Question

Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed v1 = v and has mass m1 = 2m. Object 2 moves with speed v2 = √2v and has mass m2 = m.Part A:Which object has the larger momentum?A) Object 1 has the greater momentum.B) Object 2 has the greater momentum.C) Both objects have the same momentum.Part B:Which object has the larger kinetic energy?Object 1 has the greater kinetic energy.Object 2 has the greater kinetic energy.The objects have the same kinetic energy.

Answer 1

1) A) Object 1 has the greater momentum

The magnitude of the momentum of an object is given by:

`p=mv`

where

m is the mass of the object

v is its speed

Object 1 has a mass of
`m_1 = 2m` and a speed of
`v_1 = v`, so its momentum is

`p_1 = m_1 v_1 = (2m)(v)=2mv`

Object 2 has a mass of
`m_2 = m` and a speed of
`v_2 = √(2) v`, so its momentum is

`p_2 = m_2 v_2 = (m)(√(2) v)=√(2)mv`

So we see that
`p_1 > p_2`, so object 1 has the greater momentum.

2) The objects have the same kinetic energy.

The kinetic energy of an object is given by

`K=(1)/(2)mv^2`

where

m is the mass of the object

v is its speed

Object 1 has a mass of
`m_1 = 2m` and a speed of
`v_1 = v`, so its kinetic energy is

`K_1 = (1)/(2)m_1 v_1^2 = (1)/(2)(2m)(v)^2=mv^2`

Object 2 has a mass of
`m_2 = m` and a speed of
`v_2 = √(2) v`, so its kinetic energy is

`K_2 = (1)/(2)m_2 v_2^2 = (1)/(2)(m)(√(2) v)^2=mv^2`

So we see that
`K_1 =K_2`, so the objects have same kinetic energy