A 18 kg object and a 26 kg object are connected by a massless compressed spring and rest on a frictionless table. After the spring is released, the object with the smaller mass has a velocity of 2 m/s to the left.

What is the velocity of the object with the larger mass?

Total momentum remains zero.

65 To find the velocity of the object with the larger mass, we need to apply the principle of conservation of linear momentum. According to this principle, when two objects collide or interact, the total momentum before the interaction is equal to the total momentum after the interaction, provided no external forces are acting on the objects.

In this case, the smaller mass object (18 kg) has a velocity of 2 m/s. Let's call the velocity of the larger mass object (26 kg) V.

Since the spring is massless and there is no friction, we can assume that the interaction between the two objects happens instantaneously, and the magnitude of the momentum is conserved. Therefore, we can equate the initial and final momenta:

Initial momentum = final momentum

The initial momentum is the sum of the momenta of the two objects before the spring was released:

Initial momentum = (mass of smaller object) × (velocity of smaller object) + (mass of larger object) × (velocity of larger object)

Final momentum = (mass of smaller object) × (velocity of smaller object) + (mass of larger object) × (velocity of larger object)

Using the given information, we know that the mass of the smaller object is 18 kg, its velocity is 2 m/s, and the mass of the larger object is 26 kg. So, we can write:

18 kg × 2 m/s + 26 kg × V = 18 kg × 0 m/s + 26 kg × (velocity of larger object)

Simplifying this equation:

36 kg m/s + 26 kg × V = 0 kg m/s + 26 kg × V

Now, we can solve for V:

36 kg m/s = 26 kg × V

Dividing both sides by 26 kg:

(36 kg m/s) / 26 kg = (26 kg × V) / 26 kg

1.385 m/s = V

Therefore, the velocity of the object with the larger mass is approximately 1.385 m/s to the left.