Physics 121, Physics 201 Class 070822
Address for syllabus: http://vhmthphy.vhcc.edu/ > Physics I > homepage > Info > (look under in-class section and click on syllabus for your course)
Text: Giancoli Physics text, latest edition (earlier editions can also be supported)
Measure the washer: Measure the inner and outer diameters of your washer.
How did you measure the diameter?
What is the best way to measure the diameter using the materials provided?
How accurately do you think the diameter could be measured using these materials (e.g., to within what percent error do you think you could measure the diameter)?
What is the maximum measurement you can get and what is the minimum for the outer diameter of the washer?
What is the percent difference between these measurements?
Construct a pendulum and observe its period: Construct a pendulum and indicate the measurements you used to determine its length from the knot in the string to the center of the washer.
Determine as accurately as possible how long it takes the pendulum to complete a small swing. 'Small' means that the amplitude of the motion is not greater than .1 of the length of the pendulum.
The period of the pendulum is the time required to swing from one extreme position to the other and back.
Keep the details of your measurements in your lab notebook but on your initial sheet report diameter, length and period.
Standard Assignment for Every Class: In addition to other assignments, for every class come in with either a good question or a statement that you know everything. A good question consists of a statement of a situation or problem and a summary of what you do and do not understand about it.
Request your access code: http://vhmthphy.vhcc.edu/ > General Information and scroll down to Request Access Code. Fill out and submit.
Instructor's email address: dsmith@vhcc.edu
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Physics I Class 070824
Length vectors on the coordinate plane; definition of a vector:
Angles are measured from the positive x axis, in the counterclockwise direction.
The length vector for a pendulum is the vector from the fixed point (the point at which the end of the string is attached) to the center of the pendulum mass.
When the pendulum hangs at equilibrium its length vector is along the negative y axis, at 270 degrees.
The length vector reported by one student had length 28 units; so the corresponding length vector is 28 units at 270 degrees. This vector is represented by an arrow of length 28 units, originating at the origin and directed at an angle making 270 degrees with the positive x axis.
A vector is a quantity with a magnitude and an angle.
Sketch the length vector for your pendulum when it was at its maximum displacement from equilibrium: Sketch your pendulum at the point where it is has achieved its maximum displacement from equilibrium, as experienced during your observation of 'small' swings.
On another set of axes sketch the length vector for your pendulum and estimate the magnitude and angle of that vector.
One estimate is a magnitude of 28 units at an angle of 290 deg. The length vector would originate at (0, 0) and would extend 28 units (to scale) in the direction 290 deg (into the fourth quadrant, closer to the y axis than to the x axis).
Sketch the force vector representing the action of the tension in the string on the washer, at the equilibrium position: The force vector represents the tension of string acting on pendulum mass (tension vector).
Sketch the washer and center an x-y coordinate system at the center of the washer, with the x axis representing horizontal and the y axis representing the vertical direction. Assuming the pendulum hangs at its equilibrium point, sketch the vector which represents the tension force acting on the washer.
The gravitational force represents action of gravitational pull exerted on the mass by the Earth. Sketch the vector which represents the gravitational force acting on the washer.
In your sketch the tension vector should be straight up and the gravitational force straight down, both along the vertical axis.
Tension force arises because gravitational force stretches the thread a bit.
Since the washer is not accelerating, the net force on it is zero. The only forces acting in the vertical direction are the gravitational and tension forces. Since the net force is zero, these forces must be equal and opposite.
The thread's length changes in response to the gravitational force and inertial effects until its tension comes into balance with the gravitational force.
Sketch the force vectors away from equilibrium and consider the effect of the horizontal component of the tension: Now sketch the pendulum when it has swung as far as it will go out to the right, away from equilibrium. Sketch the tension and gravitational forces in this position.
The tension force is parallel to the string, so if the pendulum is pulled to the right of the equilibrium position the string will be up and to the left of the washer. The tension, which must pull in the direction of the string, therefore pulls the washer up and to the left.
Though the tension is a single force, it can be regarded as the resultant of two forces, one up and one to the left. The further the pendulum is from equilibrium, the greater the proportion of the force force which is directed to the left. As the pendulum swings back toward equilibrium, the leftward component of the force decreases.
Pendulum speed builds in response to this leftward component of the tension force. Though the leftward component decreases as the pendulum swings toward equilibrium, its effect is to speed the pendulum up.
After the pendulum has swung through its equilibrium position, it moves to the left of the origin and the tension force now has a rightward component. This component is in the direction opposite motion, so it serves to slow the pendulum as it swings out to the left. The further the pendulum swings out to the left, the greater becomes the rightward component of the tension force, and the more quickly the pendulum loses speed.
Eventually the pendulum comes to rest, and starts swinging back toward equilibrium, again in response to the rightward horizontal force.
The motion of the pendulum will cycle in this manner, with the horizontal component of the tension force always pulling it in the direction of the equilibrium position, slowing the pendulum as it swings away from equilibrium and speeding it up when it swings back toward equilibrium.
