A red ball slides off a table as shown in the animation (position is in meters and
time is in seconds). Ignore air friction. The ball hits the other
table after moving an x displacement you will measure by clicking on the ball's
center. Note the ball leaves the table at the
exact value of 1 second. Times are exact, so there is no limitation of sig
figs in your time value. Remember to ALIGN, CLICK and drag a little to find
the x and y coordinates which you will subtract to get displacements.
When you place your cursor in the motion area, the arrow turns into a
cross. Align the cross with the crossed lines at the center of the circles
marking the ball location. Once aligned, when you click you will see
x and y coordinates in a small YELLOW BOX at the lower left hand side of
the motion area. The coordinates are in meters and are precise to
the 1/100 place's or to 1 cm-there is an uncertainty in a single
measurement affecting the 1/100's place.
Start
(Reference: Ch. 1,3 and 4. )
Question 1
What is Vx just before the collision ? To find this quantity,
all you need is the horizontal displacement, or change in x, since
you are already given the change in time t on screen. Please
measure the ball's change in x, or x displacement, four times and take the average of
the four measurements. Assume the measurements are in meters and are
precise to the 1/100 place--- there is an uncertainty in a single
measurement affecting the 1/100's place. Fill in the table below with the
measurements by shooting the ball 4 times and measuring the x displacement each
launch. . Note: Your measurements are extremely precise so there is going to be
no variation (zero spread) if you measure the ball location correctly and
carefully. I want you to confirm this reproducibility. Just center the cursor
cross hairs carefully over the crossed lines defining the ball's center and
location on screen at two spots: just as the ball leaves the table and at the
point of collision. Note the ball leaves the table at the exact value of
1 second. So there is no limitation of sig figs in your time value.
(Note the number of significant digits in the value of the
X-component of velocity you compute. For example, when you compute the average x
displacement, the number of sig figs will increase, even if the data points are
identical, affecting the number of sig. figs in the computation of Vx.
However, there is a limitation on the number of sig. figs from the
inherent uncertainty in a single measurement assumed to be in the 1/100's place
when that uncertainty is rounded to 1 sig. fig. ) If you
measure carefully, all your x and y displacement values will
be the same. Please also measure 4 y displacement values for the next
round of thinking below.
| first x | second x | difference |
| average difference |
||
Vx = ____________________________
SHOW WORK, BOX ANSWER
| first y | second y | difference |
| average difference |
||
Question 2
What is Vy just before the collision ? Find Vy
by using the average y displacement and the time of flight t on screen.
Compare your result with the value predicted by theory. Compute the percent
error between your result and the value predicted by Newton and inferred by
Galileo, Vy = -g*t using the time of flight for t. Assume
g = 9.80 m/s2
( 3 sig.fig.) . (Note the significant digits in the two
values of the Y-component of velocity you compute. For example, in the first
case, when you compute the average y displacement, the number of sig figs
will go up by one, even if the data points are identical, affecting the
number of sig. figs in the computation of Vy. However, there is
a limitation on the number of sig. figs from the inherent uncertainty in a
single measurement assumed to be in the 1/100's place when that uncertainty is
rounded to 1 sig. fig. ) Abide by sig fig rules for subtraction and division in computing the
percent error.
SHOW WORK, BOX ANSWER
Question 3
What is the speed just before the collision? Use your values of Vx
and Vy computed in 1 and 2. Review Ch. 1, 3 and 4. Abide by sig
fig rules for multiplication, addition, and other operations in computing
the the speed.
SHOW WORK, BOX ANSWER
Question 4
What is the magnitude of the angle the velocity vector makes with the
horizontal just before the collision? Abide by sig fig rules for the
mathematical operations required to compute the angle.
SHOW WORK, BOX ANSWER
QUESTION 5
EXPRESS THE FINAL VELOCITY IN TERMS OF STANDARD CARTESIAN UNIT VECTORS "i" and "j"; SEE CHAPTER 1. Note unit vectors have magnitude 1.
Unit vector "i" points in the positive x direction and "j" points in positive
y direction
QUESTION 6 In the range of time (0 SEC., 1.0 SEC ), what is the net force on the ball? EXPLAIN.
QUESTION 7 In the range of time (1.0 SEC., 1.4 SEC), what is the
direction and magnitude of the net force on the ball? HINT: ASSUME THE BALL
MASS IS 2.00 kg. EXPLAIN.