class 091026

Class 091026

short-answer questions

`q001. ** Give your answers to the following one-step questions:

What is the KE of a 10 kg object moving at 5 m/s?
What is `dPE for a 10 kg object raised 3 meters against the force of gravity?
What is `dPE for a block of dominoes pulled 15 cm in such a way to stretch a spring, if as a result the spring force changes linearly from 4 N to 16 N?
If on a certain interval, the KE and PE of a system change so that `dKE = + 8 J and `dPE = -12 J, then how much work is done by nonconservative forces on the system?
If on a certain interval nonconservative forces do 20 J of work on a system and its KE increases by 15 J, does the PE of the system increase or decrease, and by how much?

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`q002. ** A slingshot shoots a pebble in the upward direction. While the slingshot is in contact with the pebble:

Does the elastic force exerted by the slingshot act in the direction of the pebble's motion or opposite this direction?
Does the elastic force therefore do positive or negative work on the pebble?
Does its elastic PE therefore increase or decrease?
Does the force of gravity act in the direction of the pebble's motion or opposite this direction?
Does the gravitational force therefore do positive or negative work on the pebble?
Does its gravitational PE therefore increase or decrease?
Assuming that the gravitational and elastic forces are the only conservative forces acting on the pebble, does its total PE increase or decrease?

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`q003. ** For the ball rolling in two directions along the 'constant-velocity' incline (i.e., an incline on which the velocity of the ball as it rolls down the incline remains unchanged), as you observed it in class:

What were your data?
Explain how you determined the acceleration of the ball the roll in each direction.
If the ramp was completely level, would it be a 'constant-velocity' incline?
If the ramp was completely level, what would be the acceleration in each direction?
On a 'constant-velocity' ramp, how are the parallel component of the gravitational force and the force of rolling friction related? (the 'parallel component' of the gravitational force is the component of that force in the direction of the incline)
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`q004. The rolling friction between a steel ball and a steel incline exerts a force opposed to the direction of motion. If this force is equal to .3% of the weight of the rolling ball, then

What is the frictional force on a 60 gram steel ball?
What would be the acceleration of the ball on a perfectly level ramp?
What would be its acceleration down a ramp with a 1 degree slope?
What would be its acceleration up the same ramp?
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`q005. The ball in the preceding rolls 50 cm down the 1 degree ramp, subject to only gravity, normal force and rolling friction. For this roll:

What is `dPE?
What is `dW_NC_ON?
What therefore is `dKE?
If the ball started from rest, what therefore is its final velocity?
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`q006. The acceleration of a 60-gram steel ball on a certain ramp with a small incline is observed to be 2.5 cm/s^2 when the ball moves in one direction, and -1.5 cm/s^2 when the ball moves in the opposite direction.

What is the net force on the ball as it moves in each direction?
Assuming that the force of rolling friction has the same magnitude in both directions, what is the force of rolling friction on the ball?
Does the ramp slope in the positive or the negative direction?
What is the slope of the ramp?
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`q007. ** My mass is about 75 kg. In about 40 minutes, my altitude and velocity change as follows:

I start at rest on a level runway in Atlanta, accelerate to 50 m/s before beginning to rise, rise to an altitude of 10 000 meters at a velocity of 200 m/s, descend to a level runway 300 miles away which I first contact at a speed of 60 m/s, and come to rest at the other end of the runway.

This scenario naturally breaks into five intervals, one occurring on the first runway, another between the end of that runway and cruising altitude, a third between cruising altitude and the beginning of descent, the fourth between the beginning of the descent and first contact with the second runway, and the last on the second runway.

Give quantitative answers to each of the following:

What happens to my gravitational potential energy during each phase?
What happens to my kinetic energy during each phase?
What nonconservative forces act during each phase?
What total work is done by nonconservative forces during each phase?
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`q008. A certain Atwood machine has 50 paperclips on each side. The paperclips have reasonably uniform mass. A positive direction has been declared, and the following observations are made.

