The Conservation of Momentum in Frictionless Roller Skates Experiment

How does momentum conservation work in a scenario involving a frictionless roller skates experiment?

Given the scenario where a friend, wearing frictionless roller skates, catches a pumpkin thrown at her with a specific velocity, what will be the resultant velocity of the friend and the pumpkin?

Answer:

Approximately 0.48 m/s

When analyzing the conservation of momentum in a scenario like the frictionless roller skates experiment, we need to consider the initial momenta of the objects involved and how they would change once they interact with each other.

In this particular scenario, the friend is initially standing still with a mass of 68 kg, wearing frictionless roller skates, while a pumpkin weighing 3.6 kg is thrown at her with a velocity of 9.5 m/s. When the friend catches the pumpkin, momentum conservation dictates that the combined momentum of the friend and the pumpkin before and after the interaction remains constant.

To calculate the resultant velocity of the friend and the pumpkin, we need to find the initial momentum of each object and then determine the combined mass of the system to obtain the final velocity.

By using the formula for momentum (p = m * v), where p is momentum, m is mass, and v is velocity, we can determine the initial momentum of the friend as 0 kg*m/s since she was stationary. The initial momentum of the pumpkin is calculated to be 34.2 kg*m/s.

After the interaction, the resultant momentum of the friend and the pumpkin is equal to 34.2 kg*m/s. To find the resultant velocity, we need to divide this resultant momentum by the combined mass of the friend and the pumpkin (68 kg + 3.6 kg) to get approximately 0.48 m/s. This signifies the final velocity of the friend and the pumpkin after the interaction.

Therefore, in this frictionless environment, the conservation of momentum principle allows us to determine the outcome of the scenario involving the friend, roller skates, and the thrown pumpkin accurately.