A Ballistic Pendulum. A 12.0 g rifle bullet is fired with a speed of 380 m / s into a ballisti

step 1 Hi, here in this given problem, mass of the rifle bullet, that is M is equal to 12 .0 gram, and

A Ballistic Pendulum. A 12.0 g rifle bullet is fired with a...

A Ballistic Pendulum. A $12.0 \mathrm{~g}$ rifle bullet is fired with a speed of $380 \mathrm{~m} / \mathrm{s}$ into a ballistic pendulum with mass $9.00 \mathrm{~kg}$, suspended from a cord $70.0 \mathrm{~cm}$ long (see Example 8.8 in Section 8.3 ). Compute (a) the vertical height through which the pendulum rises, (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the wood.

A Ballistic Pendulum. A $12.0 \mathrm{~g}$ rifle bullet is fired with a speed of $380 \mathrm{~m} / \mathrm{s}$ into a ballistic pendulum with mass $9.00 \mathrm{~kg}$, suspended from a cord $70.0 \mathrm{~cm}$ long (see Example 8.8 in Section 8.3 ). Compute
(a) the vertical height through which the pendulum rises,
(b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the wood.

Key Concepts

Ballistic Pendulum

A ballistic pendulum is an experimental apparatus used to measure the speed of a projectile, such as a bullet, by embedding it into a pendulum mass and analyzing the resulting swing. The key principle is that the projectile’s momentum is transferred to the pendulum, which then rises to a maximum height that can be used to determine the projectile's initial velocity.

Inelastic Collision

In an inelastic collision, two bodies collide and stick together, meaning that while momentum is conserved, some of the kinetic energy is converted into other forms of energy such as heat or deformation. In a ballistic pendulum, the bullet embeds itself into the pendulum, making this type of collision crucial for understanding the energy and momentum transfer.

Conservation of Momentum

The conservation of momentum is the principle stating that the total momentum of a closed system remains constant if no external forces act upon it. During the collision in a ballistic pendulum experiment, this principle is applied to relate the momentum of the incoming projectile to that of the combined system of the bullet and the pendulum immediately after the collision.

Conservation of Energy

After the collision, the mechanical energy of the combined bullet-pendulum system is conserved as it converts its kinetic energy into gravitational potential energy during the pendulum’s ascent. This principle allows us to calculate the vertical height to which the pendulum rises, by equating the kinetic energy immediately after the impact with the gravitational potential energy at the maximum height.

Kinetic Energy and Gravitational Potential Energy

Kinetic energy is the energy that an object has due to its motion, and gravitational potential energy is the energy stored by an object due to its position in a gravitational field. In a ballistic pendulum, the bullet’s initial kinetic energy is partly lost during the inelastic collision, and the remaining kinetic energy of the combined system is then converted to gravitational potential energy as the pendulum rises.

Transcript

Please give Ace some feedback