Question

Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.39 kg and a speed of 0.99 m/s. Cart 2 has a mass of 0.64 kg.

PART A

What speed must cart 2 have if the total momentum of the system is to be zero?

Express your answer using two significant figures.

PART B

Since the momentum of the system is zero, does it follow that the kinetic energy of the system is also zero?

YES or NO

PART C

Verify your answer to part B by calculating the system's kinetic energy.

Express your answer using two significant figures.

K=?

Answer 1

SInce they are moving towards each other each should have equal momentum to cancel each other out

let m₁ be the mass of cart 1 and v₁ be its velocity. In cart 1 m₁ and v₁ are both given.

Similarly let m₂ be the mass of cart 2 and v₂ be its velocity. In this case only m₂ is given.

So according to the condition we write,

B) No having zero momentum does not mean that the system will have zero kinetic energy. The reason is that while momentum may cancel because of vector properties. Kinetic energy is always scalar in nature. Also it contains squared of velocity so it can never be negative itself.

C)Kinetic Energy of system K.E_T is the summation of Kinetic energy of cart 1, K.E₁ and cart 2, K.E₂

As we can see even though the momentum of system is zero the total kinetic energy is not zero.