Question

Figure 9-32: A block on a horizontal floor is initially either stationary, sliding in the positive direction of an x-axis, or sliding in the negative direction of that axis. Then the block explodes into two pieces that slide along the x-axis. Assume the block and the two pieces form a closed, isolated system. Six choices for a graph of the momenta of the block and the pieces are given, all versus time t. Determine which choices represent physically impossible situations and explain why.

Short answer

The choices (a), (c), (e), and (f) represent physically impossible situations because, in these situations, the momentum is not conserved.

Step-by-step solution

The given data

Six choices for the graph of momentum of block and the pieces versus time are given.

Understanding the concept of the conservation of momentum

Using the law of conservation of momentum, we can find the choices which represent the physically impossible situations that are for non-conserved momentum.

Formula:

According to the conservation of momentum, ${\mathrm{P}}_{\mathrm{i}}={\mathrm{P}}_{\mathrm{f}}$ (1)

Calculation of the choices of physically impossible situations

Let P be the momentum of the block and P₁ and P₂ are the momenta of pieces.

According to the law of conservation of momentum of equation (1), we get that

$\mathrm{P}={\mathrm{P}}_1+{\mathrm{P}}_2$

From plot (a) we can infer that

$\mathrm{P}<{\mathrm{P}}_1+{\mathrm{P}}_2$.

This implies that momentum is not conserved.

Therefore, choice (a) represents a physically impossible situation.

From plot (b) we can infer that

$\mathrm{P}={\mathrm{P}}_1+{\mathrm{P}}_2$.

This implies that momentum is conserved.

Therefore, choice (b) represents a physically possible situation.

From plot (c) we can infer that

$\mathrm{P}<{\mathrm{P}}_1+{\mathrm{P}}_2$

.

This implies that momentum is not conserved.

Therefore, choice (c) represents a physically impossible situation

From plot (d) we can infer that,

$\mathrm{P}={\mathrm{P}}_1+{\mathrm{P}}_2$.

This implies that momentum is conserved.

Therefore, choice (d) represents a physically possible situation

From plot (e) we can infer that

$\mathrm{P}>{\mathrm{P}}_1+{\mathrm{P}}_2$.

This implies that momentum is not conserved.

Therefore, choice (e) represents a physically impossible situation

From plot (f) we can infer that,

$\mathrm{P}<{\mathrm{P}}_1+{\mathrm{P}}_2$.

This implies that momentum is not conserved.

Therefore, choice (f) represents a physically impossible situation.