The center of mass of the you-raft system from the end of the pier when you are at the very rear.

Question

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Answer 1

Question

Chapter 5, Problem 138P

(a)

To determine

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

(a)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Explanation of Solution

Given:

Length and mass of the raft are $6 m$ and $120 kg$ respectively.

Your mass is $60 kg$ .

Formula used:

The edge of the pier is taken as the origin and the right side of the pier is taken as positive $X−$ direction, as shown in the Figure $1$ .

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 1

Figure: $1$

In the figure $2$ , $d$ is the distance of the end of the raft from the pier after you have walked to its front.

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 2

Figure: $2$

The center of mass of the you-raft system ( $xcm$ ) before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(1)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

Calculation:

By substituting numerical values in equation $(1)$ ,

$xcm=(60 kg)(7.5 m)+(120 kg)(4.5 m)60 kg+120 kg$

$= 5.5 m$ .

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

(b)

To determine

The center of mass of the you-raft system from the end of the pier when you are at front

(b)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Explanation of Solution

Formula used:

$xcm$ before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(2)$

$xcm$ after you have walked to the front of the raft is given by

$xcm=myxy,f+mrxr_cm,fmy+mr$ $(3)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

$xy,f$ is your final position

$xr_cm,f$ is the final position of the center of mass of the raft, that is after you have walked to the front of the raft

Calculation:

The distance of the raft from the pier after you have walked to the front of the raft is,

$d=0.50 m+xy,f$ $(4)$

Because $Fext,net=0$ , the center of mass remains fixed and hence one can equate the expressions $(2)$ and $(3)$ , that is

$myxy,i+mrxr_cm,i=myxy,f+mrxr_cm,f$

$xy,f=xy,i−mrmy(xr_cm,f−xr_cm,i)$

Since, $xr_cm,f−xr_cm,i$ = $xy,f$

Substituting $xy,f$ for $xr_cm,f−xr_cm,i$ in the above equation,

$xy,f=myxy,imy+mr$

By substituting the numerical values in the above equation,

$xy,f=(60 kg)(6 m)60 kg+120 kg$ = $2 m$

Substituting this value in equation (4),

$d=2 m+0.5 m=2.5 m$

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

(c)

To determine

The distance between you and the end of the pier when you are at the front of the raft.

(c)

Expert Solution

Answer to Problem 138P

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Explanation of Solution

Formula used:

$xcm$ after you’ve walked to the front of the raft is given by

$xcm=myd+mr(d+xr_cm)my+mr$ $(5)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm$ is the center of mass of the raft

$d$ is the distance of the raft from the pier after you have walked to the front of the raft

Calculation:

Substituting numerical values in equation in equation $(5)$ ,

$xcm=(60 kg)(2.5 m)+(120 kg)(2.5 m+3 m)60 kg+120 kg$

$= 4.5 m$

Conclusion:

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

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Answer 2

Question

Chapter 5, Problem 138P

(a)

To determine

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

(a)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Explanation of Solution

Given:

Length and mass of the raft are $6 m$ and $120 kg$ respectively.

Your mass is $60 kg$ .

Formula used:

The edge of the pier is taken as the origin and the right side of the pier is taken as positive $X−$ direction, as shown in the Figure $1$ .

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 1

Figure: $1$

In the figure $2$ , $d$ is the distance of the end of the raft from the pier after you have walked to its front.

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 2

Figure: $2$

The center of mass of the you-raft system ( $xcm$ ) before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(1)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

Calculation:

By substituting numerical values in equation $(1)$ ,

$xcm=(60 kg)(7.5 m)+(120 kg)(4.5 m)60 kg+120 kg$

$= 5.5 m$ .

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

(b)

To determine

The center of mass of the you-raft system from the end of the pier when you are at front

(b)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Explanation of Solution

Formula used:

$xcm$ before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(2)$

$xcm$ after you have walked to the front of the raft is given by

$xcm=myxy,f+mrxr_cm,fmy+mr$ $(3)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

$xy,f$ is your final position

$xr_cm,f$ is the final position of the center of mass of the raft, that is after you have walked to the front of the raft

Calculation:

The distance of the raft from the pier after you have walked to the front of the raft is,

$d=0.50 m+xy,f$ $(4)$

Because $Fext,net=0$ , the center of mass remains fixed and hence one can equate the expressions $(2)$ and $(3)$ , that is

$myxy,i+mrxr_cm,i=myxy,f+mrxr_cm,f$

$xy,f=xy,i−mrmy(xr_cm,f−xr_cm,i)$

Since, $xr_cm,f−xr_cm,i$ = $xy,f$

Substituting $xy,f$ for $xr_cm,f−xr_cm,i$ in the above equation,

$xy,f=myxy,imy+mr$

By substituting the numerical values in the above equation,

$xy,f=(60 kg)(6 m)60 kg+120 kg$ = $2 m$

Substituting this value in equation (4),

$d=2 m+0.5 m=2.5 m$

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

(c)

To determine

The distance between you and the end of the pier when you are at the front of the raft.

