acting on the object.
45. Equilibrium You are hanging a painting using two lengths of wire. The wires will break if the force is too great. Should you hang the painting as shown in the top or the bottom image of Figure 20? Explain.
46. Vector Addition Can the coefficient of friction ever have a value such that a child would be able to slide up a slide at a constant velocity? Explain why or why not. Assume that no one pushes or pulls on the child.
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