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Physics I Major Quiz

Completely document your work and your reasoning.

You will be graded on your documentation, your reasoning, and the correctness of your conclusions.

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Instructions:

Test is to be taken without reference to text or outside notes.
Graphing Calculator is allowed, as is blank paper or testing center paper.
No time limit but test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..

Directions for Student:

Completely document your work.
Numerical answers should be correct to 3 significant figures. You may round off given numerical information to a precision consistent with this standard.
Undocumented and unjustified answers may be counted wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get partial credit. So show your work and explain your reasoning.
Due to a scanner malfunction and other errors some test items may be hard to read, incomplete or even illegible. If this is judged by the instructor to be the case you will not be penalized for these items, but if you complete them and if they help your grade they will be counted. Therefore it is to your advantage to attempt to complete them, if necessary sensibly filling in any questionable parts.
Please write on one side of paper only, and staple test pages together.

Test Problems:

Problem Number 1

If at clock times t = 0 s, 8 s and 18 s a horse has velocities 10.5 m/s, 10 m/s and 3.25 m/s, then during each of the two time intervals, 0- 8 seconds and 8 - 18 seconds, approximately how far does it move and at what average rate does its velocity change?

Directly reason out your results using the concept of rate.
Show how you could use a graph of velocity vs. time to obtain your results.
If the automobile is coasting, and if air resistance is not a significant factor, then over which time interval do you think the average slope of the road is greatest?

Problem Number 2

A straight ramp is inclined at various slopes.

The differences in elevation between one end and the other, for the different slopes, are 1.9, 3.6 and 6.1 cm.
The time required for a cart to coast 78 cm down the ramp, starting from rest, is 2.673299 seconds on the first incline, 2.601031 seconds on the next, and 2.483171 seconds on the last.

How well do the data support the hypothesis that a graph of average acceleration vs. slope will be linear?

For the 2.67 sec run we know v0 = 0, `ds = 78 cm and `dt = 2.67 sec. We can use direct reasoning to find vAve, then find vf then find a.

We can do the same for each of the other two trials.

So we have 3 accelerations.

The three slopes are 1.9 cm / (78 cm) = .026, 3.6 cm / (78 cm) = .046, 6.1 cm / (78 cm) = .08.

We graph accel vs. ramp slope and eyeball the points to see if a single straight line would come close to the data points.

Problem Number 3

A projectile leaves the edge of a table and, while traveling horizontally at a constant 31 cm/s, falls freely a distance of 58 cm to the floor. If its vertical acceleration is 980 cm/s², how long does it take to fall and how far does it travel in the horizontal direction during the fall?

<h3>You need to analyze the vertical motion first to see how long it takes the object to fall.

To analyze vertical motion:

First we pick the positive direction. Let's let downward be positive.

The initial velocity is in the horizontal direction, so the initial vertical velocity is zero.

The acceleration in the vertical direction is 980 cm/s^2, and is positive because we picked positive as downward.

The vertical displacement is 58 cm, again positive since downward has been chosen as the positive direction.

So we know v0, a and `ds. We want to find `dt.

The third equation of motion contains v0, a, `ds and `dt so we could use it, but we would get a quadratic equation for `dt. So we won't use that equation.

The fourth equation contains v0, a, `ds and vf. We can use it to find vf.

The fourth equation is

vf^2 = v0^2 + 2 a `ds. Solving for vf we get

vf = +-sqrt(v0^2 + 2 a `ds) = +-sqrt( 0^2 + 2 * 980 cm/s^2 * 58 cm) = +-sqrt(114,000 cm^2 /s^2) = +-350 cm/s, approx.

We reject the negative result, knowing that motion will be downward and therefore positive (consistent with our choice of positive direction).

So our final velocity is 350 cm/s.

Initial velocity was 0 and acceleration is uniform, so average velocity is

vAve = (0 + 350 cm/s) / 2 = 175 cm/s.

To fall 58 cm therefore requires

`dt = `ds / vAve = 58 cm / (175 cm/s) = .33 sec, approx..

Now for the horizontal motion.

In the horizontal direction the velocity does not change, be remains at the original 31 cm/s.

So in .33 sec, the object will travel (31 cm/s) * .33 sec = 10 cm, approx., in the horizontal direction.</h3>

Problem Number 4

An object which accelerates uniformly from rest, ending up with velocity 4.2 cm/sec after traveling a distance of 36 cm from start to finish. What are the average acceleration and final velocity of the object?

