PROJECTILE MOTION

GOAL

To determine the initial velocity of a sphere fired from spring “gun”, based on the measurements of horizontal and vertical displacements of the sphere.

PREREQUISITES

R.D. Knight, Physics for scientists and engineers, chapter 6.

EQUIPMENT

Ballistic Pendulum Set

Meter Stick

Ruler

THEORY

The spring gun from the ballistic pendulum set hurls a sphere in a horizontal direction. After release the sphere exhibits what we call projectile motion. It moves in two dimensions under the influence of only the gravitational force. The force of gravity points down and is responsible for the vertical acceleration of the sphere

a_y =g=9.8 m/s². Thus, we have the free-fall motion in the vertical direction. At the same time there are no forces acting on the sphere in the horizontal direction a_x=0 and the sphere moves uniformly with the same initial velocity v_i, supplied by the spring gun. Note, that we can neglect the influence of air resistance due to relatively small initial velocity of the sphere and relatively small traveled distances.

You have to 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=v_i∙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 v_i

PROCEDURE

Position the assembled ballistic pendulum at the edge of a table or lab bench. CAUTION: Use care when operating this device. Do not stand or place hands or any part of your body in the path of the projectile.

Fire the sphere out onto a clear area on the floor to determine approximately where it will fall. Put a clear sheet of paper on the determined place.

Fire the sphere again and measure its horizontal and vertical displacements. CAUTION: Use care when operating this device. Do not stand or place hands or any part of your body in the path of the projectile once the mechanism is armed.

Repeat the measurements at least five times recording the results in the table together with relevant errors of measurements.

	R	H
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Average value

ANALYSIS

1. Calculate the average values for both measured quantities.

2. Use averages to find the value of initial velocity.

3. Using the data from your table try to estimate the accuracy with which you have found initial velocity of the sphere.

LAB REPORT

1. Write your name and list names of all your partners.

2. Write the date of experiment.

3. Write the title, goal, and list of equipment of the experiment.

4. Supply the table with your results.

5. Give the derivation of the working formula and your calculations of the sphere’s initial velocity.

6. Examine the possible sources of errors in measurements. Identify where the largest errors come from. Write a small (a few statements) essay.

7. Estimate (on the physical level) how errors of measurements are transformed in the error of calculation of sphere’s initial velocity.