A 11 kg object and a 19 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 12 m/s to the left.

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

The answer: Whatever it takes to make the total momentum of the two objects zero.

Their individual momenta will be equal in magnitude and opposite in direction.

Use that fact to solve for the larger object's velocity.

To find the velocity of the object with the larger mass, we can use the principle of conservation of momentum. According to this principle, the total momentum before the spring is released should be equal to the total momentum after the spring is released.

Momentum is given by the equation: momentum = mass x velocity.

Let's assume the velocity of the larger mass (19 kg) is v, and the velocity of the smaller mass (11 kg) is -12 m/s (since it moves to the left).

Before the spring is released, the total momentum is:

(11 kg) x (-12 m/s) + (19 kg) x 0
= -132 kg⋅m/s

After the spring is released, the total momentum must still be -132 kg⋅m/s.

Now, let's set up the equation to find the velocity of the larger mass:

(11 kg) x (-12 m/s) + (19 kg) x v = -132 kg⋅m/s

Simplifying the equation:

-132 kg⋅m/s + 19 kg⋅v = -132 kg⋅m/s
19 kg⋅v = 0
v = 0

Hence, the velocity of the object with the larger mass is 0 m/s. It means that the larger mass object remains at rest after the spring is released.