Projectile Motion

Theoretical description:

After the sphere is released from the ballistic pendulum set it hurls in a horizontal direction. At its release it exhibits projectile motion. Under the influence of only gravitational force the sphere moves in two dimensions. The vertical acceleration of the sphere ay =g=9.8 m/s2 the force of gravity is responsible for the acceleration as it points down. Thus, we have the free-fall motion in the vertical direction. We also know that horizontal velocity is constant therefore our acceleration in the x direction is ax=0 and the sphere moves uniformly with the same initial velocity vi, supplied by the spring gun. Since it is a small initial velocity and small distance traveled we can also ignore air resistance.

Derivation of the working formula of the sphere's initial velocity:

We measure the horizontal displacement of the sphere R - the horizontal distance between the point at which sphere lost the contact with spring and the point where sphere hit the floor

R=vi∙t

where t is the elapsed time. To determine the point at which sphere hit the floor it is handy to use clean sheet of paper. The sphere leaves a noticeable trace on the paper which allows you not only to determine the final point of travel but gives you possibility to estimate the accuracy of your measurements.

The time of flight t is governed by another quantity you have to measure - the vertical displacement of the sphere H

H=½gt2

H has to be measured as a vertical distance between the point of release and the point where the sphere hit the floor. Think about this distance carefully - you have to determine which point of the sphere you have to follow to take into account the final size of the sphere correctly.

Eliminating the time from two equations you end up with your working equation for the initial velocity vi

Procedure:

At the edge of the or lab bench position the assembled ballistic pendulum.

To determine where it will fall put a clear sheet of paper of where the sphere will land.

Measure the vertical and horizontal displacement of the sphere

Record your results in the table below and repeat at least five times.

Analysis:

Enter all measured data in the table below.

Calculate the average values for both measured quantities.

Calculate the standard deviation of both measured quantities.