A 17 g rifle bullet traveling 220 m/s buries itself in a 3.9 kg pendulum hanging on a 3.0 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's displacement.
Horizantal ____ J
Vertical _____ J
Find the velocity at the time of impact from KE. Then, you can use conservation of momentum to find the penduluem/bullet combo at impact. From that, you know the KE of the combo, and it rises in height to have an increase in PE equaling the iniitial KE. At the max height, use geometry to find the angle it goes upwards.
bob, how can he solve for h if we don't know the initial height of the pendulum? we can't assume that's at zero.
To determine the vertical and horizontal components of the pendulum's displacement, we need to consider the conservation of momentum and the conservation of energy.
1. Conservation of momentum:
Since the bullet buries itself in the pendulum, we can assume that the total momentum before and after the collision is conserved. The initial momentum of the bullet can be calculated as the product of its mass and velocity:
Initial momentum (bullet) = mass (bullet) x velocity (bullet)
= 0.017 kg x 220 m/s
The momentum of the pendulum and the bullet after the collision is zero because both objects are at rest after the collision.
2. Conservation of energy:
The initial kinetic energy of the bullet is equal to the final potential energy gained by the pendulum. The pendulum's potential energy can be calculated using the equation:
Potential energy (pendulum) = mass (pendulum) x gravity x height
Given that the mass of the pendulum is 3.9 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height is equal to the length of the string (3.0 m), we can calculate the potential energy.
3. Analyzing displacement:
The displacement of the pendulum will have both vertical and horizontal components. The vertical component corresponds to the height to which the pendulum swings upward, while the horizontal component corresponds to the distance the pendulum swings to one side.
To calculate the vertical component of the displacement, we can use the conservation of energy equation mentioned above. The horizontal component of the displacement can be determined using the Pythagorean theorem, as the displacement forms a right-angled triangle with the vertical and horizontal components.
To calculate the exact values, we need the height of the pendulum swing. Please provide the height, and I will help you calculate the vertical and horizontal components of the pendulum's displacement.