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1 A flowerpot falls freely from a windowsill (Ignore any forces due to air resistance) 2 A sky diver falls downward through the air at constant velocity (The air exerts an upward force on the person) 3 A cable pulls a crate at a constant speed across a horizontal surface The surface provides a force that resists the crate s motion 4 A rope lifts a bucket at a constant speed (Ignore air resistance) 5 A rope lowers a bucket at a constant speed (Ignore air resistance)

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How does an object move when one or more forces are exerted on it One way to find out is by doing experiments As before, begin by considering a simple situation Once you fully understand that situation, then you can add more complications to it In this case, begin with one controlled force exerted horizontally on an object The horizontal direction is a good place to start because gravity does not act horizontally Also, to reduce complications resulting from the object rubbing against the surface, do the experiments on a very smooth surface, such as ice or a very well-polished table, and use an object with wheels that spin easily In other words, you are trying to reduce the resistance to motion in the situation To determine how force, acceleration, and velocity are related, you need to be able to exert a constant and controlled force on an object How can you exert such a controlled force A stretched rubber band exerts a pulling force; the farther you stretch it, the greater the force with which it pulls back If you always stretch the rubber band the same amount, you always exert the same force Figure 4-3a shows a rubber band, stretched a constant 1 cm, pulling a low-resistance cart If you perform this experiment and determine the cart s velocity for some period of time, you could construct a graph like the one shown in Figure 4-3b Does this graph look different from what you expected What do you notice about the velocity The constant increase in the velocity is a result of the constant acceleration the stretched rubber band gives the cart How does this acceleration depend upon the force To find out, repeat the experiment, this time with the rubber band stretched to a constant 2 cm, and then repeat it again with the rubber band stretched longer and longer each time For each experiment, plot a velocity-time graph like the one in Figure 4-3b, calculate the acceleration, and then plot the accelerations and forces for all the trials to make a force-acceleration graph, as shown in Figure 4-4a What is the relationship between the force and acceleration It s a linear relationship where the greater the force is, the greater the resulting acceleration As you did in s 2 and 3, you can apply the straight-line equation y mx b to this graph.

Figure 4-3 Because the rubber band is stretched a constant amount, it applies a constant force on the cart, which is designed to be low-friction (a) The cart s motion can be graphed and shown to be a linear relationship (b)

Failed to connect to mailserver at "localhost" port 25 then you don t have your server properly configured for e-mail In fact, if you are using Zend Server CE and/or a web development server, you may not actually want to run a mail server on that machine anyway, and should probably test this code on a server already configured for mail

Cart Pulled by Stretched Rubber Band (1 cm)

Here the KPIs are redone as measures This fixes a number of problems in the previous query The KPITrend has been added and two years are shown to illustrate how KPITrend works

Velocity (m/s)

150 100 050 0

Acceleration (m/s2)

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Acceleration (m/s2)

1 2m

00 0 1 2 3 4 0 Application of force (in cm of stretch)

Force (N)