Physics. Here's the video of the experiment: https://youtu.be/3d3UeFPcOcU. Please use this.

Introduction: You will launch a ball and can calculate its initial velocity with TWO DIFFERENT METHODS. The first will be based on projectile motion and the second will be based on the conservation of energy and momentum. Procedure (method 1): Attach the ball to the firing rod, pull back until it locks, move the pendulum out of the way, and fire the ball. Mark exactly where it lands, and measure both the exact horizontal and vertical distances that it travelled. Analysis (part 1): It is not easy to accurately measure the time of flight, so we should use y = y_o + V_ot + 1/2at^2 to find the time of flight, where y is the vertical distance travelled, and a is the acceleration due to gravity. This equation, in this case, can be put more simply as y = 1/2gt^2 . Solving for t yields = sqrt(2/) You can then solve for velocity using the definition of velocity, v=x/t (where t is the time you solved for and x is the horizontal distance travelled). This is the average horizontal velocity and also the initial velocity because the horizontal component of velocity remains constant during the flight. Inserting the definition of t we just found yields a general equation with variables that can be accurately measured with a meter stick (remember to use SI units (NOT cm!)): = /sqrt(2/)

Procedure (method 2): Attach the ball to the firing rod, pull back until it locks, let the pendulum hang down, and fire the ball into the pendulum, where it should stick. The pendulum will rise and lock. Figure out how far the CENTER OF MASS of the pendulum (with the ball in it) raises vertically (in the y direction) from its initial position. This will be y in the equation below. Here is the video of the experiment: https://youtu.be/3d3UeFPcOcU Analysis (part 2): Work backwards. Use the conservation of energy to figure out how fast the system (ball + pendulum) was moving the instant after the collision: (PE_1 + KE_1 = PE_2 + KE_2) where 1 means the instant after the collision and 2 means after the pendulum rises to the top of its arc. This equation becomes, simply: 0 + (m_b+m_p)v2 = (m_b+m_p)gy + 0. After solving for v (the velocity of the ball AND the pendulum together, the instant AFTER the collision), use the conservation of momentum to find the velocity of the ball alone the instant BEFORE the collision: m_b*v_b = (m_b+m_p)v_p+b

Questions/Report (The questions on BB will be kind of like this) 1. During which part of the process is kinetic energy converted to potential energy? a. When the spring fires. b. from the instant before the collision to the instant after the collision c. from the instant after the collision until the pendulum rises all the way up. d. While the ball is falling toward the floor.

2. What is the problem with using 2.48 m for x and 15.5 cm for y? Select all that apply: a. 15.5 cm was the height that the center of mass reached, but you should use the height that the bottom of the pendulum reached. b. The units for distance are not consistent, and you should probably convert cm to m. c. Since we have set up our equation as 0 + (m_b+m_p)v2 = (m_b+m_p)gy + 0 we are saying that the pendulum had no PE initially, so that means we are assigning the initial height 8.2cm to be 0 height, essentially, so therefore, y, the final height, would be however far ABOVE 8.2cm the pendulum swung, or the difference between the two heights, 15.5-8.2 cm. (If we had set up our equation using the table level as 0 height, then we would use 15.5 as y, the final height, and our equation would look like this, after converting cm to m: (mb+mp)g(0.082m) + (mb+mp)v2 = (mb+mp)g(0.15m) + 0 but that is just a more complicated version of the equation we are using.) d. The ball actually flew further than 2.48 meters. That is the length measured from the end of the table, but the ball was released some distance before the end of the table.

3. When all the energy in the system has been converted to gravitational potential energy, the total energy is equal to the PE which equals (m_b+m_p)gy. When this is true, where is the ball? a. top of arc b. in spring c. on floor d. on Jacob's foot

4. T or F: The collision between the ball and pendulum was elastic. (Be able to justify your answer!)

5. If the force constant of the launching spring was doubled, how would that affect the kinetic energy of the ball immediately after launching? (Hint- how would this change effect the potential energy stored in the spring?) a. no effect b. doubled c. quadrupled d. cut in half

6. Why can't we just set the initial kinetic energy of the ball alone, immediately after fired, KE = m_bv_b^2, equal to the potential energy of the system at the top of the arc, PE = (m_b+m_p)gy, solve this equation, m_bv_b^2 = (m_b+m_p)gy for vb, call it a day, and forget about this conservation of momentum stuff? a. no one thought to until now b. too much time elapses. while the pendulum swings. c. mechanical energy is never conserved d. Energy is lost to heat (thermal energy) in the collision so the initial KE isn't really equal to the final KE. A non-conservative force did work on the ball (force from pendulum that slowed down the ball) so mechanical energy was lost in the collision.

7. Show how you solved for the initial speed of the ball using kinematic equations (method one where it flew across the room. This doesn't really require much more than inserting the appropriate variables in the given equation and plugging into your calculator. By the way, this is nearly identical to the problem in Sapling where you have to figure out the velocity of the cue ball that flies off the billiards table.)

8. Show clearly how you solved for v (the velocity of the ball AND the pendulum together, the instant AFTER the collision) in method 2. Show every step, and identify what numerical value you decide each variable has.

9. Clearly show how you solved for vb (the initial speed of the ball) in the analysis for part 2. Show every step, and identify what numerical value you decide each variable has. Compare this answer to the answer you got using methed 1, in Q 7.

10. The equation m_b*v_b = (m_b+mp)v_p+b is based on the fact that momentum is conserved during which part of the process? a. When the spring fires. b. from the instant before the collision to the instant after the collision c. from the instant after the collision until the pendulum rises all the way up. d. from the instant before the collision until the pendulum rises all the way up. Bonus: What percentage of kinetic energy was conserved in the collision? (Compare the total KE of the ball and KE of pendulum the instant before the collision to either (the total KE of the ball + pendulum the instant after the collision) or (the PE of ball + pendulum at the top of the swing). You can do either or because these values are equal!

11. What percentage of kinetic energy was conserved in the collision? (Compare the total KE of the ball and KE of pendulum the instant before the collision to either (the total KE of the ball + pendulum the instant after the collision) or (the PE of ball + pendulum at the top of the swing). You can do either or because these values are equal!