Physical measurements Lab #3: Projectile Motion

Objective:

To study projectile motion and determine the muzzle velocity of the PASCO mini-launcher.

Apparatus:

Pasco mini-launcher, carbon paper, white paper, meter stick, c-clamp, masking tape.

Theory:

The coordinate system used in this experiment is assumed to be at the edge of the table where the projectile (a steel ball) is given its initial speed v_o.

In general, projection angle θ and

time t can be eliminated between the

equations

to yield,

.

Note that when θ=0, the equation above simplifies further.

Procedure:

A-Measuring the muzzle velocity:

1) Clamp the projectile launcher to the tabletop using C-clamps. Set the angle of projection to zero by using the plumb line and protractor attached to the launcher.

2) Place the steel ball inside the launching tube and push it with the clear plastic rod into the first trigger locking position. At the first click, the ball is in the first firing position. Now the projectile is ready to fire. CHECK TO SEE THAT THE RANGE IS CLEAR OF ANY OBSTACLE, ESPECIALLY A HUMAN BEING!

3) Fire the projectile (by pulling the yellow string) to see roughly, where it will land. It should be about 1.25 m from the initial position. Tape a piece of paper at the point where the projectile hit. Place a carbon paper on top of it, with the inked face down. Do not tape the carbon paper.

4) Also tape a blank paper on the floor to mark the point (x = 0), which will be right underneath the projectile’s starting point. You can mark it either with the help of a plumb bob (if you have available) or a dangling meter stick. Measure the distance y as indicated in the figure above.

5) Now you are ready to fire the projectile. Fire the projectile five times (x_i, i=1,2,3,4,5) and record the distance between the plumb line and the point on the white paper ( distance x in the figure). Compute the average x.

6) Use the equation to compute the muzzle velocity v_o.

B) Projection at an angle:

7) Incline the launcher to 20.0^o, and lock it in place.

8) Fire the projectile as a practice shot to determine where you should lay the white paper.

9) Lay the white paper and the carbon paper as instructed earlier.

10) Repeat the shots five times and record in the second table. Take and average of the measured range record as x _measured.

11) Compute the expected distance (x _expt.) from with θ=20^o. Note that this will give you a quadratic equation in x. Seek help if you do not know how to solve the quadratic equation.

7) Compute the percentage difference from,

C) Maximum Range:

To find the maximum range, fire the projectile at20,25,30,35,40,45,50,55,60,65 agnles and record the range. Enter your data into

Projectile Motion NAME_______________

TABLE 1: Horizontal projection

x1(cm)

x2(cm)

x3(cm)

x4(cm)

x5(cm)

Average =x=_______________

Height of the projection position = y =_______________

Muzzle velocity v_o =________________

TABLE 2: Projection with θ=20^o.

x1(cm)

x2(cm)

x3(cm)

x4(cm)

x5(cm)

average = x_measured = _________________

x _expt. = ___________________

% Error = _____________________

Table 3:

20^o

25^o

30^o

35^o

40^o

45^o

50^o

55^o

60^o

65^o

The maximum rage occurs at______degree.