A 0.156 kg ice puck collides with a 0.170 kg ice puck. Both were originally moving at the same speed. Which one has the larger change in velocity?

Or do they have the same change in velocity?

To determine which ice puck has the larger change in velocity, we first need to understand the concept of momentum.

The momentum of an object is defined as the product of its mass and velocity: momentum = mass × velocity. It is a vector quantity, meaning it has both magnitude and direction.

In a collision, the law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, provided no external forces are acting on the system.

Let's denote the initial velocity of both ice pucks as v. Since they are originally moving at the same speed, their initial momenta will be equal.

Now, let's consider the collision. The change in velocity of an object after a collision depends on the forces acting on it and its mass. In this case, both ice pucks experience the same force since they are colliding with each other. However, their masses are different.

To find the change in velocity for each ice puck, we can use the principle of conservation of momentum:

Initial momentum of ice puck 1 (m1 × v) + Initial momentum of ice puck 2 (m2 × v) = Final momentum of ice puck 1 (m1 × v1) + Final momentum of ice puck 2 (m2 × v2)

Since the initial velocities are the same (v), we get:

m1 × v + m2 × v = m1 × v1 + m2 × v2

Since the masses (m1 and m2) and initial velocities (v) are the same for both ice pucks, we can simplify the equation to:

v × (m1 + m2) = v1 × m1 + v2 × m2

We can rearrange the equation to solve for the change in velocity:

v1 - v = (m2 / (m1 + m2)) × (v2 - v)

Now, let's calculate the change in velocity for each ice puck:

For ice puck 1:
m1 = 0.156 kg
m2 = 0.170 kg
v = initial velocity

For ice puck 2:
m1 = 0.170 kg
m2 = 0.156 kg
v = initial velocity

Using the above values, you can substitute them into the equation to find the change in velocity for ice puck 1 and ice puck 2. Comparing those values will provide the answer to your question.

To determine which ice puck has the larger change in velocity, we need to consider the principle of conservation of momentum.

According to the principle of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision, assuming no external forces act on the system.

Mathematically, we can express this as:

m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final

Where:
m1 and m2 are the masses of the ice pucks
v1_initial and v2_initial are the initial velocities of the ice pucks
v1_final and v2_final are the final velocities of the ice pucks

Given that the ice pucks were originally moving at the same speed, we can assume:

v1_initial = v2_initial

Now, let's consider the possible scenarios:

1. If the two ice pucks stick together after the collision (perfectly inelastic collision), they will have a common final velocity. In this case, both ice pucks will have the same change in velocity.

2. If the two ice pucks rebound off each other after the collision (elastic collision), they will have different final velocities. In this case, one ice puck will have a larger change in velocity compared to the other.

Without specific information about the type of collision, we cannot determine whether both ice pucks have the same change in velocity or if one has a larger change in velocity.