A girl of mass mG İs standing on a plank of mass mp.Both are originally at rest on a frozen lake thatconstitutes a frictionless, flat surface. The girl beginsto walk along the plank at a constant velocity VGP tothe right relative to the plank. (The subscript GPdenotes the girl relative to the plank.)(a) What is the velocity vp, of the plank relative tothe surface of the ice? (Use the following asnecessary: VGP, MG, and mp. Indicate the directionwith the sign of your answer. Let the positivedirection be in the direction that the girl walks.)MGVGPmg+m,(b) What is the girl's velocity vGI relative to the icesurface? (Use the following as necessary: VGp, mGand mp. Indicate the direction with the sign of youranswer. Let the positive direction be in thedirection that the girl walks.)(m,VGp)mg+m,

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Description: A girl of mass mG İs standing on a plank of mass mp.Both are originally at rest on a frozen lake thatconstitutes a frictionless, flat surface. The girl beginsto walk along the plank at a constant velocity VGP tothe right relative to the plank. (The

Answered: A girl of mass mg is standing on a…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter9: Linear Momentum And Collisions

Section: Chapter Questions

Problem 66P: Two particles of masses m1 and m2 , move uniformly in different circles of radii R1 and R2 R2 about...

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A girl of mass mG İs standing on a plank of mass mp.
Both are originally at rest on a frozen lake that
constitutes a frictionless, flat surface. The girl begins
to walk along the plank at a constant velocity VGP to
the right relative to the plank. (The subscript GP
denotes the girl relative to the plank.)
(a) What is the velocity vp, of the plank relative to
the surface of the ice? (Use the following as
necessary: VGP, MG, and mp. Indicate the direction
with the sign of your answer. Let the positive
direction be in the direction that the girl walks.)
MGVGP
mg+m,
(b) What is the girl's velocity vGI relative to the ice
surface? (Use the following as necessary: VGp, mG
and mp. Indicate the direction with the sign of your
answer. Let the positive direction be in the
direction that the girl walks.)
(m,VGp)
mg+m,

Expert Solution

Part (a)

The girl plank system is isolated, so horizontal momentum is conserved.

The expression for the law of conservation of momentum relative to the ice,

${\vec{p}}_{g i} + {\vec{p}}_{p i} = {\vec{p}}_{g f} + {\vec{p}}_{p f}$

The motion is in one dimension,

$\begin{array}{rcl} v_{g i} \hat{i} & = & v_{g p} \hat{i} + v_{p i} \hat{i} \\ v_{g i} & = & v_{g p} + v_{p i} \end{array}$

Step 2

Rewrite the expression for equation (1) relative to momentum,

$\begin{array}{rcl} m_{g} v_{g i} \hat{i} + m_{p} v_{p i} \hat{i} & = & 0 \\ m_{g} v_{g i} + m_{p} v_{p i} & = & 0 \end{array}$

Substitute,

$\begin{array}{rcl} m_{g} (v_{g p} + v_{p i}) + m_{p} v_{p i} & = & 0 \\ m_{g} v_{g p} + m_{g} v_{p i} + m_{p} v_{p i} & = & 0 \\ m_{g} v_{g p} & = & - v_{p i} (m_{g} + m_{p}) \\ v_{p i} & = & - (\frac{m_{g}}{m_{g} + m_{p}}) v_{g p} \end{array}$

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