physics 1 lab
standing still on position vs time graph =
straight horizontal line
average velocity =
(change in position) / (time interval) m/s
For the position-time graph shown, sketch below it the corresponding acceleration-time graph. graph: increasing position steadily, steeper increase, then less steep than before but still increasing
0 --> hill to 1 --> 0 --> dip to negative 0.5 --> 0
how would a position graph be different if you moved faster? slower?
-faster = more distance covered, bigger/steeper slope -slower = start down closer to the zero line, smaller slope when slowing down to a stop
how would a velocity graph be different if you moved faster? slower?
-faster = start up higher (bigger velocity), when stopping there would be a steeper slope down -slower = start down closer to the zero line, smaller slope when slowing down to a stop
What is the difference between a linear and a proportional relationship?
-proportional = when "x" changes, "y" changes by the same percent when proportional -linear = a straight line, defined by y = mx + b where b = 0
describe the difference between the graph made by walking toward and the one made walking away from the motion detector
-reached the detector sooner when increasing speed -steeper slope when increasing speed -away = positive slope -toward = negative slope
How does the acceleration graph vary in time? Does this agree with your prediction? Does a constant applied force produce a constant acceleration?
-remains constant -yes -yes
How does the velocity graph vary in time? Does this agree with your prediction? What kind of change in velocity corresponds to a constant applied force?
-velocity increases over time -yes -a constant applied force results in an increasing velocity
velocity vs time graph walking towards the detector at a steady and constant rate
straight horizontal line that is negative
velocity vs time graph walking away from the detector at a steady and constant rate
straight horizontal line that is positive
object standing still
straight line, acceleration of zero
when given an acceleration graph that goes up (to positive one) then down (to negative one) then up (to 1.5) then down (to negative one) then up (to positive one) 1.) what would the force graph look like? 2.) what would the velocity graph look like?
1.) exactly the same 2.) constant increase, then a little dip down, then keeps increasing, then a little dip down, then keep going up
three graphs that represent the motion of an object whose velocity is constant (not changing)
1.) picture from previous card 2.) straight line, velocity of 1 3.) straight line, acceleration of zero
three graphs that represent the motion of objects whose acceleration is changing.
1.) s shape position graph, increasing 2.) velocity increasing then decreasing (volcano shape) 3.) acceleration decreasing constantly from 1.5 to zero
a velocity graph is given: constant increase, straight line, constant increase with over double the slope as the first one 1.) what would the acceleration graph look like? 2.) what would the force graph look like?
1.) straight line at 0.5 across, goes straight down to zero, then straight up to a straight line across at 1.5
with a graph of a constant increasing velocity 1.) what would the acceleration graph look like? 2.) what would the force graph look like?
1.) straight line at positive one 2.) straight line at positive one
An object can move in either direction along a horizontal line (the + position axis). Assume that friction is so small that it can be neglected. Which graph corresponds to the force applied to the object that would produce the motion described? 1.) The object moves away from the origin with a constant velocity. 2.) The object moves toward the origin with a constant velocity. 3.) The object moves away from the origin with a steadily increasing velocity (constant acceleration.)
1.) zero, straight line 2.) zero, straight line 3.) straight line at positive one
acceleration graph: The car moves away from the origin, increasing its speed at a stready rate twice as the one that the top acceleration-time graph describes.
goes from a straight line on .5 to 1
can you tell which object is "ahead" in a velocity time graph?
Can't tell. Velocity graph does not show the starting positions.
is it possible for an object to move so that it produces an absolutely vertical line on a velocity-time graph? explain?
No!, a vertical line like this implies the object is moving an infinite distance in a zero time interval which means that the object is moving at an infinite speed; even light has a finite speed so it is impossible
what explains the previous question?
Newton's second law. -The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
The mathematical relationship that you have been examining be- tween the acceleration of the cart and the applied force is known as
Newton's second law. In words, when there is only one force acting on an object, the force is equal to the mass of the object times its acceleration.
Do your force probe readings correspond to your spring scale readings? Can you use the force probe to make reasonably accurate force mea- surements?
No No
acceleration graph: The car starts from rest, and moves toward the origin, increasing its speed at a steady rate.
graph: acceleration of negative one, straight line
acceleration graph: The car is moving away from the origin at a constant velocity.
graph: acceleration of zero, straight line
You have seen that pulling more rubber bands to the same length requires a larger pull. To be more precise about the pulls and pushes you are applying, you need a device to measure forces accurately.
The electronic force probe is designed to do this.
acceleration graph: The car is moving toward the origin at a constant velocity.
graph: acceleration of zero, straight line
acceleration graph: constant increase of change in position over time
graph: acceleration of zero, straight line
acceleration graph: The car starts from rest, and moves away from the origin, increasing its speed at the steady rate.
graph: positive acceleration, straight line
the (average) slope of an object's velocity-time graph is also
the (average) acceleration of the object
An object moving along a line (the + position axis) has the acceleration-time graph below. Choose the answer below that best describes how the object might move to create this graph if it is moving away from the origin graph: positive acceleration, straight line
The object would need to move away from the origin with a constantly increasing velocity
y is proportional to x.
