Projectile motion

Name: Haley Smith Partners: _______________________________ ____

PHY 111 Remote Lab #3 Projectile Motion

Purpose

•To describe projectile motionObjectives

•To measure speeds along two and/or three coordinates

•To apply the Pythagorean Theorem to find a projectile’s overall velocity

•To discuss independence of motion along separate coordinates

•To apply rules of vector mathematics

Materials & Resources

•Grooved rail

•Steel balls and/or marbles

•Meter sticks

•Protractors

•Wooden blocks

•Graph paper

•Carbon paper (if available)

•Masking tape

Introduction

Most of the important motion quantities can be explored by studying motion along one dimension. But, of course, most objects actually move along multiple dimensions. Many real-life motions appear extremely complicated as a consequence. So how do we describe motion in many dimensions?

We will study a special case of multiple-dimensional motion called projectile motion. Along the way, we will discover some important properties of motion that allow us to simplify our descriptions of motion.

Part #1: Experiments with (originally) horizontal projectiles To get started, choose a location where you can set up the apparatus on a smooth horizontal surface (such as a table or countertop) with room on the floor for the projectile to land (see Figure 3-1). Figure 3-1. A projectile motion apparatus. A steel ball is released from rest at the top of a ramp or grooved track (upper left) on top of a table. The ball flies off the ramp, rolls briefly on the table, then flies off the table and lands on the floor. A sheet of carbon paper is laid upon a sheet of graph paper in order to record the location of the impact. Not everything needed is shown.

1.Set up the apparatus as depicted in Figure 3-1. Align the edge of the ramp so that the ball can roll smoothly across the table before falling off the table. Experiment with the apparatus to see the approximate location of the impact of the ball.

2.Measure the initial height of the ball when it leaves the ramp – that is, the distance from the floor to the top of the table. Record your result below: Initial height of ball y = .9105meters

3.Tape a sheet of graph paper to the floor at the approximate landing position of the ball. Place a sheet of carbon paper on top of that. (If you do not have carbon paper, you will need to watch carefully to mark the spot at which the ball lands)

4.Release the ball from rest from its starting point. After the ball has landed on the carbon paper, it should have made a mark on the graph paper below. Take the carbon paper off the graph paper, and label the mark #1.

5.Repeat this process for a total of 5 marks. Be sure that the ramp does not move (or that you restore it to its original position before each launch). 6.Measure the horizontal distance from the edge of the table to each mark, and record the results in Table 3-1: Table 3-1. Measurements of an initially horizontal projectile. Horizontal Trial Distance (m) 1 .35 2 .34 3 .33 4 .33 5 .33Average .347.Calculate the average horizontal distance and record the result below: .35 + .34 + .33 + .33 + .33= 1.68 1.68/ 5= .34Average horizontal distance (x) =.34 m8.Calculate the average amount of time spent by the ball in flight (we’re calculating rather than measuring due to difficulty in measuring such short times with good precision): Where y is the initial height of the ball found earlier and g is acceleration due to gravity (9.81 m/s2). Record the result below:

t= √ 2(.09105)/9.81Time in flight (t) = .14 s9.Finally, calculate the initial velocity of the ball using the average horizontal distance and average time: v= .34/.14Initial velocity v =2.4 m/sPart #2: Experiments with angled projectiles Our next task is to study the effects of initial launch angle for our projectile. In this case, we will align the grooved ramp so that the ball launches at an angle below the horizon (see Figure 3-2): Figure 3-2. A curved projectile motion apparatus. The set-up is similar to the horizontal launch apparatus used earlier. 1.Set up the apparatus as depicted in Figure 3-2. This time, align the edge of the ramp with the edge of the table – so that the ball is moving both forward and downward when it leaves the ramp – and experiment with the apparatus to see the approximate location of the impact of the ball.