The terms resultant and component have specific definitions we will study later in the course.
Sketch the marble and incline, and the forces acting on the marble as it rolls down the incline: Sketch the marble and incline, and the forces exerted on the marble when my finger is removed. Assume that there is no significant frictional force (this really isn't so, but for now assume it anyway; we'll deal with friction later).
The gravitational force is straight down. (note the 'weight' is another word for the gravitational force on an object)
That's not the only force, because the incline is 'in the way' of the gravitational force.
The incline bends and/or compresses in response to the gravitational force. Just as the tension in the string arises in response to the gravitational force on the washer, the incline has an elastic response to the weight of the ball. This elastic response consists of a force directed perpendicular to the incline. We call this force the normal force. The word 'normal' means 'perpendicular to'.
The normal force exerted by an incline cannot be vertical unless the incline is horizontal (in which case we wouldn't call it an 'incline'). So the normal force has a horizontal component.
The gravitational force exerted on the ball is however vertical, with no horizontal component. Since there is nothing to oppose the horizontal component of the normal force, the ball is accelerated by this horizontal component. And that's why it rolls downhill.
If the incline is straight, then its angle does not vary as the ball rolls down the incline, and neither does the angle of the normal force vary. The horizontal component of the normal force is constant as the object travels down the incline, unlike the pendulum, in which the horizontal force decreases as the pendulum approaches the equilibrium position.
Always modify the word 'velocity': 'Velocity' is usually a bad word to use by itself; for now, assume that this word always has to be modified.
If you divide the 30 cm length of the incline by the 2 seconds it took the ball to roll the length of the incline, you get 30 cm / (2 sec) = 15 cm / sec. You probably want to call this the 'velocity' of the ball, but the velocity of the ball is constantly changing as it rolls down the incline. So you can't just say 'the velocity of the ball is 15 cm/sec'.
What you are actually calculating when you divide the displacement by the time required for that displacement is the average velocity of the ball. On this interval, the ball also has an initial velocity (if you release it from rest the initial velocity is 0) and a final velocity. If the velocity of the ball continually increases on the incline its average velocity will be somewhere between its initial and final velocities.
Average velocity might and might not be equal to the average of initial and final velocities: You might think that the average velocity would be the average of the initial and final velocities. For the ball on the incline you would be right. For the pendulum you would be wrong.
If a graph of velocity vs. clock time is a straight line, then the average velocity over any interval is the average of the initial and final velocities over that interval.
If a graph of velocity vs. clock time is a curve which is concave downward, then the average velocity over any interval is greater than the average of the initial and final velocities over that interval. (If concave upward then it's less).
If the concavity of the curve changes over the interval, then it's possible that the average velocity is equal to the average of initial and final velocities, but over most intervals this will not be the case.
If the net force acting on the object is constant, the graph of velocity vs. clock time is a straight line. If the net force isn't constant, then the graph of velocity vs. clock time is not a straight line.
Remember that the horizontal component of the pendulum string tension changes from point to point, so the net force on the pendulum isn't constant and its v vs. t graph is not a straight line. For a pendulum you can't expect the average velocity over an interval to be the average of the initial and final velocities over that interval.
However the horizontal component of the normal force exerted by the incline on the ball does not vary. So the v vs. t graph for the ball will be a straight line. For a ball rolling down a uniform incline, if friction and air resistance are negligible, you can expect the average velocity over an interval to be the average of the initial and final velocities over that interval.
If the graph of v vs. t is a straight line, then the average velocity over an interval occurs at the midpoint of the interval and is equal to the average of the initial and final velocities on that interval.
Physics I Class 070827
When submitting questions you need to tell me what you do and do not understand. About half the class is explaining both what they do and do not understand. I'm getting a lot of questions about what people don't understand, the questions do not always explain what you do understand.
Get your access codes so I can start posting this stuff to your page. Deadline is Tuesday at 5:00 p.m.. http://vhmthphy.vhcc.edu/ > General Information, scroll down to 'Request Access Code'.
Using one domino on its side, a 2-ft ramp, a pendulum and and a large marble, determine as accurately as possible the pendulum length and the number of cycles required for the ball to travel down the ramp.
Repeat, using a different pendulum length.
Report in the following format:
Additional report: If you roll the ball down the ramp and off the edge, allowing it to fall to the floor, what is its horizontal range (relative to a straight drop from the edge of the ramp)?
The period of a pendulum of length L is
where T is in seconds when L is in cm.
Analysis of experiment:
Using the above formula for T and your data, determine the period of each pendulum you used.
Using the period determine from your data the time required for the ball to roll down the ramp.
Using the time required determine the average velocity of the ball on the ramp (just divide displacement by the time required).
Graph the velocity vs. clock time for the ball rolling down the ramp. Locate the average velocity on the graph. Determine the final velocity. Assume that the graph is a straight line and that average velocity is halfway between initial velocity and final velocity.
What is the slope of each graph?