Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 7, Problem 95P

(a)

To determine

The distance between the raft and pier when the women walks toward the pier until she gets to the other end of the raft and stops there.

(a)

Expert Solution
Check Mark

Answer to Problem 95P

The distance is 2.5m.

Explanation of Solution

Mass of women is 60.0kg, mass of raft is 120kg, length of raft is 6.0m, and the distance to the end of raft from the pier is 0.50m.

Imagine that the initial position of women is x=0 and the position of pier is left to the women.

Write the equation for the center of mass for the woman, pier, and the raft system.

xcm=mwxwi+mrxrimw+mr (I)

Here, xcm is the distance from origin to the center of mass of the system, mw is the mass of women, mr is the mass of raft, xwi is the initial distance from the center of mass to the position of women, and xri is the initial distance from the center of mass to the position of raft.

Initially, xcm will be right to xri.After the women reached the other end of raft, xcm will be the left of xri.

Write the relation between xri,xcm, and the final distance between the raft from the center of mass arises due to the symmetry of system.

xcmxri=xcmxrfxrf=2xcmxri

Write the equation for the final distance of raft from the pier.

df=xrf(l2)

Here, df is the final distance of raft from the pier and l is the length of raft.

Rewrite the above relation by substituting 2xcmxri for xrf.

df=2xcmxri(l2) (II)

Write the equation for xwi.

xwi=l+drp (III)

Here, drp is the initial distance from the end of raft to the pier.

Write the equation to find xri.

xri=l2+drp (IV)

Conclusion:

Substitute 6.0m for l and 0.5m for drp in equation (IV) to find xri.

xri=(6.0m2)+0.5m=3.5m

Substitute 6.0m for l and 0.5m for drp in equation (III) to find xwi.

xwi=6.0m+0.5m=6.5m

Substitute 6.5m for xwi, 60.0kg for mw, 3.5m for xri, and 120kg for mr in equation (I) to find xcm.

xcm=(60.0kg)(6.5m)+(120.0kg)(3.5m)(60.0kg)+(120.0kg)=810kgm180kg=4.5m

Substitute 4.5m for xcm, 3.5m for xri, and 6.0m for l in equation (II) to find df.

df=2(4.5m)3.5m(6.0m2)=2.5m

Therefore, the distance is 2.5m.

(b)

To determine

The distance travelled by the woman relative to pier in part (a).

(b)

Expert Solution
Check Mark

Answer to Problem 95P

The distance travelled is 4.0m.

Explanation of Solution

Mass of women is 60.0kg, mass of raft is 120kg, length of raft is 6.0m, and the distance to the end of raft from the pier is 0.50m.

Imagine that the initial position of women is x=0 and the position of pier is left to the women.

Write the equation for the distance travelled by women relative to pier.

|Δxw|=|dfxwi|

Here. |Δxw| is the distance travelled by women relative to pier.

Conclusion:

Substitute 2.5m for df and 6.5m for xwi in the above equation to find |Δxw|.

|Δxw|=|2.5m6.5m|=4.0m

Therefore, the distance is 4.0m.

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Chapter 7 Solutions

Physics

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