Question

A toy rocket is launched upward with a spring, and you want to determine the time that the spring is in contact with the rocket causing acceleration. Your friend claims that's easy: just measure the mass of the rocket, the height it goes, and do the math. You disagree and say that you also need the force of the spring on the rocket. Make a claim: who is correct, and provide evidence and reasoning for your answer.

Answer 1

The correct claim is that you need to know the force of the spring as well as the mass of the rocket and the height it reaches to determine the spring's contact duration.

Step-by-step explanation:

You are correct in suggesting that to determine the time the spring is in contact with the rocket causing acceleration, knowledge of the force of the spring is necessary. Just measuring the mass of the rocket and the height it reaches does not provide enough information to calculate the duration of the spring's contact without the force exerted by the spring. To explain further, the equation F = ma (Force equals mass times acceleration) is central to this calculation. If you know the spring force (F) and the mass (m) of the rocket, you can solve for the acceleration (a). Knowing the acceleration and using the impulse-momentum theorem, one can determine the change in velocity and, subsequently, calculate the contact time.

Additionally, the rockets reaching different heights due to the variable force exerted by the spring reinforces that the force is a crucial measurement. Without that variable, we cannot solve for the contact time accurately. Thus, your friend's suggestion to only measure mass and height for calculation would result in an incomplete analysis, because crucial information—the spring force—is missing from their equation.