A body at rest breaks into two pieces of equal masses. The parts will move

When a body at rest breaks into two pieces of equal masses, the behavior of those pieces can be understood through the principles of conservation of momentum. Since the initial momentum of the system is zero (because the body is at rest), the total momentum after the break must also equal zero. This means that the two pieces will move in opposite directions with equal momentum.

Understanding Momentum Conservation

Momentum is defined as the product of an object's mass and its velocity. Mathematically, it is expressed as:

Momentum (p) = mass (m) × velocity (v)

In this scenario, we have a body that is initially at rest, so its total momentum is:

Initial Momentum = 0

Breaking into Two Equal Masses

Let’s say the body has a mass of M. When it breaks into two equal pieces, each piece will have a mass of:

m1 = m2 = M/2

Since the total momentum must remain zero after the break, we can express the momentum of each piece. If we denote the velocities of the two pieces as v1 and v2, the conservation of momentum gives us:

m1 × v1 + m2 × v2 = 0

Setting Up the Equation

Substituting the masses into the equation, we have:

(M/2) × v1 + (M/2) × v2 = 0

This simplifies to:

v1 + v2 = 0

Interpreting the Results

This equation tells us that the velocities of the two pieces are equal in magnitude but opposite in direction. If one piece moves to the right with a velocity v, the other piece must move to the left with a velocity of -v. This ensures that the total momentum remains zero, adhering to the law of conservation of momentum.

Example Scenario

Imagine a 10 kg object at rest that breaks into two 5 kg pieces. If one piece moves to the right at 3 m/s, we can find the velocity of the other piece:

5 kg × 3 m/s + 5 kg × v2 = 0

This leads to:

15 kg·m/s + 5 kg × v2 = 0

Solving for v2 gives:

v2 = -3 m/s

This means the second piece moves to the left at 3 m/s, perfectly balancing the momentum of the first piece.

Visualizing the Concept

To visualize this, think of a seesaw. If one side goes up, the other side must go down to maintain balance. Similarly, when the body breaks apart, the movement of one piece in one direction is balanced by the movement of the other piece in the opposite direction, keeping the system's momentum at zero.

In summary, when a body at rest breaks into two equal masses, those pieces will move in opposite directions with equal speeds, ensuring that the total momentum of the system remains conserved. This principle is fundamental in physics and helps us understand various phenomena in mechanics.