Spring 2006 Name___________________________

Projectile
Motion

Conservation
of Energy, Conservation of Momentum.

Read
this entire lab and complete steps 1 through 7 before coming to lab class. (NOTE THAT QUESTION 7 is ON THE NEXT PAGE AND
THAT YOU MUST HAVE AN EQUATION WRITTEN IN QUESTIONS 12 AND 16!)

Object:
Use the laws of Conservation of Energy and Conservation of Momentum to
calculate the speed of a ball shot from a spring-gun.

Calculate
the range of the ball when shot as a projectile.

Read
pages 67-76 in your textbook.

1)
Write the principle of the conservation of linear momentum.

2)
The following equation represents the conservation of momentum when objects of
mass m1 and m2, which initially have velocities of
v_{1i} and v2i, collide
with each other and after the collision have velocities v_{1f} and v_{2f}. Explain in words
what each term in this equation represents and tell how this equation expresses
the idea of conservation.

m_{1} v_{1i}+ m_{2} v_{2i} = m_{1} v_{1f} + m_{1} v_{2f}

Copy
this equation into the blank on part 14 of this experiment.

3)
What is kinetic energy? (explain in words and give two examples, i.e. book
falling from table, etc.).

1.

2.

4)
Write the equation, which is used to calculate potential energy. Explain what
each letter represents.

5)
Write the equation for kinetic energy, explaining what each letter represents.

Read
step 15, then proceed with question 6.

6)
Set the formula for potential energy equal to that for kinetic energy and solve
for the velocity. (Assume that the masses for both objects are equal.) **Write your answer below and also in steps
12 and 16.**

7)
Use the equation you developed on question 6 to calculate the velocity of an
object after it has fallen 3 meters.

When
you arrive in class:

8)
a) Record the mass of the plastic ball mB1 = ___________________

b) Record the mass of the metal ball mB2 = ___________________

9)
Record the mass of the pendulum MP = _______________

When
the ball is shot into the pendulum the pendulum has a velocity VP just after the ball strikes it. We
will later use the law of conservation of energy to calculate V, starting with
the height to which the pendulum rises. The height is determined as follows:

10)
Shoot each ball into the pendulum several times, recording the angle at which
the pendulum stops each time (if the ball falls out of the pendulum. Do not
include that reading in your list).

a)
Plastic ball _______ _______
_______ _______ ______
______

a)
Metal ball _______ _______
________ _______ ______
______

Best

Best

11)
Hold the pendulum at the angle selected as representing the best reading and
measure the height of the pendulum.

h = average highest point - starting point

a) h
= ___________ - ____________ = __________________ (Plastic)

(at angle)
(lowest) (change in height)

b) h
= ___________ - ____________ = __________________ (metal)

(at angle) (lowest)
(change in height)

12)
Using the conservation of energy, we find that the algebraic formula for the
velocity necessary to cause a rise in height h is: v =

__________

a) plastic VP1 = Write Eq. here

b)
metal VP2 =

13)
Using the formula from step 12, and the height measured in

step
11, calculate VP.

a) plastic VP = __________________ =
__________________

(work) (answer)

b) metal VP = __________________ =
__________________

(work) (answer)

(This is the velocity of the ball and the
pendulum, just after the ball strikes
the pendulum.)

14)
We are now going to use the law of conservation of momentum to calculate the
speed of the ball before it hits the pendulum.

The
general equation for the conservation of momentum during the collusion of two
objects is:

_______________________________________________________________

(Write equation here)

In
our special case this equation becomes:

mv + MVI = mV + MV, VI = 0

mv +
(M x O) = (m + M)V

mv = (m + M)V

v = [(m+M)V]/m

putting
in our numbers, we calculate the speed of the ball before it hits the pendulum
as

plastic vB1 = _______________________________ =
____________________

(Show
work here) (answer)

metal vB2 = ________________________________
= ____________________

(Show
work here) (answer)

15)
We will now use the principle of the conservation of energy to calculate how
far the ball will travel before striking the floor, when shot horizontally at a
known height (H) from the floor.

To
find the distance the ball will travel, we must first find how long it will
stay in the air. The problem will then be easy because d = v x t and as we
already know v, d can then be calculated.

To
find t (the time the ball is in the air) we remember that an object shot
horizontally requires the same length of time to reach the ground as one, which
falls straight down.

We
will begin by calculating the velocity with which the ball, or any object
falling from a height (H) strikes the floor.

From the conservation of energy

Potential energy = Kinetic energy

mgH = ½ mv2

16)
Solve the equation for v, the velocity with which an object dropped from a
height H takes to reach the ground. find the algebraic relation for v.

v = __________________

(Write equation here)

17)
Use measured height of the gun above the floor H = ________

in
the equation from part 15 to calculate the velocity with which the ball strikes
the floor.

v =
______________________________=__________________

(work) (answer)

18)
Considering that the ball started from rest, (VI = 0) and suffers a constant
acceleration until it strikes the floor, the average vertical velocity is half
of the final velocity.

the average vav = ½ vf so the average velocity is vav =_______

19)
d = vav×t so:

t =
d/v = time to fall = ______________________

20)
The distance to ball travels in the air should be d = v×t so v = horizontal velocity of the
ball when it leaves the gun

(from
step 14)

plastic d_{1} =v×t = __________________ = _______________________

(work) (answer)

metal d_{2} =v×t = __________________ = _______________________

(work) (answer)

21)
Shoot the gun five times and measure the average distance the ball was in the
air.

Plastic __________ __________
__________ __________ __________

Average = ___________

metal __________ __________
__________ __________ __________

Average = ___________

22) Total distance traveled = distance in
front of table + distance on table

a) plastic ball dmeasured =

b) metal ball dmeasured =

22)
Calculate the percentage difference between the calculated distance (step 21)
and the measured distance (step 20)

dmeasured - dcalculated

----------------------- x 100
=

dmeasured

Show
your work

% diff (plastic) = ______________ =

% diff (metal) = ______________ =

For
which ball did the calculations and measurement come out closer?

Why
do you think this ball gave the better results?

Tell what you believe to be the sources of
error in this experiment and **what could be done to improve the results.**

This
is a required question. Tell what you
believe to be the most important thing you learned in this experiment.