Physics Mechanics Lab Experiment, Lab Report Example

Objective

The objective of this laboratory experiment is to assess the speed of a projectile by applying the ballistic pendulum and to review this evaluation be a direct measurement of the vertical distance that is covered by the projectile in its fall and the range.

Theory

The fundamental principle that is applied in the laboratory experiment is the law of conservation of momentum. This law applies to a system when the external sum of the forces thatinfluence the system is equivalent tozero. A bullet that possesses a mass equal to m and a velocity that is equal to v is shot at a pendulum that is a wooden block that is suspended and possesses a mass of m. There is a completely inelastic collision and the bullet remains inside of the pendulum in an embedded state. Thecollision takes place with the pendulum in its resting equilibrium position. The sums of the forces that are influencing the pendulum are zero. The momentum of the bullet and the wooden block are conserved. Consequently, in the event that v is representative of the speed of the bullet and the block right after the collision, the following formula applies:

Mv= (m + M) V

The kinetic energy that is manifested by the system subsequent to the collision is demonstrated by the following relationship:

E_k = ½ (m + M) v²

The pendulum moves in an upward motion until the kinetic energy is transformed to gravitational potential energy. Consequently, the center of the mass of the pendulum will become elevated by a distance y that is manifested by the equation:

E_k = (m + M) gy

In the resolution of the first and second equations the formula that is derived is the following;

V_B = m+ M/ m * (2gy)^1/2

In this formula the subscript b demonstrates that the speed of the bullet is ascertained from the ballistic pendulum. As a result the speed of the bullet prior to impact can be computed in the event that one should evaluate the masses of the bullet and the pendulum. These masses can be reviewed with regards to the height that the pendulum raises subsequent to impact.

The speed that is manifested by the bullet may also be ascertained by causing the bullet to shoot in a horizontal direction from an assumed height that is positioned above the floor. In this manner the speed can be computed. The fight time of the bullet can be calculated by t. Consequently, the horizontal part of the movement of the bullet can be detailed by the equation:

R =vt

The vertical portion of the bullet’s movement can be calculated by the following formula:

h= ½ gt²

The flight time of the bullet can be removed from the equations in order to provide:

V_p = R (g/ 2h)^1/2

Discussion

Collisions that have an elastic quality take place when two objects become engaged in a collision and the momentum is conserved in addition to the kinetic energy. The collisions that are inelastic take place when the kinetic energy possessed by the objects is not conserved and the momentum is conserved. In the event that a vector amount of energy is conserved, this infers that the aggregate of the product of the initial action must be equal to the aggregate of the final actions.

Conclusion

The error could be attributed to measurement error of the length of the pendulum or the distance traveled by the projectile. The errors could be attributed to the measurement of time or distances. A pulsating beam would have provided more accuracy with regards to the measurements of the height and speed.