Question

Question #4444b

Answer 1

I found 224Joules

Explanation:

Kinetic energy is equal to:

`K = (m*v^2)*7/10`

Assuming there are no losses, the speed is constant = 8m/s

So, `K = (7*8^2)*7/10` = 313,6 Joules

Answer 2

`313,6J`

Explanation:

If we also take into account the rotational kinetic energy due to the rolling motion, then we get :

`(E_K)_(Total)=(E_k)_(Translation) + (E_k)_(Rotation)`

`=1/2mv^2+1/2Iomega^2`, where I is the moment of inertia of the sphere, and omega is the angular velocity at which the sphere is rotating.

`=(1/2xx7xx8^2)+(1/2xx2/5xx7xxR^2xxomega^2)`

`=(224+7/5R^2omega^2)` Joules

where R is the radius of the solid sphere.

But since the linear and angular velocities may be related by the equation `v=r omega`, we may substitute this into the expression to yield :

`=(224+7/5R^2(v/R)^2) = 224+(7xx8^2)/5=313,6 J`

Answer 3

KE =`1/2mv^2`

Explanation:

The question phrasing implies frictionless motion, and NO dimensions of the mass are given, so shape is irrelevant (and also rotational motion).

Some equations posted omitted the "1/2" and are incorrect.