PHYS LB- Ballistic Pendulum PDF

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Summary

The purpose of the laboratory is to verify the mechanical energy and conservation of linear momentum. Moreover, to determine the loss of kinetic energy in the collision of the ball with the pendulum. The law of mechanical or linear momentum states that the energy is constant and the total energy is ...

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EXPERIMENT IN Ballistic Pendulum     PHYSICS 1433 GENERAL PHYSICS I LAB REPORT   NEW YORK CITY COLLEGE OF TECHNOLOGY 

 DEPARTMENT OF PHYSICS SPRING 2020

Ballistic Pendulum

  

Touheda Khanom Prof. Lusik Hovhannisyan 04.29.2020

Contents 1-0 OBJECTIVES

4

1-1 THEORETICAL BACKGROUND

4-5

1-2 PROCEDURE

5-6

1-3 DATA

6

1-4 GRAPH

7

1-5 SAMPLE CALCULATIONS

7-8

1-6 QUESTIONS

8-9

1-7 CONCLUSION 

9

OBJECTIVES The purpose of the laboratory is to verify the mechanical energy and conservation of linear momentum. Moreover, to determine the loss of kinetic energy in the collision of the ball with the pendulum. The law of mechanical or linear momentum states that the energy is constant and the total energy is always equal to zero if no external forces are applied. THEORETICAL BACKGROUND The ballistic pendulum measures the velocity of projectiles through the conservation of linear momentum and mechanical energy. In this experiment, we can determine the initial velocities of the projectile motion by measuring the distance on which the center of mass of the projectile rises through the law of conservation of linear momentum and conservation of mechanical energy. The initial velocity can also be determined by measuring the displacement and time it takes place for the ball to travel. In this experiment, we can vary the conservation of linear momentum and conservation of mechanical energy by comparing the two differential velocities of the ball. The formulas given below are related to the experiment. mv = (m + v)V (Horizontal Component of linear momentum) E i = .5(m = M )V 2 + (m + M )gy 1(Kinetic energy after the collision) E f = (m + M )gy 2 (Total Mechanical Energy) E i = E f (Conservation of mechanical energy)

.5(m + M )V 2 + (m + M )gy 1 = (m + M)gy 2 V =

√2g(y

2

− y 1 ) = √2gh (Solving for velocity)

v=

m+M m

√2gh (Velocity)

The equations above show that by measuring the masses m and M and the difference of the heights of the center of mass of the ball pendulum system. d = vt (Horizontal displacement formula) v = dt (Another formula for velocity) This equation above is used to compute the initial velocity of the launched ball by measuring the horizontal distance between any two points of the projectile path and the time of the flight.

η = 1−

Kf Ki

(Fractional loss in kinetic energy)

2

K i = mv2 (Initial Kinetic Energy)

Kf =

(m+M )V 2 2

(Final Kinetic Energy)

m η = 1 − m+M (Frictional Loss in Kinetic Energy)

PROCEDURE

1. I measured the mass of the ball m and the pendulum M and recorded in Data Table 18.1. 2. I measured the vertical distance y 1 between the point marking the position of the center of mass and the base of the apparatus and recorded it in the Data Table 18.1. 3. Then I measure the vertical distance y 2 between the center of mass of the ball pendulum system and the base of the apparatus. 4. I measure the horizontal distances d between the photogates and recorded the distance in Table 18.2. 5. I opened the DataStudio Window and clicked to create the experiment. 6. I created an experiment in the Data Studio Window and then found the photogate and set up channel 1 and channel 2. 7. In channel 1 select blocked, and then unblocked 8. In channel 2 select blocked, and then unblocked 9. Record the time t1 and t1

DATA

SAMPLE CALCULATIONS In the experiment, I used the following formulas to get the values I put on the table. The formulas and calculations are shown below: Mass of ball = .0688 kg Mass of the pendulum= .229 kg Distance y i = .057 m Distance y 2 = .14 m height = y 2 − y 1 height =.14 - .057 height = .083 m The velocity of the pendulum = √2gh Velocity = √2 * 9.8 * .083 Velocity = 1.28 m/s

Initial Velocity(v1) ,. v =

m+M m

√2gh

v = 5.52 m/s mass of the ball = .0688 kg Distance between the photogates = .065 m time of the flight = .0113 s Initial Velocity = d/t = 0.065/.0113 v = 5.75 m/s Average Velocity = 5.75 m/s % difference = abs(5.52-5.75)/((5.75+5.52)/2)*100

% difference = 4.1% Mass of the ball = .0687 kg Kinetic Energy before collision= 1.13 J Kinetic Energy after collision =.24 J

Frictional Loss = 1-(Kf/Ki) = .798 Frictional Loss = 1-(m/m+M) = .769 % difference = abs(.798-.769)/((.769+.798)/2)*100

% diff = 3.70% QUESTIONS 1. A 15g bullet is fired horizontally into a block of wood with a mass of 2.5kg and embedded in the block. Initially, the block of wood hangs vertically and the impact causes the block to swing so that it’s center of mass rises 15cm. Find the velocity of the bullet just before the impact. bullets mass, m= 15g= 0.015kg Wood block’s mass, M=2.5kg Height, h=15cm=0.15m v=?

v=

m+M m

√2gh

v = 287.5 m/s 2. Prove that the fractional loss in kinetic energy for the “ball-pendulum” system is given by equation (18.14)?

η =1−

mv 2 2

Ki =

Kf =

(m+M )V 2 2

η =1−

η =1−

Kf Ki

(m+M )V 2 mv

m2(m+M )2gh 2 m(m+M) 2gh

η =1−

m m+M

CONCLUSION In conclusion, the law of conservative mechanical energy is when the total mechanical energy is conserved in the system in an isolated system. Kinetic energy is dependent on mass and velocity. The energy is neither created nor destroyed. However, it can be converted into different forms. In the experiment, it was hard to experiment that the energy is conserved because of air resistance and the friction caused due to the slider of the glider....