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IMPORTANT: Wear safety goggles while anyone in lab is launching their projectile.Equipment Needed:PASCO Short Range Projectile Launcher ME-6800Yellow acrylic ballMeter stickCarbon paperWhite paper Masking tapeTape measure (with metric units)Large C-clampFig. 1: Launcher set to shoot horizontally off tablePurpose:The purpose of this experiment is to predict and verify the range of a ball launched at an angle. The initial velocity of the ball is determined by shooting it horizontally and measuring the range and the height of the Launcher.Theory:To predict where a ball will land on the floor when it is shot off a table at an angle, it is necessary to first determine the initial speed (muzzle velocity) of the ball. This can be determined by launching the ball horizontally off the table and measuring the vertical and horizontal distances through which the ball travels. Then the initial velocity can be used to calculate where the ball will land when the ball is shot at an angle. Air friction is assumed to be negligible.INITIAL HORIZONTAL VELOCITY:A ball launched horizontally off a table has an initial velocity, v0 (v0=v0x; v0y=0). If t is the time the ball is in the air, then the horizontal distance it travels is given by x=v0t (Eq.1). The vertical distance the ball drops in time t is given by y=12gt2 The time of flight of the ball can then be found using t=2yg (Eq.2). Use this time in Eq.1 to find the initial velocity v0=xtINITIAL VELOCITY AT AN ANGLE:To predict the range, x, of a ball launched with an initial velocity at an angle, , above the horizontal, first predict the time of flight using the equation for the vertical motion –y=y0+v0sinθt-12gt2 (Eq.3)where y0 is the initial height of the ball and y is the position of the ball when it hits the floor. Then use x=v0Cosθt (Eq.4)to find the range. Remember, if the ball is shot at an angle below the horizontal, then is negative.PART ASetup:Clamp the Launcher near one end of a sturdy table as shown in Fig. 1.Adjust the angle of the Launcher to zero degrees so the ball will be shot off horizontally. Use the attached plumb bob to adjust the angle.Carefully measure the height of the ball from the floor using a meter stick. (Measure to the bottom of the ball diagram shown on the side of the launcher). This is the initial vertical distance at which the ball is launched. Record this in Table 1.Hold a meter stick vertically flush against the edge of the Launcher base to find the location on the floor directly beneath the release point of the Launcher. Use a piece of masking tape and mark the location on the floor. This will be the initial horizontal location. See Fig. 2.Place the ball into the Launcher and use the rod to push it carefully in till you hear the first click (the SHORT-range position). Do not use in MEDIUM or LONG range. DO NOT STAND IN FRONT OF OR LOOK INTO THE LAUNCHER!Fire a test shot to determine where the ball will hit the floor. At this location, tape a piece of white paper to the floor. Place the carbon paper on top with the carbon side down. Do not tape the carbon paper to the floor.Fire the ball again. It should land on the carbon paper (if it doesn’t, readjust your carbon-white paper combo). Pick up the carbon paper and you should see a black dot on the white paper. Carefully, measure the horizontal distance from the front edge of the masking tape to the dot on the paper. Record this distance in Table 1. Cross out the dot.Reload the Launcher and fire the ball to repeat this measurement for a total of 10 trials. Fig. 2: Use a vertical meter stick to locate initial horizontal position.Table 1Trial NumberDistance (meters)12345678910Average Distance (meters)Launcher Height (meters)Use the distance and height data to determine the initial horizontal velocity, v0. Show your work below-Horizontal launch velocity of ball, v0=____________We will take this to be the initial launch speed of the launcher for the short range position at any angle.Part BSetup:Use the side screws (Fig. 3) to adjust the launcher to launch at an angle between 20 and 60 degrees above the horizontal. Record this angle in Table 2.Fig. 3Fig. 4Re-measure the vertical launcher height. Record this in Table 2.Use the initial launch speed from Part A and initial vertical height from Part B to calculate a predicted time of flight. Then calculate and predict the horizontal distance that the ball will travel. Show your work below – Predicted horizontal distance _____________________Record this in Table 2.Draw a line across the middle of a white piece of paper and tape the paper on the floor so the line is at the predicted horizontal distance from the Launcher. Cover the paper with carbon paper.Fire a test shot. If the ball does not fall on the paper, check your calculations and adjust the paper if necessary.Load and shoot the ball so that it lands on the paper. Record the horizontal distance. Repeat 10 times. Record in Table 2.Table 2: Confirming the Predicted RangeAngle above horizontal = ________ Vertical Height of Launcher = _________Calculated time of flight = ________ Predicted Horizontal Range = ___________Trial NumberHorizontal Distance (m)123 45678910AverageAnalysis:Calculate the experimental average distance and record in Table 2.Calculate the percent difference between the predicted value and the resulting average distance when shot at an angle. Show your work below – Percent Diff.=pred.-exp.pred.+exp2×100To calculate the precision of range, use the % difference from above and multiply it by the predicted range. Add and subtract this value from the predicted range. For example, if your predicted range is 1.60m and your % difference is 5%, you will find that your range values should be within 5% of 1.60m, or +/- 0.08m (1.52m to 1.68m).Make a graph plotting distance traveled by the ball on the y-axis and the trial number on the x-axis. Plot the predicted range line and the +/- difference lines. See example graph below. Additional Questions:Use the four kinematic equations to derive Eq.1-4 (from the Theory section) that were used for this lab. Show your work below—Describe at least three specific sources of experimental error. Do not say “Human error”! ................
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