Question

Two friends, Burt and Ernie, are standing at opposite ends of a uniform log that is floating in a lake. The log is 3.2m long and has mass 290kg . Burt has mass 33kg and Ernie has mass 32kg, Initially the log and the two friends are at rest relative to the shore. Burt then offers Ernie a cookie, and Ernie walks to Burt's end of the log to get it,then Relative to the shore, what distance has the log moved by the time Ernie reaches Burt? Neglect any horizontal force that the water exerts on the log and assume that neither Burt nor Ernie falls off the log.

Answer 1

Answer:

x = 0.29 m

Explanation:

As we know that the net external force on the system of mass is ZERO

so here the COM of whole system will always remain at rest

So we will have

$m_1\Delta x_1 + m_2\Delta x_2 + m_3\Delta x_3 = 0$

here we know that Ernie walks to Burt's position so we have

$33 x + 290 x + 32(-3.2 + x) = 0$

$355 x = 102.4$

so we have

$x = \frac{102.4}{355}$

$x = 0.29 m$

Answer 2

The distance has the log moved by the time Ernie reaches Burt relative to shore, is 0.29 meters.

What is center of mass?

The center of mass of a object or for a system of object is the point, where the center of distribution of mass in space. The center of mass for the for bodies to be remained at rest must be equal to the zero.

It can be given as,

$\sum m_i\Delta x_i=0$

Here, (m) represents the mass and (x) represents the distance.

The log is 3.2m long and has mass 290kg . Burt has mass 33kg and Ernie has mass 32kg.

Burt then offers Ernie a cookie, and Ernie walks to Burt's end of the log to get it.

Let the distance has the log moved by the time Ernie reaches Burt is x meters. Therefore, from the above equation,

$33(x)+290(x)+32(x-3.2)=0\\x=0.29\rm \; m$

Hence, the distance has the log moved by the time Ernie reaches Burt is 0.29 meters.

Learn more about the center of mass here;

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