If one of the clips is transferred to the positive side the system remains at rest.

If another clip is transferred to the positive side the system still remains at rest.

If a third clip is transferred to the positive side, the system accelerates at 15 cm/s^2.

After restoring the system to its original state, the system remains at rest after a transfer of 2 clips to the negative side.

A third clip transferred to the negative side results in an acceleration of - 10 cm/s^2.

First answer the following:

If there was no friction involved, what acceleration would result from transferring a single paperclip, so that one side has 51 clips and the other 49 clips?
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Now, in terms of the stated data:

As a multiple of the weight of a paperclip, what do you conclude is the magnitude of the frictional force resisting the motion of the system?
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`q009. ** A 40 kg block rests on an incline which makes an angle of 37 degrees with the horizontal. The coefficient of friction between the block and the incline is mu = .5. Sketch a free-body diagram for this block, sketch x and y axes with the x axis parallel to the ramp, and estimate the x and y components of the weight of the block. Then using the sine and cosine functions, calculate these components.

Give your estimates of the x and y components, as well as the calculated x and y components of the weight.
Using the fact that the block remains in equilibrium in the y direction, determine the normal force between block and incline.
What therefore is the maximum possible frictional force between the block and the incline?
If the block is released, what will be the net force in the x direction?
What therefore will be the acceleration of the block?
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`q010. In the preceding, what coefficient of friction would be required for friction alone to hold the block stationary?

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`q011. Continuing the same situation, suppose the block is sliding up the incline, subject only to gravitational, normal and frictional forces. What would be the acceleration of the block?

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Homework:

ic_class_091026

Copy and paste this label into the form.

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

** Note: Five very basic questions have been marked **. It is suggested you do these problems first, and you should make every effort to answer as many of those questions as possible prior to the next class. Most of the remaining questions are based on or at least related to these five. **

Read Chapter 4 of the text and take notes on things you do and do not understand. I might ask for a synopsis next time.

Work through and submit q_A_17 and q_A_18. These qa's are concerned primarily with vectors, and you should find them straightforward.

URL's of qa's 10-19:

http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_10.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_11.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_12.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_13.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_14.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_15.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_16.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_17.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_18.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_19.htm

In preparation for the upcoming test, you should be sure you understand the problems and solutions in the Introductory Problem Sets 3, 4 and 5. For Phy 121 students, the test is generated almost entirely from these problems. For Phy 201 students, about 50% of the test comes from these problems.

The following will be used as sample tests (tests are included for both Phy 121 and Phy 201). It is recommended that you at least read over these tests before the next class. It is not expected that everyone will have time to work through the tests before the next class.

Principles of Physics (Phy 121) Test_1

Problem Number 1

Two objects collide and remain stuck together after collision.

One object has mass 9 kg and is moving in the positive direction at 20 m/s and the other has mass 9 kg and and moves at 16 m/s in the negative direction.

What is their total momentum, and what will be the velocity of this system immediately after collision?

Problem Number 2

You walk along level ground in a straight line from some initial point to some terminal point.

If I walk 2.37 miles to the East, then I will be directly South of your terminal point. Your terminal point will lie 3.04 miles to the North.

What angle does your path make with East?
How far did you walk?

Problem Number 3

What are x and y the components of the velocity vector obtained when we add the two following velocity vectors:

vector A, with x and y components 7.1 m / s and 3.6 m / s, and
vector B whose x and y components are 6.4 m / s and -6.2 m / s?

What are the magnitude and angle of the resultant vector?

Problem Number 4

An object with mass 15 kilograms, initially at rest, is acted upon by a force of 4650 Newtons.

If the force acts for 9 seconds, what will be KE increase of the object, based on its velocity change?
During the 9 seconds, based on the distance it travels, how much work is done by the net force on the object?

Problem Number 5

What are the magnitude and angle of a vector whose x and y components are respectively 5.8 and 7.5?