2.Determine the angle by using trigonometry (see Figure 3-3). The ramp forms the hypotenuse of the triangle; measure the horizontal and vertical legs of the triangle formed by the ramp and the table and record them below: Horizontal leg Δx = 5.65 cm Vertical leg Δy = 9.15 cm3.The tangent function is defined as the vertical leg divided by the horizontal leg. So use the inverse tangent function to calculate the angle. (Make sure your calculator is set to “degree” mode) tan^-1(9.15/5.65)θ (“theta”) = 5.83°We will repeat the procedure used earlier for the horizontal-only initial motion (Part #1), but with a few extra calculations to deal with the 2-D nature of our launch. 4.Measure the initial height of the ball when it leaves the ramp – that is, the distance from the floor to the top of that part of the ramp at the edge of the table. Record your result below: Initial height of ball (y) = .0915 meters5.Tape a sheet of graph paper to the floor at the approximate landing position of the ball. Place a sheet of carbon paper on top of that. 6.Release the ball from rest from its starting point. After the ball has landed on the carbon paper, it should have made a mark on the graph paper below. Take the carbon paper off the graph paper, and label the mark #1. 7.Repeat this process for a total of 5 marks. Be sure that the ramp does not move (or that you restore it to its original position before each launch). ΔxΔyθ

8.Measure the horizontal distance from the edge of the table to each mark, and record the results in Table 3-2. 9.Calculate the average horizontal distance and record the result below: Average horizontal distance x = .34 mTable 3-2. Measurements of an initially angled projectile. Horizontal Trial Distance (m) 1 .33 2 .35 3 .32 4 .35 5 .35Average .3410.Calculate the amount of time spent by the ball in flight: Where y is the initial height of the ball found earlier and g is acceleration due to gravity (9.81 m/s2). The formula is more complicated because we are now launching the ball at angle instead of purely horizontally. Record the result below: t= √ 2(.0915 – .34tan(58.3)) / 9.81

Time in flight (t) = .63 sHere is where it becomes different than earlier. The initial launch angle was not perfectly horizontal, which means the initial velocity had both horizontal and vertical components. 11.Recall the basic trigonometric functions sine, cosine and tangent. What are their definitions? Sine (angle) = opposite/ hypotenuse Cosine (angle) = adjacent/hypotenuse Tangent (angle) = opposite/adjacent Pythagorean Theorem= a^2 + b^2= c^2Now let’s look at the initial velocity of our projectile. We can sketch a right triangle in terms of velocities (Figure 3-4): 1Figure 3-4. A velocity triangle made from the initial speed (v0) and angle (θ). 12.Using your data (the average horizontal distance and the time to drop), solve for the initial horizontal speed (vx0) and calculate its numerical value: vxO= .34/ .63Initial horizontal speed (vx0) = .54 m/s13.Next, use a trig relation and the initial horizontal speed to find the initial vertical speed: Tan(58.3)= 1.62 A physicist may term this “velocity space”, to distinguish from ordinary space1v0θvx0vy0

(.54) 1.62= x/ .54(.54) X= .54 (1.62) Initial vertical speed (vy0) =.87 m/s14.Finally, use the Pythagorean Theorem to combine both speeds to find the overall initial speed of the projectile: .54^2 + .87^2 = c^2 √1.0485= √c^2 Initial speed of the projectile (v0) = 1.2 m/s Summary 1.Motions in x and y are “independent” of each other. Does this mean they are completely unrelated? Briefly explain. No, they are not independent of each other. They both work together to form a right angle and they form a projectile motion. If either one did not have the other it would be an one dimensional motion

2.Suppose keep the overall initial speed the same, but change the launch angle. Will the ball land at the same spot on the floor? Briefly explain. The ball would land in a different location. When increasing or decreasing the angle affects how much time the ball will stay in the air.

3.Suppose we keep the launch angle the same, but increase the overall initial speed. Will the ball land on the same spot on the floor? Briefly explain. The ball should land in the same spot. When increasing the speed that just gets the ball to a spot quicker, it does not adjust where it will land.