EQUIPMENT - University of Mississippi



Experiment 4: Projectile Motion 685799145726EQUIPMENTComputer capable of running html simulation Equipment? PhET “Projectile Motion Simulation” objectives of this experiment is to examine the factors affecting a projectile and to predict the landing point when the projectile is fired at a nonzero angle of elevation from a non-zero height. TheoryProjectile motion (in the absence of air resistance) is an example of motion with constant acceleration. In this experiment, a projectile will be fired from some height above the ground and the position where it lands will be predicted (calculated). To make this prediction, one needs to know how to describe the motion of the projectile using the laws of physics. The position as a function of time is r=r0+ v0t+12a0t2(1)By measuring appropriate quantities, one can predict where the projectile will strike the floor. Eq. (1) is a general form describing the position of an object as a function of time. It can be resolved into x and y components as x=x0+v0xt+12axt2(2)and y=y0+v0yt+12ayt2(3)which give the position of the projectile in the x and y directions. The x and y components of the initial velocity are (Fig. 4-1) v0x=v0cosθ and v0y=v0sinθ.(4)For a projectile fired (in a vacuum), there is no horizontal component of acceleration after the gun is fired. The only acceleration is due to the gravitational attraction of the earth. This acceleration has magnitude g acting in the negative vertical direction (Fig. 4-1). Hence, equations. (2) and (3) become x=x0+v0xt (5)and y = y0+v0yt-12gt2 . (6) These equations of motion describe the motion of a projectile. Fig. 4-1 Projectile motion. The trajectory is a parabola.The range equation describes the horizontal range that a projectile will travel if projected with initial velocity at an angle θ and gravity is the only force acting the projectile.(7)The equation above assumes the launch point and landing point are both on the same horizontal plane.Name: Section: Date: Worksheet - Exp 4: Projectile Motion 68580015938500Objective: The objective of this lab is to investigate projectile motion, ?rst when a projectile is ?red horizontally and then when a projectile is ?red from a non-zero angle of elevation.PROCEDUREPart 1: Horizontal Launch (θ0 = 0?)Open the Projectile Motion simulation in your browser and select the ”Lab” option. Ensure gravity is set to 9.8 m/s2 and the ”air resistance” box is unchecked.Set the initial height of the object as 10m if your lab section # is even and 5 m if your lab section number is odd by clicking and dragging the crosshairs at the back of the cannon upward.Set the launch angle to 0? by clicking and dragging the front of the cannon.Choose the origin of your coordinate system. You will need to decide whether the origin is at the launch position or at the ground, and which direction is positive and which is negative. Record your decision below: (5 points)Set the initial launch velocity v0 to 10 m/s if your lab section # is even and 5 m/s if your lab section number is odd by clicking the arrows or dragging the slider under ”Initial Speed”.Predict (calculate) the time of ?ight and landing position using the kinematic equations and record them in the table on the next page (x-calc) and (t-calc), show your work here. (10 points)Fire the cannon by clicking the red ?re button. Drag the investigation device from the top right of the screen and measure the time of ?ight and landing position of the projectile by placing the crosshairs at the landing position. Record these values in the table pare your calculated and experimental (measured) values for time of ?ight and landing position and record the percent difference in the table below.Repeat steps 1 through 8 for initial velocities of 2v0 m/s and 3v0 m/s. You can change size of simulation by using the buttons. Please note that v0 is the initial velocity from step 5 above. Fill in all table values.v0 (m/s)x -calc(m)x -meas(m) % differencet-calc(s)t- meas(s)% differencev0 = 2* vo= 3* vo=a) Does the time of ?ight change as the initial velocity is increased? b) Is this the result you would have expected? Why or why not? (5 points)Check the ”air resistance” box and ?re the projectile at the same three initial velocities and investigate any changes. Does the time of ?ight change from no air resistance? What about when you change the size of the ball? Explain your answers. (5 points)Part 2: Launch from non-zero angle of elevationReset the Projectile Motion simulation in your browser by clicking the reset button on the bottom right of the screen. Ensure gravity is set to 9.8 m/s2 and the ”air resistance” box is unchecked.Set the initial height of the object to the same height as in step 2 by clicking and dragging (upward) the crosshairs at the back of the cannon.Set the launch angle to 30? by clicking and dragging the front of the cannon.Choose the origin of your coordinate system. You will need to decide whether the origin is at the launch position or at the ground, and which direction is positive and which is negative. Record your decision below: (5 points)Set the initial launch velocity v0 to the same velocity as in step 5 above by clicking and dragging the crosshairs at the back of the cannon. Predict (calculate) the time of ?ight and landing position using the kinematic equations and record them in the table on the next page (x-calc) and (t-calc), show your work here. (15 points)Fire the cannon by clicking the red ?re button. Drag the investigation device from the top right of the screen and measure the time of ?ight and landing position of the projectile by placing the crosshairs at the landing position. Record these values in the pare your calculated and experimental values for time of ?ight and landing position and record the percent error in the table.Repeat steps 12 through 19 for initial velocities of 2* v0 m/s and 3* v0 m/s.Please note that v0 is the initial velocity from step 5 above. Fill in all table values.v0 (m/s)x -calc(m)x -meas(m) % differencet-calc(s)t- meas(s) % differencev0 = 2* vo= 3* vo=a) Does the time of ?ight change as the initial velocity is increased? b) Is this the result you would have expected? Why or why not? (5 points) Check the ”air resistance” box and ?re the projectile at the same three initial velocities and investigate any changes. Does the time of ?ight change from no air resistance? Does the time of ?ight now di?er when the velocity is increased from v0 to 2vo and 3vo? What about when you change the size of the ball? Explain your answers. (5 points)Part 3: Post lab QuestionsIf a projectile has twice the mass but the same initial velocity, what e?ect would this have on its the horizontal range of the projectile? What effect would this have on the kinetic energy of the projectile? Ignore air resistance. (5 points)When an archer ?res an arrow at a target, should they aim directly at the bullseye? If not, where should they aim? Discuss whether your answer depends on the distance between the archer and the target. (5 points)When ?ring from a non-zero angle of elevation at ground level, assuming zero air resistance, what angle will achieve maximum range? Explain your reasoning and test your answer using the simulation (5 points)If air resistance is present, does the angle for maximum range increase or decrease? Explain your reasoning and test your answer using the simulation. (5 points)Using methods of ‘The Calculus’ show that the maximum range of a projectile (using the range equation) is obtained when the angle 45 degrees. This is a max-min type problem from Cal one. This is done as follows: take derivative of the range equation, set the derivative equal to zero and solve for angle. (5 points). ................
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