Kinetic energy/rotational kinetic energy

[reb659]

Homework Statement

Imagine two scenarios. The system in both is the object and ruler.

In case 1, a rectangular object undergoes a collision with a ruler, which is initially at rest. It strikes the ruler on its center of mass.

In case 2, it is the same situation except the object strikes the ruler in some point between its center of mass and the end of the ruler.

In which case does the ruler have greater kinetic energy and why? Explain in terms of conserved quantities.

Homework Equations

The Attempt at a Solution

The net torque and net force in both cases would be zero by the laws of conservation of linear and angular momentum.

I'm reasoning that the kinetic energy in case 2 would be greater because in case 2, both rotational kinetic energy and kinetic energy are conserved while in case 1, only kinetic energy is conserved.

 

[reb659]

Sorry about the bump, but I have an exam soon and an answer to question would really help me piece things together.

 

[krogoth]

im going to give you my thoughts because you require some kind of answer now

this may not be correct, but it may help...so take it with a grain of salt...

case1:

there is a net force due to forward motion of ruler

there is a 0 net torque as the object strikes the ruler at its CG so there is no moment

and kenitic energy is present due to the forward motion of the ruler

case2:

there is a net force due to forward motion of ruler

there is a net force as the object strikes ruler a distance away from the CG of the ruler, so a moment is created allowing the ruler to spin

there is a higher kenetic energy in this case as the ruler is moving forward and spinning

hope that helps