This is a special case of a linear relationship where y = mx, and b, the y intercept, is zero. -graph: positive slope through zero
lab 3
force and motion
How did the larger force applied to the cart compare to that with the smaller force in Activity 2-2?
force applied increased with the larger force/mass
The toy car moves away from the origin, speeds up, and then slows down.
force graph that starts at zero, goes up to about 0.5 and then starts to decrease then goes down to negative 0.5
The toy car moves away from the origin with a steadily decreasing velocity (a constant acceleration).
force graph with a straight line at negative 1
A toy car can move in either direction along a horizontal line (the + position axis). Assume that friction is so small that it can be ignored. Pick the graph of the applied force that would keep the car moving as described. The toy car moves away from the origin with a constant velocity.
force graph with straight line at zero
The toy car moves toward the origin with a constant velocity.
force graph with straight line at zero
Suppose you grasp the force probe hook and move the cart forward and backward in front of the motion detector. Do you think that either the velocity or the acceleration graph will look like the force graph? Is either of these motion quantities related to force? (That is to say, if you apply a changing force to the cart, will the velocity or acceleration change in the same way as the force?) Explain.
acceleration graph will look like the force graph yes, acceleration (F=ma)
For the position-time graph shown, pick the corresponding acceleration-time graph. graph: picture
acceleration graph would be a straight line with an acceleration of 1
Suppose that you have a cart with very little friction and you pull this cart with a constant force as shown below on the force-time graph. Sketch on the axes below your predictions of the velocity-time and acceleration-time graphs of the cart's motion.
acceleration is constant because force is constant, and a constant acceleration means an increasing velocity
when velocity remains constant
acceleration remains at zero
a velocity vector is represented by
an arrow pointing in the direction of motion (positive or negative) -length of the arrow is proportional to the speed
Why is it necessary that a force probe be calibrated?
because there is a slight variance between sensors, this improves repeatability and helps neutralize drift
During the pulley attachment experiment: After the cart is moving, is the force that is applied to the cart by the string constant, increasing, or decreasing? Explain based on your graph.
constant -graph shows a straight line
graph that definitely indicates an object has reversed direction
constant decreasing velocity that starts at 2 and goes to negative 2
velocity vs time graph
describes how fast and in what direction you are moving
We are interested in the nature of the mathematical relationship between the reading of the force probe and force (in rubber band units). This can be determined from the graph by
drawing a smooth curve that fits the plotted data points. Some definitions of possible mathematical relationships are shown below. In these examples, y might be the force probe reading and x the number of rubber bands.
to figure out which is moving faster on a position graph
find out which one covers more distance in the same amount of time
Does there appear to be a simple mathematical relationship between the acceleration of a cart (with fixed mass and negligible friction) and the force applied to the cart (measured by the force probe mounted on the cart)? Write down the equation you found and describe the mathematical relationship in words.
if y = mx + b and y is zero (because of the zero slope), then x would be zero -the bigger the force = the bigger the acceleration -m is slope -b is the point where the line crosses the y axis
"ahead" on a position graph means
it starts at a higher number/farther away from the detector
How does the combined force of two rubber bands compare to what you felt when only one rubber band was used?
it took a greater force to pull the 2 rubber bands compared to the one
velocity graph: The car moves away from the origin, increasing its speed at a stready rate twice as the one that the top velocity-time graph describes.
just make it steeper
describe the difference between the graph made by walking away slowly and the one made by walking away quickly
more distance was covered in the same amount of time when increasing the speed
distance vs time graph towards the detector
negative slope
does a velocity graph tell you where to start
no because it is measuring speed
Your graph relates two different ways of measuring force,
one with standard stretches of different numbers of rubber bands (rubber band units) and the other with a force probe. Such a graph is called a calibration curve and is used to compare measurements of quantities made with two different measuring instruments. You could use it to convert forces measured in force probe units to rubber band units, and vice versa.
If you increased the force applied to the cart by a factor of 10, how would you expect the velocity-time graph of the cart's motion to change? Explain based on your graphs.
our velocity would increase because out graphs showed an increase in velocity with increasing mass
distance vs time graph walking away from the detector
positive slope
velocity graph: The car is moving away from the origin at a constant velocity.
positive velocity
how should the position and velocity graphs look if you move the cart at a constant velocity away from the motion detector starting at the 0.5 mark?
positive velocity and increasing position -straight line in the velocity graph -positive slope in the position graph
velocity graph: The car starts from rest, and moves toward the origin, increasing its speed at a steady rate
pretend the point starts at zero and is going negative
Suppose you stretched a rubber band to your standard length by pulling on it. Now you want to create a force six times as large. How could you create such a force?
