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 v1i and v2i, collide with each other and after the collision have velocities v1f and v2f. Explain in words what each term in this equation represents and tell how this equation expresses the idea of conservation.

 

m1 v1i+ m2 v2i = m1 v1f + m1 v2f

 

 

 

 

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 Reading (Plastic ball)= ____________

Best Reading (metal ball)= ____________

 

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 = 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 = vf so the average velocity is vav =_______

 

 

19) d = vavt so:

t = d/v = time to fall = ______________________

 

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

(from step 14)

 

plastic d1 =vt = __________________ = _______________________

(work) (answer)

 

metal d2 =vt = __________________ = _______________________

(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.