Question

A man standing on frictionless ice throws a boomerang, which returns to him. Choose the correct statement::: a) Since the momentum of the man-boomerang system is conserved, the man will come to rest holding the boomerang at the same location from which he threw it. b) It is impossible for the man to throw a boomerang in this situation. c) It is possible for the man to throw a boomerang, but because he is standing on frictionless ice when he throws it, the boomerang cannot return. d) The total momentum of the man-boomerang system is not conserved, so the man will be sliding backward holding the boomerang after he catches it.

Short answer

Answer: The man comes to rest holding the boomerang at the same location from which he threw it, and the momentum of the man-boomerang system is conserved.

Step-by-step solution

Analyze statement (a)

In this statement, it is mentioned that the momentum of the man-boomerang system is conserved and the man comes to rest holding the boomerang at the same location from which he threw it. The momentum of the system can be written as: \(p_{system} = p_{man} + p_{boomerang}\) Initially, both the man and the boomerang are at rest, so \(p_{system} = 0\). The man throws the boomerang, which gains some momentum, but as there is no external force acting on the man, he must experience an opposite momentum to keep the total momentum of the system conserved so that still \(p_{system} = 0\). Thus, this statement is plausible.

Analyze statement (b)

This statement claims that it's impossible for the man to throw a boomerang in this situation. This is not correct because the man is still able to exert a force on the boomerang to throw it, even though he's standing on a frictionless surface. However, as discussed in step 1, throwing the boomerang would also cause an opposite momentum on the man.

Analyze statement (c)

This statement claims that the boomerang cannot return due to the man standing on frictionless ice. However, the boomerang's trajectory is determined by the aerodynamic forces that it experiences during its flight and is independent of the initial conditions that the thrower is in which has no effect on whether the boomerang returns or not. Thus, this statement is false.

Analyze statement (d)

This statement claims that the total momentum of the man-boomerang system is not conserved, which implies that there is an external force acting on the system. However, since the man is standing on frictionless ice, no external force (other than negligible air resistance) is acting on the man. So, the momentum conservation principle must hold true. Thus, this statement is false.

Conclusion

By analyzing each statement, we find that statement (a) is the correct statement and is based on the conservation of momentum principle. As there is no external force acting on the man-boomerang system, the momentum will be conserved, and the man will come to rest holding the boomerang at the same location from which he threw it.

Key concepts

Momentum Conservation Principle

Understanding the momentum conservation principle is like understanding a cosmic rule of fairness; in an isolated system, the total momentum must remain constant.

In simpler terms, if you imagine a pair of skaters pushing off each other on ice, they move in opposite directions, but their combined momentum remains the same as before they pushed. This principle is incredibly crucial in physics because it allows us to predict the outcomes of various interactions without knowing all the nitty-gritty details.

When a man on frictionless ice throws a boomerang, regardless of the fact that he's standing on an extra slippery surface, as long as no external forces interfere - like wind or a sneaky ice monster - the momentum before and after he throws the boomerang must be the same. The action of throwing the boomerang forwards will cause an equal and opposite momentum that pushes him backwards, maintaining the balance of the system's momentum. This is why the initial scenario suggests that the man could come to rest holding the boomerang at the same location from which he threw it.

Frictionless Surface Dynamics

Let's now put the spotlight on frictionless surface dynamics, which seem to perplex many a student with visions of eternal sliding and graceful, unending glides. A frictionless surface is a theoretical concept where no force opposes the motion of objects. In the real world, everything would grind to a halt without friction but in thought experiments and physics problems, magical ice or super-slick surfaces give us a perfect stage to observe momentum conservation.

Our boomerang-flinging man on the fictional ice is a prime example. The absence of friction means that when he throws the boomerang, he will move in the opposite direction. No friction to slow him down means he'll keep moving until he grabs hold of that returning boomerang, and only the forces involved in the catch can change his momentum and bring him to rest.

It's important in these frictionless scenarios to understand that movement in one direction will always spur an equal and opposite movement. These are the perfect conditions to observe pure momentum transfer, untainted by the sticky meddling of friction.

Boomerang Physics

Finally, let's delve into the mesmerizing world of boomerang physics. A boomerang, when thrown correctly, traces out a curved path in the air and then – almost like it has a mind of its own – returns to the thrower. This is down to its unique flat, two-winged shape and the way it's thrown with a spin.

The wings of a boomerang are airfoils, shaped to create lift as they move through the air, much like an airplane’s wings. When you throw a boomerang with a spin, one wing moves in the direction of the throw while the other moves against it. This difference in speed between the wings creates an uneven lift force known as the 'Magnus effect,' causing the boomerang to veer off to one side – curving through the air on its return journey.

The Physics of the Catch

Even on a frictionless surface, the physics behind a boomerang's return isn't bothered by what the thrower is standing on. The return of the boomerang is influenced by its spin, lift, and the Magnus effect - working together with the precision of a Swiss watch to guide it back. If you take into account the lack of friction underfoot, catching the boomerang is simply another act in the play of forces, and with the correct approach, our ice-standing man can indeed catch it and bring himself to rest at the point of origin – all in compliance with the immutable law of momentum conservation.