Files X (Freezing Point X Screen Shot 2022 x Screen Shot 2022 x ()Ballistic Pendulum X Files X * Course Hero X C canvas.uncp.edu/courses/21711/assignments/525015 G # O Learning Strategie... ATI TEAS Basic Pa... ATI TEAS Basic Pa... G Google G Google Hillsong United Ja.. Hillsong United Ja.. sms Lab 4: Enzymes a... Report 4 Ballistic Pendulum Data Sheet Fall 22.xisx & Download @ Info X _Close ZOOM + m (kg) M (kg) Rem (m) Gave (degrees) avg (radian) h = Rcm (1 - cose) (m) (M+m)/m (kg) vo= ((M+m)/m)v(2gh) (m/s) m/(M+m) v= = v(2gh) (m/s) Vavg Vstd Vgraph: %diff: Chapter_15.pdf Equilibrium_Prac..pdf download 6Uniform Circula..pdf A Show All X Failed - Network disconnect..AutoSave O OFF GP ... 3 ballistic pendulum Fall 22 (1) - Saved to my Mac Q Home Insert Draw Design Layout References Mailings Review View Tell me Share Comments Times New... A A Aa Ap ab A A AaBbCcDdEe AaBbCcDdEe Paste B IUvax x A DAVAO Normal No Spacing Styles Dictate Editor Pane L Conservation of Linear Momentum Purpose: To explore the conservation of linear momentum of an inelastic collision. Consider a particle with constant mass, m. The most general form of Newton's second law can then be expressed in terms of linear momentum: EF = ma = ml _ A(mv)_Ap At At At Now, clearly if the net force is zero then the time rate change in momentum must be zero, [F=0 = 40=0 = P,-P=0 = P, =P., and hence the total linear momentum is conserved (ie. the final momentum is the same as the initial momentum). Ballistic Pendulum Activity The ballistic pendulum will allow you to explore the concept of momentum conservation via the inelastic collision between a projectile and a pendulum bob. A projectile is fired into a hollow pendulum bob and remains embedded in it and the pendulum swings upward as seen in Figure 1. Figure 1: The PASCO ME 6832 Theory When the projectile ball of mass m is fired with initial speed v, it collides and remains embedded in the pendulum bob of mass M -- a completely inelastic collision. Since M+m is the combined mass of the ball and the pendulum and vy as the combined speed just after the collision we may apply conservation of momentum to the collision as follows (see Figure 2a): my, = (M +m)v, (1) Page 1 of 2 English (United States) Focus - + 100%AutoSave O OFF GP ... 3 ballistic pendulum Fall 22 - Saved to my Mac Q Home Insert Draw Design Layout References Mailings Review View Tell me Share Comments Times New... A A Aa Ap ab A A AaBbCcDdEe AaBbCcDdEe Paste B I UvX X A DAVAO Normal No Spacing Styles Dictate Editor Pane Theory When the projectile ball of mass m is fired with initial speed v, it collides and remains embedded in the pendulum bob of mass M -- a completely inelastic collision. Since M+m is the combined mass of the ball and the pendulum and vy as the combined speed just after the collision we may apply conservation of momentum to the collision as follows (see Figure 2a): my, = (M +m)v, (1) Just after the collision, the pendulum bob will swing upward until all of its kinetic energy is converted into gravitational potential energy. If the vertical distance traveled by the pendulum bob is h, conservation of energy tells us that the kinetic energy just after the collision is converted to potential energy (see Figure 2b): :(M + m)v; =(M+m)gh (2) The height can be expressed as: Figure 2: Westration of the basic theory h = R.(1-cose) where, R, is the distance from the pivot axle to the center of mass and is measured along the length of the pendulum. 0, is the maximum angle obtained by the pendulum a) Inelastic collision bob. In this experiment you are investigating conservation of momentum. So, your results here, can be used to calculate the velocity of the projectile immediately before the collision. The initial projectile velocity, vo may be expressed in terms of easily measurable quantities according to: m ) Vagh (3) Page 1 of 2 English (United States) Focus - + 100%AutoSave O OFF GP... 3 ballistic pendulum Fall 22 - Saved to my Mac Q Home Insert Draw Design Layout References Mailings Review View Tell me Share Comments Times New... A A Aa A abA A AaBbCcDdEe AaBbCcDdEe Paste B IUvab Normal No Spacing Styles Dictate Editor Pane The height can be expressed as: Figure 2: Westration of the basic theory h = R. (1-cose) where, R is the distance from the pivot axle to the center of mass and is measured along the length of the pendulum. 0, is the maximum angle obtained by the pendulum 4) Inelastic colision bob. In this experiment you are investigating conservation of momentum. So, your results here, can be used to calculate the velocity of the projectile immediately before the collision. The initial projectile velocity, vo may be expressed in terms of easily measurable quantities according to: vo = ) vagh (3) where again we have, h = R., (1-cose) NOTE: This is an approximation since we are neglecting the moment of inertia of the pendulum bob. Procedure: You will determine the initial velocity of a projectile (steel ball) with a spring-loaded gun, using the method outlined above and summarized in equation (3). For each trial, add an additional mass to the pendulum bob. Before the experiment: Measure the mass of the projectile, m, and record in Column A. Measure the mass of the pendulum bob, M, and record in Column B. Measure the center of mass of the pendulum with the ball inside, Rem (This will change with each trial as you add additional mass!!), and record in Column C. Measure the additional masses to be added to the bob. Write these down in a notebook for later. During the experiment: Measure the average angle of 5 trials, dave, the pendulum achieves once the projectile collides with it, and record in Column D. Don't forget to convert to radians in Column E for excel calculations. Calculate the mass of the pendulum bob with additional weights, M, and continue to record in Column B. The additional masses are the ones you wrote down from the previous steps. Page 1 of 2 English (United States) Focus - + 100%AutoSave O OFF GP... 3 ballistic pendulum Fall 22 - Saved to my Mac Q Home Insert Draw Design Layout References Mailings Review View Tell me Share Comments Times New... A A Aa A abA A AaBbCcDdEe AaBbCcDdEe Paste B IUvab Normal No Spacing Styles Dictate Editor Pane Calculate the mass of the pendulum bob with additional weights, M, and continue to record in Column B. The additional masses are the ones you wrote down from the previous steps. Calculate the height, h, according to h = R. (1-cose) and record in Column F; again, Rem will be different for each trial. So, this height should vary each trial. Calculate in Column G to make the excel equations easier. L Calculate the initial velocity, vo, according to equation 3 above. Calculate the average velocity of the table in Cell H7. Calculate the standard deviation of the velocity in Cell H8. Graphical Analysis: Calculate yu in Column I and v2gh in Column J. Plot Column J vs. Column 1: /2gh vs.- m M + m Identify what the slope of this graph represents using equation 1 and record in Cell H10. (You may have to set the y-intercept to zero in order to get comparable tabular and graphical values.) Compare the initial velocity from the graph to the initial velocity from the table using % difference in Cell HI1. Page 1 of 2 English (United States) Focus - + 100%