Problem Number 5

At clock time t = 4 sec, a ball rolling straight down a hill is moving at 5 m/s and is 78 m from the top of the hill, while at clock time t = 9 sec it is moving at 7.5 m/s and is 114 m from the top of the hill. What is its average velocity during this time? What is its average acceleration during this time? Is it possible that the acceleration is uniform?

Problem Number 1

Give an example of a situation in which you are given a, Ds and Dt, and reason out all possible conclusions that could be drawn from these three quantities, assuming uniform acceleration. Accompany your explanation with graphs and flow diagrams. Show how to generalize your result to obtain the symbolic expressions for v0 and vf.Problem Number 2

A straight ramp is inclined at three different slopes. The differences in elevation between one end and the other, for the different slopes, are 2.1, 4.2 and 5.8 cm.

The time required for a cart to coast 54 cm down the ramp, starting from rest, is 1.682856 seconds on the first incline, 1.667749 seconds on the next, and 1.688278 seconds on the last.

How well do these data confirm our suspicion that the acceleration on the ramp is linearly dependent on the slope?

Problem Number 3

Solving Uniform Acceleration Problems

Possible Combinations of Variables Direct Reasoning

Using Equations Problem

Possible Combinations of Variables

There are ten possible combinations of three of the the five variables v0, vf, a, Dt and Ds. These ten combinations are summarized in the table below:

1

v0

vf

a

2

v0

vf

dt

3

v0

vf

ds

4

v0

a

dt

5

v0

a

ds

*

6

v0

dt

ds

7

vf

a

dt

8

vf

a

ds

*

9

vf

dt

ds

10

a

dt

ds

If we know the three variables we can easily solve for the other two, using either direct reasoning or the equations of uniformly accelerated motion (the definitions of average velocity and acceleration, and the two equations derived from these by eliminating Dt and then eliminating vf).

Only two of these situations require equations for their solution; the rest can be solved by direct reasoning using the seven quantities v0, vf, a, Dt, Ds, Dv and v_Ave. These two situations, numbers 5 and 8 on the table, are indicated by the asterisks in the last column.

Direct Reasoning

We learn more physics by reasoning directly than by using equations. In direct reasoning we think about the meaning of each calculation and visualize each calculation.

When reasoning directly using v0, vf, `dv, v_Ave, `ds, `dt and a we use two known variables at a time to determine the value of an unknown variable, which then becomes known. Each step should be accompanied by visualization of the meaning of the calculation and by thinking of the meaning of the calculation. A 'flow diagram' is helpful here.

Using Equations

When using equations, we need to find the equation that contains the three known variables.

We solve that equation for the remaining, unknown, variable in that equation.
We obtain the value of the unknown variable by plugging in the values of the three known variables and simplifying.

At this point we know the values of four of the five variables.
Then any equation containing the fifth variable can be solved for this variable, and the values of the remaining variables plugged in to obtain the value of this final variable.

Problem

Do the following:

Make up a problem for situation # 6, and solve it using direct reasoning.
Accompany your solution with an explanation of the meaning of each step and with a flow diagram.
Then solve the same problem using the equations of uniformly accelerated motion.
Make up a problem for situation # 5, and solve it using the equations of uniformly accelerated motion.

Problem Number 4

A projectile leaves the edge of a table and falls freely a distance of 150 cm to the floor. It travels a horizontal distance of 6.1 cm during its fall. How long does it take to fall and what is its horizontal velocity during the fall?

Problem Number 5

If the velocity of the object changes from 5 cm / sec to 16 cm / sec in 5 seconds, then at what average rate is the velocity changing?

A cart rolling from rest down a constant incline of length 64 cm requires 8.8 seconds to travel length of the incline.

What is its average velocity?

An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.

What therefore is the final velocity of this cart?
What average rate is the velocity of the cart therefore changing?

At what average rate does the velocity of an automobile change, if it accelerates uniformly down a track, starting from rest, and if it requires 14 seconds to cover a distance of 169 meters.

1	v0	vf	a
2	v0	vf		dt
3	v0	vf			ds
4	v0		a	dt
5	v0		a		ds	*
6	v0			dt	ds
7		vf	a	dt
8		vf	a		ds	*
9		vf		dt	ds
10			a	dt	ds

1	v0	vf	a
2	v0	vf		dt
3	v0	vf			ds
4	v0		a	dt
5	v0		a		ds	*
6	v0			dt	ds
7		vf	a	dt
8		vf	a		ds	*
9		vf		dt	ds
10			a	dt	ds

1	v0	vf	a
2	v0	vf		dt
3	v0	vf			ds
4	v0		a	dt
5	v0		a		ds	*
6	v0			dt	ds
7		vf	a	dt
8		vf	a		ds	*
9		vf		dt	ds
10			a	dt	ds