Problem Number 6

How far must an object be pushed by a force of 9 Newtons, always exerted parallel to the direction of motion, in order to gain 16 Joules of energy, if the energy gained is equal to the work done on the object?

Problem Number 7

Over an interval of .05 seconds, the velocity of an object of constant mass 3 Kg is observed to change from 7 m/s to 1.9 m/s.

Find the average force on the object using the Impulse-Momentum Theorem.
Verify your results using your knowledge of uniformly accelerated motion.

Problem Number 8

An object of mass 10 kg experiences a variable force F(t) (here F(t) indicates function notation, not multiplication of F by t; F(t) is the force at clock time t) for 2 seconds.

If the average force over this time is 9800 Newtons,

Use Newton's Second Law and your knowledge of uniformly accelerated motion to find the change in the object's velocity.
Use the Impulse-Momentum Theorem to obtain the same result.

Problem Number 9

Assuming that 12096 Joules of kinetic energy are dissipated in the process, how much kinetic energy increase should be expected as a result of a 90 Newton force being exerted over a distance of 160 meters?

General College Physics (Phy 201) Test 1

Problem Number 1

A block of mass 6 kg on an incline angled at 24 degrees above the horizontal experiences a frictional force resisting its tendency to slide along the ramp. The upper limit on this frictional force is .13 of the normal force between the block and the ramp. What force must be exerted parallel to the ramp so that the block will slide at a uniform velocity up the ramp?

Problem Number 2

The velocity of an object increases at a uniform rate from 9 m/s to 27 m/s in 6 seconds.

How far does it travel and what is its acceleration?

Sketch the corresponding velocity vs. clock time graph.

Explain the meaning of the slope of the graph and its area.

Problem Number 3

A cart of mass 1.2 kg coasts 55 cm down an incline at 4 degrees with horizontal. Assume that the frictional force is .049 times the normal force, and that other nongravitational forces parallel to the incline are negligible.

What is the component of the cart's weight parallel to the incline?
How much work does this force do as the cart rolls down the incline?
How much work does the net force do as the cart rolls down the incline?
Using the definition of kinetic energy determine the velocity of the cart after coasting the 55 cm, assuming its initial velocity to be zero.

Problem Number 4

A system consists of a cart pulled along a constant-velocity ramp by the force of gravity on a single paper clip, whose mass is much less than that of the cart, attached by a thread over a pulley with negligible friction. If the system accelerates at 4.9 cm/s², and if F = m a describes the relationship among net force F, mass m and acceleration a, give the acceleration of each of the following:

The same system but with 6 paper clips instead of one.

The same system but with a single paper clip and a cart of twice the mass.

The same system but with a single paper clip with a cart of half the mass.

The same system but with 9 paper clips and a cart of 19 times the mass.

What would be the acceleration of the same system but with a number of paper clips whose mass equals that of cart?

How would the slope of a graph of total paper clip weight vs. acceleration for the original system (for a small number of paper clips) compare with a slope of a similar graph for a system with half the cart mass, and how would it compare for the slope of a system with 9 times the cart mass?

Problem Number 5

A pendulum of mass .7 kg and length 3.17 meters is initially displaced .8242 cm in the horizontal direction from its equilibrium position. The pendulum is released from rest at this position.

How much work does gravity therefore do on the pendulum during its fall to the equilibrium position, and how much work does the pendulum do against gravity?
What therefore will be the change in the kinetic energy of the pendulum as it falls?
Using energy considerations determine the velocity of pendulum at its equilibrium position.

Problem Number 6

When masses of 45, 90 and 135 grams are hung from a certain rubber band its respective lengths are observed to be 28, 36 and 44 cm. What are the x and y components of the tension of a rubber band of length 40.31 cm if the x component of its length if 22.78722 cm?

What force directed at 149 degrees, when added to this force, will result in a horizontal net force?

Problem Number 7

Give an example of a situation in which you are given v0, a and Ds, 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 vf and a.