Question

marble momentum lab
fold the index card in half so that it stands up (see picture). the idea is that marble will roll down the ruler and bump the card. the farther the index card moves, the more momentum the marble has. use a ruler (centimeters) to measure how far the index card moved back.
next, prop the ruler up on two books. roll the same marble down the ruler. will the card get pushed away farther?
mass of the small marble

height	distance the card moved	total time the marble traveled	marble speed v = d/t	p=mv momentum
2 books height	30	1.85	25.2	188.0
3 books height	25	0.82	30.4	188.9

1. how do your results compare to each other?
2. why did one height have more momentum than the other? explain.

Explanation:

Step1: Analyze momentum formula

Momentum \(P = mv\), where \(m\) is mass and \(v\) is velocity. As the mass of the marble is constant, momentum depends on velocity.

Step2: Consider velocity - height relationship

When the ruler is propped up higher (more books), the marble has a greater potential - energy at the start. By conservation of energy, more potential energy is converted to kinetic energy, resulting in a higher velocity.

Step3: Analyze results comparison

As the height of the ruler (number of books) increases, the velocity of the marble increases (from \(v=\frac{d}{t}\) values). Since \(P = mv\) and \(m\) is constant, the momentum also increases. The card moves farther when the marble has more momentum.

Step4: Answer question 1

The results show that as the height of the ruler (number of books) increases, the distance the card moves increases, the speed of the marble increases, and the momentum of the marble increases. This is because a higher starting - height gives the marble more potential energy which is converted to more kinetic energy and higher velocity.

Step5: Answer question 2

A higher height has more momentum because, according to the conservation of mechanical energy, a greater initial potential energy \(U = mgh\) (where \(h\) is the height) is converted into more kinetic energy \(K=\frac{1}{2}mv^{2}\) at the bottom of the ruler. Since \(P = mv\) and \(m\) is constant, a higher velocity \(v\) (from higher \(h\)) leads to more momentum.

Answer:

1. As the height of the ruler (number of books) increases, the distance the card moves, the speed of the marble, and the momentum of the marble all increase. This is due to more potential energy being converted to kinetic energy for higher starting - heights.
2. A higher height has more momentum because more potential energy is converted to kinetic energy, resulting in a higher velocity. Since \(P = mv\) and mass \(m\) is constant, higher velocity means higher momentum.