Question

In a ballistic pendulum, a spring pushes a ball from rest. It flies through the air and sticks in the base of a pendlum that swings upwards.

Given that the ball and pendulum reach a maximum angle of 45º, the pendulum is 30 cm long, the mass of the ball is 76 g, and the mass of the pendulum is 250 g, calculate the speed of the ball after it has left the spring but before it hits the pendulum. Do not include the units in your response.

Answer 1

The speed of the ball after it has left the spring but before it hits the pendulum is approximately 3.89 m/s.

To calculate the speed of the ball after it has left the spring but before it hits the pendulum, we can use the principle of conservation of mechanical energy. The initial potential energy of the ball is converted into kinetic energy as it moves through the air.

The formula for the speed of an object at a given height is v = sqrt(2gh), where v is the speed, g is the acceleration due to gravity, and h is the height. In this case, the height is given by the maximum angle reached by the pendulum, which is 45º.

We can use the formula v = sqrt(2gh) with the given values to calculate the speed of the ball. The acceleration due to gravity is approximately 9.8 m/s^2.

Therefore, the speed of the ball after it has left the spring but before it hits the pendulum is approximately 3.89 m/s.