produce an acceleration 6 times as large
You can use your measurements to define a
quantitative force scale. You might call it the "rubber band scale," or give it yours or your part- ner's name. Whenever the force probe has the reading corresponding to the pull of one rubber band stretched the standard length, the force is equivalent to one "rubber band," or one "Mary" or one "Sam." Any larger force can be measured as some number of these units.
velocity
rate of change of position with respect to time -quantity that takes into account your speed (how fast you are moving) and also the direction you are moving
when you examine the motion of an object moving along a line, the direction the object is moving is indicated by the
sign (positive or negative) of the velocity
An object moving along a line (the + position axis) has the following acceleration-time graph. Which of the following velocity-time graphs is corresponding to the motion that the object is moving toward the origin graph: positive acceleration, straight line
starts at negative 2 or so and increases steadily to zero
If you increased the force applied to the cart by a factor of 10, how would you expect the acceleration to change? How would you expect the acceleration-time graph of the cart's motion to change? Explain based on your graphs.
the acceleration graph would also change by a factor of 10 -the line on the graph would increase by a factor of 10 and look similar to the force vs time graph
How did the acceleration of the cart with the larger force compare to that caused by the smaller force in Activity 2-2? Did this agree with your prediction? Explain.
the acceleration increased with the larger force -yes
average acceleration during a particular time interval is defined as
the average rate of change of velocity with respect to time-the change in velocity divided by the change in time
Since forces are detected by the computer system as changes in an electronic signal, it is important to have
the computer "read" the signal when the force probe has no force pushing or pulling on it. This process is called "zeroing." Also, the electronic signal from the force probe can change slightly from time to time as the temperature changes. Therefore, if it is possible to zero your force probe, it is a good idea to do so with nothing attached to the probe before making each measurement.
Physicists have defined a standard unit of force called
the newton, abbreviated N. For the rest of your work on forces and the motions they cause, it will be more convenient to have the force probe read directly in newtons. Then the forces you measure can be compared to forces anyone else measures. Most spring scales have already been calibrated in newtons. All you need to do is to calibrate the force probe to read forces in newtons by using the spring scale to input standard force measurements.
intersection on position graphs means
the objects are at the same position at the same time
slope of the curve
the rate of change of a quantity graphed with respect to time
acceleration
the rate of change of velocity with respect to time
acceleration
the rate of change of velocity with respect to time change in velocity / change in time = a
kinematics
the study of motion and its mathematical and graphical representation -position vs time graph -velocity vs time graph -acceleration vs time graph
Based on your observations, does it appear that there is a mathematical relationship between either applied force and velocity, applied force and acceleration, both, or neither? Explain.
there is a relationship between applied force and acceleration because F = ma
intersections in a velocity graph mean
they are moving at the same speed at that moment in time.
velocity graph: The car is moving toward the origin at a constant velocity.
this only it is negative one not positive
Suppose you applied a force with a stretched rubber band one day, and several days later you wanted to feel the same force or apply it to some- thing. How could you assure that the forces were the same? Explain.
use tools to measure force -use a rubber band with the same mass and use the same acceleration
line of best fit
v = b + mt
finding final vector quantity: velocity
vector velocity at final second - vector quantity at initial second
with the previous question, what would the 3 graphs look like if the object was twice as large
velocity = steeper slope acceleration = straight line at positive two force = straight line at positive two
velocity graph and an acceleration graph that could describe the motion of the same object during the time shown
velocity = straight line of 1 acceleration = straight line of zero
For the position-time graph shown, pick the corresponding velocity-time graph. graph: picture
velocity graph would be a flipped version of this (negative)
For the position-time graph shown, pick the corresponding velocity-time graph graph: increasing position steadily, steeper increase, then less steep than before but still increasing
velocity starts at 0.5, quick increase to 1.5 (hill), then down to 0.25
displacement found on a velocity graph =
velocity x time
y is a linear function of x,
which increases as x increases according to the mathematical relationship y = mx + b, where b is a constant called the y intercept. -graph: positive slope above zero
y is a function of x,
which increases as x increases. -graph: squiggle line s above zero
These graphs show the differences between these three types of mathematical relationship.
y can increase as x increases, and the relationship doesn't have to be linear or proportional. Proportionality refers only to the special linear relationship where the y intercept is zero, as shown in the example graph on the right
Attach one end of the rubber band to something on the table that can't move. Also attach the meter stick to the table. Now stretch the rubber band so it is sev- eral centimeters longer than its relaxed length. Does it always seem to exert the same pull on you each time it is stretched to the same length?
yes
Do side-by-side rubber bands provide a convenient way of accurately reproducing forces of many different sizes? Explain.
yes because the more force you apply to the rubber bands the farther they will stretch, this way you can compare them
Does either graph—velocity or acceleration—resemble the force graph? Which one? Explain how you reached this conclusion.
yes, the acceleration graph, because at points where acceleration increased, so did the force
velocity vs time graph standing still
zero
