Conservation of Linear Momentum Problem

In summary, two identical twins with mass 52.6 kg each are on frictionless ice skates on a frozen lake. Twin A is carrying a backpack of mass 12.0 kg and throws it horizontally at 3.40 m/s to Twin B. Using conservation of linear momentum, the subsequent speeds of Twin A and Twin B can be calculated by setting up two equations, one for when the backpack is thrown and one for when it is caught. Gravity effects are neglected in this scenario.
  • #1
MG5
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Identical twins, each with mass 52.6 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 3.40 m/s to Twin B. Neglecting any gravity effects, what are the subsequent speeds of Twin A and Twin B?

I think I'd use conservation of linear momentum wouldn't I?

m1v1i + m2v2i = m1v1f + m2v2f

Would I do it twice? Once for when the backpack is thrown and then again for when it is caught?
 
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  • #2
Hi MG5! :smile:
MG5 said:
I think I'd use conservation of linear momentum wouldn't I?

m1v1i + m2v2i = m1v1f + m2v2f

Would I do it twice? Once for when the backpack is thrown and then again for when it is caught?

Yes! :smile: And yes! :smile: And yes! :smile:
 

What is the conservation of linear momentum problem?

The conservation of linear momentum problem is a fundamental principle in physics that states that the total momentum of a system remains constant when there are no external forces acting on the system. This means that the total momentum before an event or interaction is equal to the total momentum after the event or interaction.

How is the conservation of linear momentum problem applied in real-life situations?

The conservation of linear momentum problem is applied in many real-life situations, such as in collisions between objects, rockets launching into space, and even when walking or riding a bike. It is also used in the design of vehicles and structures to ensure their stability and safety.

What are the key equations used in solving conservation of linear momentum problems?

The key equations used in solving conservation of linear momentum problems are the momentum equation (p=mv), the impulse-momentum theorem (FΔt = Δp), and the law of conservation of momentum (m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'). These equations relate the mass, velocity, and forces involved in a system to determine the outcome of an interaction.

What are some common misconceptions about the conservation of linear momentum problem?

One common misconception is that momentum is only conserved in collisions, when in fact it is conserved in all interactions where there are no external forces acting. Another misconception is that the total momentum of a system must be zero, when in reality it can have a non-zero value as long as it remains constant.

How does the conservation of linear momentum problem relate to other principles in physics?

The conservation of linear momentum problem is closely related to other principles in physics, such as the conservation of energy and Newton's laws of motion. It is also applicable in the study of rotational motion, as angular momentum is conserved in the absence of external torques.

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