Final answer:
The momentum of the ball-pendulum system at the moment the ball is caught can be calculated by first finding the velocity of the ball just before it is caught. Using the conservation of mechanical energy, we can equate the gravitational potential energy gained by the pendulum to the initial kinetic energy of the ball. Solving this equation will give us the velocity of the ball. Then, multiplying the total mass of the system by the velocity will give us the momentum of the system.
Step-by-step explanation:
The momentum of an object is defined as the product of its mass and velocity. In this case, we have a steel ball and a stationary pendulum. The ball has a mass of 65 grams and is shot horizontally. The pendulum has a mass of 260 grams and is stationary. When the ball is caught by the pendulum, the system gains momentum.
Assuming no energy losses due to friction or air resistance, the gravitational potential energy gained by the system is equal to the initial kinetic energy of the ball.
Gravitational potential energy gained = Initial kinetic energy of the ball
mgh = 0.5mv^2
Where m is the mass of the ball, g is the acceleration due to gravity, h is the height gained by the pendulum, and v is the velocity of the ball just before it is caught.
Plugging in the known values:
(0.065 kg)(9.8 m/s^2)(0.12 m) = 0.5(0.065 kg)v^2
Using this equation, we can solve for the velocity of the ball just before it is caught. Once we have the velocity, we can calculate the momentum of the ball-pendulum system by multiplying the total mass of the system (ball + pendulum) by the velocity.