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When the net external force on a closed system is zero, the system is described as an isolated system No system on Earth can be said to be absolutely isolated, however, because there will always be some interactions between a system and its surroundings Often, these interactions are small enough to be ignored when solving physics problems Systems can contain any number of objects, and the objects can stick together or come apart in a collision Under these conditions, the law of conservation of momentum states that the momentum of any closed, isolated system does not change This law will enable you to make a connection between conditions, before and after an interaction, without knowing any of the details of the interaction

Speed A 1875-kg car going 23 m/s rear-ends a 1025-kg compact car going 17 m/s on ice in the same direction The two cars stick together How fast do the two cars move together immediately after the collision

Define the system Establish a coordinate system Sketch the situation showing the before and after states Draw a vector diagram for the momentum Known:

Momentum is conserved because the ice makes the total external force on the cars nearly zero pi pf pCi pDi pCf pDf mCvCi mDvDi mCvCf mDvDf

The three records after the first record are displayed, and the cursor is set to the last record that is displayed So far so good, but look at what happens when you display the previous two records:

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of this chapter) is that, in addition to the translation between JavaScript-style function names and Objective-C method names, JSCocoa actually lets you write your javascript in a syntax that is hauntingly similar to Objective-C:

Because the two cars stick together, their velocities after the collision, denoted as vf, are equal vCf vDf vf mCvCi mDvDi (mC mD)vf Solve for vf vf

(1025 kg)( 17 m/s) 1025 kg)

23 m/s,

Are the units correct Velocity is measured in m/s Does the direction make sense vi and vf are in the positive direction; therefore, vf should be positive Is the magnitude realistic The magnitude of vf is between the initial speeds of the two cars, but closer to the speed of the more massive one, so it is reasonable

13 Two freight cars, each with a mass of 30 105 kg, collide and stick together One was initially moving at 22 m/s, and the other was at rest What is their final speed 14 A 0105-kg hockey puck moving at 24 m/s is caught and held by a 75-kg goalie at rest With what speed does the goalie slide on the ice 15 A 350-g bullet strikes a 50-kg stationary piece of lumber and embeds itself in the wood The piece of lumber and bullet fly off together at 86 m/s What was the original speed of the bullet 16 A 350-g bullet moving at 475 m/s strikes a 25-kg bag of flour that is on ice, at rest The bullet passes through the bag, as shown in Figure 9-7, and exits it at 275 m/s How fast is the bag moving when the bullet exits 17 The bullet in the previous problem strikes a 25-kg steel ball that is at rest The bullet bounces backward after its collision at a speed of 50 m/s How fast is the ball moving when the bullet bounces backward 18 A 050-kg ball that is traveling at 60 m/s collides head-on with a 100-kg ball moving in the opposite direction at a speed of 120 m/s The 050-kg ball bounces backward at 14 m/s after the collision Find the speed of the second ball after the collision

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Define Newton s third law Explain the tension in ropes and strings in terms of Newton s third law Define the normal force Determine the value of the normal force by applying Newton s second law

ou have learned that when an agent exerts a net force upon an object, the object undergoes acceleration You know that this force can be either a field force or a contact force But what causes the force If you experiment with two magnets, you can feel each magnet pushing or pulling the other Similarly, if you pull on a lever, you can feel the lever pulling back against you Which is the agent and which is the object

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