# Projectile Motion

Classical Physics

3 . Projectile Motion

Objectives:

Students will measure the maximum height H and the range R of a projectile motion. They will study the effect of the shooting angle on H and R. Material used:

4 rulers, track, metallic ball, landing track, A4 white paper, red carbon paper, timer + supply, gun + protractor.

Theory:

A projectile is an object upon which the only force acting is gravity. There are a variety of examples of projectiles: an object dropped from rest is a projectile (provided that the influence of air resistance is negligible), an object thrown vertically upwards is a projectile (provided that the influence of air resistance is negligible), and an object thrown upwards at an angle is also a projectile (the same assumption). A projectile is any object, which once projected, continues its motion by its own inertia and is influenced only by the downward force of gravity.

By definition, a projectile has only one force acting upon - the force of gravity. If there were any other force acting upon an object, then that object would not be a projectile. Projectiles can be launched both horizontally and vertically, and they have both horizontal and vertical velocity and horizontal and vertical displacement.1

If a body of mass m moves in a constant gravitational field (gravitational force m.g ), the motion lies in a plane. The maximum height of projection H is obtained as a function of the angle of projection θ:

2

v0

H=

sin 2 (θ )

2g

And the maximum range R is:

2

v0

R = sin (2θ )

g

A steel ball is fired by a spring at different velocities and at different angles to the horizontal. The relationships between the range, the height of projection, the angle of inclination, and the firing velocity are determined.

1

http://library.thinkquest.org/27948/projectile.html

1

Lebanese American University

Classical Physics

Fig. 1: Experimental set up for measuring the range in the projection of a body at an angle to the horizontal.

H

R

Setup and procedure:

1. The gun is adjusted so that the protractor reads 90o and the ball is fired upwards and is caught in the hand. The support base adjusting screws are turned until a vertical projection is obtained.

2. The initial velocities of the ball corresponding to the three tension stages of the firing spring can be determined using the speed measuring attachment and digital counter. 3. To mark the points of impact, the recording strip is secured to the bench with adhesive tape. It is best to measure the long ranges before the short ones and to mark the primary impact points with a felt pen.

4. The range – or the distance from the gun to the landing point – is checked with the meter scale. An empty box can be placed behind the bench to catch the balls. 5. To measure the height of projection the meter scale is clamped in the barrel base and moved parallel to the plane of projection. The heights of projection can be determined quite well by the eye.

Record your results in the Lab Report section.

2

Lebanese American University

Classical Physics

Grade:

Experiment 3

Projectile Motion

Names:

____________________

Date: ____________________

____________________

The distance between the gun and the landing track is:

D=

The length between the light barriers is:

L=

The height of the lending track is:

Y=

How do you calculate the initial velocity? (Explain)

Fill in the table below:

θ

V0

(

H

)

(

R

)

(

)

V02 . sin 2 (θ )

90o

75o

60o

45o

30o

15o

3

Hth

(

Rth

)

(

)

% error

on H

% error

on R

Lebanese American University

Classical Physics

1. Analyze the above results and comments on the sources of errors in your experiment.

2. Which angle gives you the greatest range (for the same initial speed)?

3. Which angle gives you the greatest maximum height (for the same initial speed)?

4. Sketch...

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