class 090923

Class 090928

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Fractional cycles of a pendulum

Regard the equilibrium position of a pendulum as the origin of the x axis. To the right of equilibrium x values are positive, and to the left of equilibrium x values are negative.

Suppose you release a pendulum of length 16 cm from rest, at position x = 4 cm.

Estimate its position in cm, its direction of motion (positive or negative) and its speed as a percent of its maximum speed (e.g., speed is 100 % at equilibrium, 0% at release, and somewhere between 0% and 100% at every position between) after each of the following time intervals has elapsed:

1/2 cycle

3/4 cycle

2/3 cycle

5/4 cycle

7/8 cycle

.6 cycle

Acceleration of Gravity

Drop a coin and release a pendulum at the same instant. Adjust the length of the pendulum so that it travels from release to equilibrium, then to the opposite extreme point and back, reaching equilibrium the second time at the same instant you hear the coin strike the floor. Measure the pendulum.

Give your raw data below:

Show how to start with your raw data and reason out the acceleration of the falling coin, assuming constant acceleration:

There are two delays between the events you are observing and your perceptions:

How long after the coin strikes the floor do you hear it?
How long after the light in the room reflects off the pendulum does it strike your eye?
Is either delay significant compared to other sources of uncertainty in this experiment?

Introduction to Projectile motion

Time a ball down a ramp, and measure how far it travels in the horizontal direction.

Give your raw data below:

To keep things straight, let's use the following notation in the rest of this analysis:

`dt_ramp is the time required to travel the length of the ramp starting from rest
`ds_ramp is the displacement of the ball along the ramp
vf_ramp is the ball's final velocity on the ramp
`ds_x_projectile is the horizontal displacement of the ball between leaving the ramp and striking the floor
`ds_y_projectile is the vertical displacement of the ball between leaving the ramp and striking the floor (for the tables in the lab we may assume that `ds_y_projectile is about 90 cm).
`dt_projectile is the time interval between leaving the ramp and striking the floor

Answer the following questions:

According to the time `dt_ramp required to travel down the ramp and its length `ds_ramp, what are the average and final velocities on the ramp, assuming uniform acceleration?

Moving at vf_ramp, how long would it take the ball to travel through displacement `ds_x_projectile?

Accelerating at 1000 cm/s^2, how long would it take the ball to fall from rest through displacement `ds_y_projectile?

In the time interval you just calculated, how far would the ball travel if moving at velocity v_f_ramp?

Accelerating at the rate you calculated in the preceding exercise, how long would it take the ball to fall from rest through displacement equal to `ds_y_projectile?

Ball up and down ramp

'Poke' a ball (perhaps using your pencil as a 'cue stick') so that it travels partway up a ramp then
back. Observe the clock time and position at three events: the end of the 'poke', when the ball comes
to rest for an instant before rolling back down, and its return to its original position.

Choose your positive direction.

Determine the initial velocity and acceleration of the ball for the interval between the first and second event.

Determine the final velocity and acceleration of the ball for the interval between the second and third event.

Do you think the acceleration of the ball is greater between the first and second event, or between between the second and third event? Or do you think it is the same for both? Give reasons for your answer.

Are your data accurate enough to determine on which interval the acceleration is greater? If so, on which interval do you determine it is greater? If not, how accurate do you think your data would need to be to decide this question?

Homework:

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ic_class_090928

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Report your results from today's class using the Submit Work Form. Answer the questions posed above.

You should complete the Major Quiz by Wednesday, October 7. You are urged to complete it this week. Remember if your grade isn't up to your expectations you can take another.

Note the Major Quiz sample test questions distributed by email last week.

Note the recommendation to work through the q_a_ documents listed below. This is a recommendation, not a requirement. Note that many students (though not all) find that this is the most time-effective way to learn the material. If you choose to do this: