FREE FALL AND TWO-DIMENSIONAL BALLISTIC MOTION
FIRST PART: FREE FALL
I. GOALS :
- The study of the motion of a ball dropped without initial velocity in the gravitational field.
- The experimental determination of the acceleration of gravity g.
- Study of the effect of the mass on the value of the acceleration g.
II. USED MATERIAL :
Two balls of different masses.
A vertical rod which supports at its upper end an horizontal arm.
An electronic counter.
A ruler graduated in millimeters. h_0
III. THEORY :
The relationship of distance versus time t and the initial velocity of a body
in free fall motion (oriented according to the y axis) is given by the relation :
y(t)-y_0=1/2 gt^2+v_0 t
If we fix the origin of the heights at the starting point of the body in free fall, i.e. y_0=0 (figure above) with zero initial velocity v_0=0 , the previous relation can be written in the form:
y(t)=1/2 gt^2
IV. EXPERIMENTAL PROCEDURE :
1. There is a vertical rod which supports at its upper end an horizontal arm.
2. At the free end of the horizontal arm, a mass m is held by a trigger between the tip and the slide by which it triggers a mechanical contact.
3. As soon as the mass is released with the trigger, the mechanical contact is cut and the electronic counter starts up.
4. The mass falls in free fall on the plate which will stop the counter. This system then allows us to measure the time t that the mass takes to travel a vertical distance y.
5. The experimental work consists in measuring the time t for several vertical distances y. The time t is taken using a digital meter.
6. For the measurement of y, use a ruler graduated in millimeters.
IV.1. Experience 1 : Follow the experimental procedure described above, using the ground metal ball m1. Fill in the table found in the technical sheet.
IV.2. Experience 2 : Repeat the previous experiment using the mass plastic ball m2.
Remarks : -The distance y is measured between the lower end of the ball and the plate.
To have good measurements and for the same height, take the average of at least two time measurements.
SECOND PART : TWO-DIMENSIONAL BALLISTIC MOTION
I. GOALS :
- The examination of a parabolic fall and the visualization of the corresponding parabolic trajectory.
- The determination of, the initial velocity of a parabolic falling projectile, the firing angle and the terrestrial acceleration g.
II. USED MATERIAL :
Mini launcher
Stainless metal ball
pulse generator
LED lamp
Webcam
III. THEORY : The range is the horizontal distance, x, between the muzzle of the mini-shooter and the impact point of the falling ball. : x(t)=(v_0 cos〖θ)〗 t (1)
where : v_0 : is the initial velocity of the ball,
θ : is the angle of the horizontal inclination,
t : is the flight time.
In the vertical direction, where the force of gravity applies,
the vertical position y(t) is expressed by : y(t)=-1/2 gt^2+〖(v〗_0 sin〖θ)〗 t+y_0. (2)
From the equation (1), we have : t=x/(v_0 cos〖θ)〗 (3)
By taking y_0=0 and inserting equation (3) into (2), we obtain the trajectory equation:
y(x)=-g/(2〖 〖cos〗^2 θ v〗_(0 )^2 ) x^2+(tgθ)x (4)
IV. EXPERIMENTAL PROCEDURE :
1. Choose on the device (mini-launcher) the same release point (to have the same initial speed) and this by placing the ball in the mini-launcher in the first position corresponding to the first click.
2. The angle of the mini launcher is adjusted to 78°. It is well fixed, don’t try to move it.
3. Start the pulse generator.
3. Follow the steps indicated and explained at the bench level.
4. Try to answer the questions on the technical sheet and report and calculate the quantities requested.