## Pc1431 Assignment 8 Business

Part AWhich of the following is the best explanation of the results shown in the applet? ANSWER:

The disk loses energy to friction as it rolls, but the box is frictionlessand so it speeds up more quickly and gets to the bottom first.The potential energy of the disk is converted into translational androtational kinetic energy, so the translational speed grows more slowlythan that of the box, which has no rotational energy.The net forces on the two objects are equal, but the force on the diskgets partially used up in creating the torque necessary to make it roll.The net forces on the two objects are equal, but the force on the disk isnot directed parallel to the ramp, and so does not create as great anacceleration down the ramp.

Correct

This applet shows the same situation, but it also shows, through bar graphs that change with time, theway that the energy is transformed as the box and the disk go down the inclined plane. Assume that the box and disk each have mass , the top of the incline is at height , and the anglebetween the incline and the ground is (i.e., the incline is at an angle above the horizontal). Also,let the radius of the disk be .Part BHow much sooner does the box reach the bottom of the incline than the disk?Hint B.1

How to approach the problem

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Hint B.2

Find the final speed of the box

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Hint B.3

Find the final speed of the disk

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Hint B.4

Finding the average speed

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Hint B.5

Finding the time from the average speed

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Hint B.6

Find the length of the incline

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Express your answer in terms of some or all of the variables , , , and , as well as theacceleration due to ravit .

Assignment 3: Work and Energy

Due: 2:00am on Saturday, September 18, 2010

Note:

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Bungee Jumping

Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has amass , and the surface of the bridge is a height above the water. The bungee cord, which haslength when unstretched, will first straighten and then stretch as Kate falls. Assume the following:The bungee cord behaves as an ideal spring once it begins to stretch, with spring constant .Kate doesn't actually jump but simply steps off the edge of the bridge and falls straight downward.Kate's height is negligible compared to the length of the bungee cord. Hence, she can be treated as apoint particle.Use for the magnitude of the acceleration due to gravity.Part AHow far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finallyto rest? Assume that she doesn't touch the water.Hint A.1

Decide how to approach the problem

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Hint A.2

Compute the force due to the bungee cord

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Express the distance in terms of quantities given in the problem introduction.

ANSWER:=

Correct

Part BIf Kate just touches the surface of the river on her first downward trip (i.e., before the first bounce),what is the spring constant ? Ignore all dissipative forces.Hint B.1

Decide how to approach the problem

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Hint B.2

Find the initial gravitational potential energy

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Hint B.3

Find the elastic otential ener in the bunee cord

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