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12 Direction of Velocity If you push a book in the forward direction, does this mean its velocity has to be forward 13 Free-Body Diagram Draw a free-body diagram of a water bucket being lifted by a rope at a decreasing speed Specifically identify the system Label all forces with their agents and make the arrows the correct lengths 14 Critical Thinking A force of 1 N is the only force exerted on a block, and the acceleration of the block is measured When the same force is the only force exerted on a second block, the acceleration is three times as large What can you conclude about the masses of the two blocks

Describe how the weight and the mass of an object are related Differentiate between actual weight and apparent weight

ewton s second law describes the connection between the cause of a change in an object s velocity and the resulting displacement This law identifies the relationship between the net force exerted on an object and the object s acceleration

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What is the weight force, Fg , exerted on an object of mass m Newton s second law can help answer this question Consider the pictorial and physical models in Figure 4-6, which show a free-falling ball in midair With what objects is it interacting Because it is touching nothing and air resistance can be neglected, the only force acting on it is Fg You know from 3 that the ball s acceleration is g Newton s second law then becomes Fg mg Both the force and the acceleration are downward The magnitude of an object s weight is equal to its mass times the acceleration it would have if it were falling freely It is important to keep in mind that even when an object is not experiencing free-fall, the gravitational force of Earth is still acting on the object This result is true on Earth, as well as on any other planet, although the magnitude of g will be different on other planets Because the value of g is much less on the Moon than on Earth, astronauts who landed on the Moon weighed much less while on the Moon, even though their mass had not changed Scales A bathroom scale contains springs When you stand on the scale, the scale exerts an upward force on you because you are in contact with it Because you are not accelerating, the net force acting on you must be zero Therefore, the spring force, Fsp, pushing up on you must be the same magnitude as your weight, Fg , pulling down on you, as shown in the pictorial and physical models in Figure 4-7 The reading on the scale is determined by the amount of force the springs inside it exert on you A spring scale, therefore, measures weight, not mass If you were on a different planet, the compression of the spring would be different, and consequently, the scale s reading would be different Remember that the proper unit for expressing mass is kilograms and because weight is a force, the proper unit used to express weight is the newton.

Figure 4-7 The upward force of the spring in the scale is equal to your weight when you step on the bathroom scale (a) The free-body diagram in (b) shows that the system is in equilibrium because the force of the spring is equal to your weight

If you re using Core Data in your application, it will even take care of the actual opening and saving all on its own, so your application code never even has to touch a document file In this chapter, you ll learn the basics of how to create a document-based Cocoa application, including the use of Core Data, by creating an application called ColorMix ColorMix lets the user choose two colors using the standard system color panel, and then presents a grid of color swatches demonstrating different methods of blending the two colors together Each set of two chosen colors (and its 15 blended colors) can be saved in a document, which is just like any other file and can be saved anywhere you like, and then reopened later on.

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