case study
Ballistic Pendulum
(Revised May 22, 2012)
GOALS
(1) To determine the launch speed of the steel ball for the short, medium, and long range settings on the projectile launcher apparatus using the equations for projectile motion.
(2) To use the concept of gravitational potential energy and energy conservation to determine the speed of the ball plus pendulum as it first begins to swing away from the vertical position after the “collision.”
(3) To explore the relationships between the momentum and kinetic energy of the ball as launched and the momentum and kinetic energy of the ball plus pendulum immediately after the ball is caught by the pendulum apparatus.
INTRODUCTION
The “ballistic pendulum” carries this name because it provides a simple method of determining the speed of a bullet shot from a gun. To determine the speed of the bullet a relatively large, massive block of wood is suspended as a pendulum. The bullet is shot into the wooden block without penetrating clear through it. This is a type of “sticky” collision where the two masses
(bullet and block) “stick” to one another and move together after the collision. By noting the angle to which the block and bullet swing after the collision, the initial speed can be determined by using conservation of momentum. But how do we know that momentum is conserved in this type of collision? In our case the ballistic pendulum apparatus will be used to compare the momentum of the steel ball before the “collision” to the momentum of the ball and pendulum apparatus, equivalent to the wooden block plus the bullet, after the collision. A comparison of the kinetic energy of the ball before the collision with the kinetic energy of the system afterward will also be made.
angle indicator plumb bob launcher Fig. 1. Ballistic pendulum apparatus
As shown in the diagram the projectile launcher used previously is mounted horizontally so that the pendulum can catch the emerging steel ball. The angle
(Revised May 22, 2012)
GOALS
(1) To determine the launch speed of the steel ball for the short, medium, and long range settings on the projectile launcher apparatus using the equations for projectile motion.
(2) To use the concept of gravitational potential energy and energy conservation to determine the speed of the ball plus pendulum as it first begins to swing away from the vertical position after the “collision.”
(3) To explore the relationships between the momentum and kinetic energy of the ball as launched and the momentum and kinetic energy of the ball plus pendulum immediately after the ball is caught by the pendulum apparatus.
INTRODUCTION
The “ballistic pendulum” carries this name because it provides a simple method of determining the speed of a bullet shot from a gun. To determine the speed of the bullet a relatively large, massive block of wood is suspended as a pendulum. The bullet is shot into the wooden block without penetrating clear through it. This is a type of “sticky” collision where the two masses
(bullet and block) “stick” to one another and move together after the collision. By noting the angle to which the block and bullet swing after the collision, the initial speed can be determined by using conservation of momentum. But how do we know that momentum is conserved in this type of collision? In our case the ballistic pendulum apparatus will be used to compare the momentum of the steel ball before the “collision” to the momentum of the ball and pendulum apparatus, equivalent to the wooden block plus the bullet, after the collision. A comparison of the kinetic energy of the ball before the collision with the kinetic energy of the system afterward will also be made.
angle indicator plumb bob launcher Fig. 1. Ballistic pendulum apparatus
As shown in the diagram the projectile launcher used previously is mounted horizontally so that the pendulum can catch the emerging steel ball. The angle