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Substitute a ax because all the acceleration is in the x-direction; substitute FN mg cos Substitute g 980 m/s2, 37 , 015

(015)cos 37 )

Because vi, a, and t are all known, use the following vf vi at 00 (47 m/s2)(50 s) Substitute vi 24 m/s

50 s

Are the units correct Performing dimensional analysis on the units verifies that vf is in m/s and a is in m/s2 Do the signs make sense Because vf and a are both in the x direction, the signs do make sense Are the magnitudes realistic The velocity is fast, over 80 km/h (50 mph), but 37 is a steep incline, and the friction between the skis and the snow is not large

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Figure 3 15. As you Ctrl-drag over an item, it will become highlighted, even if it would otherwise be invisible.

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38 Consider the crate on the incline in Example Problem 5 Calculate the magnitude of the acceleration After 400 s, how fast will the crate be moving 39 If the skier in Example Problem 6 were on a 31 downhill slope, what would be the magnitude of the acceleration 40 Stacie, who has a mass of 45 kg, starts down a slide that is inclined at an angle of 45 with the horizontal If the coefficient of kinetic friction between Stacie s shorts and the slide is 025, what is her acceleration 41 After the skier on the 37 hill in Example Problem 6 had been moving for 50 s, the friction of the snow suddenly increased and made the net force on the skier zero What is the new coefficient of friction The most important decision in problems involving motion along a slope is what coordinate system to use Because an object s acceleration is usually parallel to the slope, one axis, usually the x-axis, should be in that direction The y-axis is perpendicular to the x-axis and perpendicular to the surface of the slope With this coordinate system, you now have two forces, the normal and frictional forces, in the directions of the coordinate axes; however, the weight is not This means that when an object is placed on an inclined plane, the magnitude of the normal force between the object and the plane will usually not be equal to the object s weight You will need to apply Newton s laws once in the x-direction and once in the y-direction Because the weight does not point in either of these directions, you will need to break this vector into its x- and y-components before you can sum your forces in these two directions Example Problem 5 and Example Problem 6 both showed this procedure.

Prop a board up so that it forms an inclined plane at a 45 angle Hang a 500-g object from the spring scale 1 Measure and record the weight of the object Set the object on the bottom of the board and slowly pull it up the inclined plane at a constant speed 2 Observe and record the reading on the spring scale Analyze and Conclude 3 Calculate the component of weight for the 500-g object that is parallel to the inclined plane 4 Compare the spring-scale reading along the inclined plane with the component of weight parallel to the inclined plane

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 push the rope at its midpoint at right angles to the rope Draw a free-body diagram and explain why even a small force on the rope can exert a large force on the car 43 Mass A large scoreboard is suspended from the ceiling of a sports arena by 10 strong cables Six of the cables make an angle of 80 with the vertical while the other four make an angle of 100 If the tension in each cable is 13000 N, what is the scoreboard s mass 44 Acceleration A 63-kg water skier is pulled up a 140 incline by a rope parallel to the incline with a tension of 512 N The coefficient of kinetic friction is 027 What are the magnitude and direction of the skier s acceleration

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