Question

In the final scenario, both objects start at rest together on the track. Object one has a mass of 10.0 kg, and object two has a mass of 5.0 kg. Combined, they are at rest, then a spring is released, and object one moves away at 4.0 m/s. What will object two's velocity be at this point?

Answer 1

Using the conservation of momentum, object two will have a velocity of 8.0 m/s in the direction opposite to object one to conserve the total momentum of the system.

Step-by-step explanation:

The question pertains to the conservation of momentum, which is a fundamental concept in physics. When the spring is released, object one moves away at 4.0 m/s. Since both objects were initially at rest, their combined momentum was zero. After the spring is released, to conserve momentum, the velocities of the two objects must result in a net momentum of zero because no external forces are acting on the system. We can calculate object two's velocity using the formula m1*v1 + m2*v2 = 0, where m1 and m2 are the masses of the objects and v1 and v2 are their respective velocities.

Substituting object one's mass (10.0 kg) and velocity (4.0 m/s), and object two's mass (5.0 kg) and its unknown velocity, we get:

10.0 kg * 4.0 m/s + 5.0 kg * v2 = 0

Solving for v2 gives us:

5.0 kg * v2 = -40 kg*m/s

v2 = -8.0 m/s

Therefore, object two will move at 8.0 m/s in the opposite direction to conserve momentum.