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 inertia m1=2m. Object 2 moves with speed v2=2√v and has inertia m2=m. Part A Which object has the larger magnitude of its momentum? Which object has the larger magnitude of its momentum? Object 1 has the greater magnitude of its momentum. Object 2 has the greater magnitude of its momentum. Both objects have the same magnitude of their momenta. Part Part B Which object has the larger kinetic energy? 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

A)Object 1 has the greater magnitude of its momentum.

B)The objects 2 have the greater kinetic energy.

Step-by-step explanation:

For object 1 :

v₁ = v ,m₁ = 2 m

For object 2 :

`v_2=2√(v)` ,m₂=m

We know that linear momentum given as

P = M V

M=Mass , V=Velocity

For object 1 :

P₁ =m₁ v₁

P₁ =2 m v

For object 2

`P_2=m_2v_2`

`P_2=2m\sqrt {v}`

We can say that object 1 have more momentum.

The kinetic energy

`KE_1=(1)/(2)m_1v_1^2`

`KE_1=(1)/(2)* 2m* v^2`

`KE_1=mv^2`

`KE_2=(1)/(2)m_2v_2`

`KE_2=(1)/(2)* m* 4v^2`

`KE_2=2mv^2`

Therefore both the object 2 have higher kinetic energy.