Kinematics in 2-Dimensions

EC PhysicsName ______

Kinematics in 2-Dimensions

Projectile Motion

A medieval trebuchet by Kolderer, c1507

Reading Assignment:

Chapter 7, Sections 7-2 and library and Internet research

Introduction:

In medieval days, people had a very practical knowledge of projectile motion. They may not have understood the exact trajectory that a projectile would take, but by practice they could place a projectile on a target consistently from a distance of well over 200 yards. During a long siege of a castle, it was not uncommon to hurl bodies of animals (and yes, captives) back into the besieged castle’s water supply (an early form of biological warfare). Similarly, a modern day hunter does not need to know the actual path that a bullet takes to a target in order to hit the target. A sharpshooter, however, does know the path and can make adjustments in the aiming in order to hit a target at many different ranges. In this lab, you will become a sharpshooter of sorts. You will determine the launcher angle that gives the best distance for the projectile.

Neglecting frictional forces, such as air resistance, an object projected from a launcher undergoes a motion that is the simple vector combination of uniform velocity in the horizontal direction and uniform acceleration in the vertical direction. For a projectile launched it can be shown that the trajectory caused by such a combination predicts a parabolic shape.

Goals:

Predict the range of a projectile.
Determine which launcher angle gives the greatest range.

Equipment List:

projectile launcher

steel projectile

meter stick or tape measure

ring stand

test tube clamp

protractor

Lab Activity 1: Determining Launch Velocity (Tabletop to tabletop launch)

Set up a projectile launcher at an angle of 20ousing a ring stand and test tube clamp. The launcher should be adjusted so that it projects the projectile onto another tabletop. The angle that you set,  is measured with the bottom clip even with the edge of the tabletop. DO NOTpoint your launcher in the direction of the computer monitors!

Prepare the launcher by depressing the internal spring with the wooden rod and inserting the ring pin through the holes in the side of the launcher and through the slot in the wooden rod.
Carefully measure the angle.
Place a steel projectile in the launch tube.
Fire the launcher and have another person note the approximate position that the projectile strikes the table. You will need to do the same for their launcher. Tape a piece of paper to the tabletop and place a sheet of carbon paper (carbon side down) on top of the taped paper. It is not necessary to tape the carbon paper to the table.

Fire the launcher several times to obtain an average landing position. Estimate the center position of your pattern and measure the horizontal distance from this point to a point directly below the launching position of the projectile. This is the horizontal range, x.

Repeat with varying values of angles between 20o and 70o (be sure to include a data point for 45o) Record the angles and ranges in your data table.

Launch Angle (degrees) / Range (meters)

Using Graphical Analysis, make a graph of Range vs. Angle.

Based upon your graph, what angle does the maximum range occur at?

From your graph, generate an estimated list of pairs of angle measures that yield the same range values? Is each pair a set of complementary angles? Explain.