class 051007

Homework:

Phy 121: Chapter 4 problems 1-4, 7, 16

Phy 201:  Chapter 4 Problems 3, 4, 5, 7, 8, 11, 12, 13, 16, 17, 18

Text Homework:  Read sections 1-3 of Chapter 6.  Don't worry about the trigonometry part.  We'll cover that in a couple of weeks.

Master the rest of Intro Problem Set 3

Sketch a free-body diagram for each of the following situations:

• A domino resting on a table.

• A domino resting on a table, with you pushing it a little bit, but not enough to move it.

• A domino being pushed across a table at constant velocity.

• A domino coasting to rest along a level table.

• A domino coasting down a ramp which is steep enough that the domino picks up speed when released from rest.

• A domino coasting down a ramp with a slope which results in a decrease in domino speed.

You set up a ramp on a table, very much similar to the one you used in Wednesday's experiment, and someone else sets up a similar ramp on the same table.  Eyeballing the systems you can't tell which ramp is steeper.  You roll identical balls off the two ramps.  Assume that the average deviation of the horizontal ranges of the balls rolled from the first ramp is 1.2 cm, and the average deviation of ranges from the second ramp is 0.9 cm. 

Based on a single trial, the ball from your ramp shows a horizontal range of 30.4 cm while the ball from the other ramp shows a horizontal range of 31.1 cm.

• With what degree of certainty do you think you can conclude that, all other things being equal, the other ramp is the steeper?  Do you think you can be 90% certain that this is the case?  95% certain? 99% certain? 100% certain?

Based on 100 trials, you find that the mean horizontal range of a ball from your ramp is 30.6 cm, while the mean horizontal range of a ball from the other ramp is 30.9 cm.

• Are these results consistent with results given above for the single trial?
• With what degree of certainty do you think you can conclude that, all other things being equal, the other ramp is the steeper?

Square root of mean of squared distances tells us to:

First square distances.

Find the mean of these results; add them and divide by n.

Square root of mean of squared distances tells us to then take the square root of the mean we just found.

Experiment:

Set up a ramp system and measure

• the change in the vertical coordinate of the ball between the instant it is released from the top of the first ramp and the instant it leaves the ramp
• the horizontal range of the ball as it falls to the floor
• Determine how much the horizontal range changes if you start the ball a little further down the ramp, so that its vertical coordinate is 1 cm less than before.

Change the slope of the ramp and repeat.

Assuming ball mass .1 kg, find `dPE and `dKE of the ball as it rolls down the ramp.  Base `dKE on the velocity as determined by horizontal range and distance of fall.