(c)

Expert Solution

Answer to Problem 138P

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Explanation of Solution

Formula used:

$xcm$ after you’ve walked to the front of the raft is given by

$xcm=myd+mr(d+xr_cm)my+mr$ $(5)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm$ is the center of mass of the raft

$d$ is the distance of the raft from the pier after you have walked to the front of the raft

Calculation:

Substituting numerical values in equation in equation $(5)$ ,

$xcm=(60 kg)(2.5 m)+(120 kg)(2.5 m+3 m)60 kg+120 kg$

$= 4.5 m$

Conclusion:

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

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Answer 3

Question

Chapter 5, Problem 138P

(a)

To determine

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

(a)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Explanation of Solution

Given:

Length and mass of the raft are $6 m$ and $120 kg$ respectively.

Your mass is $60 kg$ .

Formula used:

The edge of the pier is taken as the origin and the right side of the pier is taken as positive $X−$ direction, as shown in the Figure $1$ .

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 1

Figure: $1$

In the figure $2$ , $d$ is the distance of the end of the raft from the pier after you have walked to its front.

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 2

Figure: $2$

The center of mass of the you-raft system ( $xcm$ ) before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(1)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

Calculation:

By substituting numerical values in equation $(1)$ ,

$xcm=(60 kg)(7.5 m)+(120 kg)(4.5 m)60 kg+120 kg$

$= 5.5 m$ .

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

(b)

To determine

The center of mass of the you-raft system from the end of the pier when you are at front

(b)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Explanation of Solution

Formula used:

$xcm$ before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(2)$

$xcm$ after you have walked to the front of the raft is given by

$xcm=myxy,f+mrxr_cm,fmy+mr$ $(3)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

$xy,f$ is your final position

$xr_cm,f$ is the final position of the center of mass of the raft, that is after you have walked to the front of the raft

Calculation:

The distance of the raft from the pier after you have walked to the front of the raft is,

$d=0.50 m+xy,f$ $(4)$

Because $Fext,net=0$ , the center of mass remains fixed and hence one can equate the expressions $(2)$ and $(3)$ , that is

$myxy,i+mrxr_cm,i=myxy,f+mrxr_cm,f$

$xy,f=xy,i−mrmy(xr_cm,f−xr_cm,i)$

Since, $xr_cm,f−xr_cm,i$ = $xy,f$

Substituting $xy,f$ for $xr_cm,f−xr_cm,i$ in the above equation,

$xy,f=myxy,imy+mr$

By substituting the numerical values in the above equation,

$xy,f=(60 kg)(6 m)60 kg+120 kg$ = $2 m$

Substituting this value in equation (4),

$d=2 m+0.5 m=2.5 m$

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

(c)

To determine

The distance between you and the end of the pier when you are at the front of the raft.

(c)

Expert Solution

Answer to Problem 138P

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Explanation of Solution

Formula used:

$xcm$ after you’ve walked to the front of the raft is given by

$xcm=myd+mr(d+xr_cm)my+mr$ $(5)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm$ is the center of mass of the raft

$d$ is the distance of the raft from the pier after you have walked to the front of the raft

Calculation:

Substituting numerical values in equation in equation $(5)$ ,

$xcm=(60 kg)(2.5 m)+(120 kg)(2.5 m+3 m)60 kg+120 kg$

$= 4.5 m$

Conclusion:

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

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Answer 4

Question

Chapter 5, Problem 138P

(a)

To determine

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

(a)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Explanation of Solution

Given:

Length and mass of the raft are $6 m$ and $120 kg$ respectively.

Your mass is $60 kg$ .

Formula used:

The edge of the pier is taken as the origin and the right side of the pier is taken as positive $X−$ direction, as shown in the Figure $1$ .

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 1

Figure: $1$

In the figure $2$ , $d$ is the distance of the end of the raft from the pier after you have walked to its front.

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 2

Figure: $2$

The center of mass of the you-raft system ( $xcm$ ) before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(1)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

Calculation:

By substituting numerical values in equation $(1)$ ,

$xcm=(60 kg)(7.5 m)+(120 kg)(4.5 m)60 kg+120 kg$

$= 5.5 m$ .

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

(b)

To determine

The center of mass of the you-raft system from the end of the pier when you are at front

(b)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Explanation of Solution

Formula used:

$xcm$ before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(2)$

$xcm$ after you have walked to the front of the raft is given by

$xcm=myxy,f+mrxr_cm,fmy+mr$ $(3)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

$xy,f$ is your final position

$xr_cm,f$ is the final position of the center of mass of the raft, that is after you have walked to the front of the raft

Calculation:

The distance of the raft from the pier after you have walked to the front of the raft is,

$d=0.50 m+xy,f$ $(4)$

Because $Fext,net=0$ , the center of mass remains fixed and hence one can equate the expressions $(2)$ and $(3)$ , that is

$myxy,i+mrxr_cm,i=myxy,f+mrxr_cm,f$

$xy,f=xy,i−mrmy(xr_cm,f−xr_cm,i)$

Since, $xr_cm,f−xr_cm,i$ = $xy,f$

Substituting $xy,f$ for $xr_cm,f−xr_cm,i$ in the above equation,

$xy,f=myxy,imy+mr$

By substituting the numerical values in the above equation,

$xy,f=(60 kg)(6 m)60 kg+120 kg$ = $2 m$

Substituting this value in equation (4),

$d=2 m+0.5 m=2.5 m$

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

(c)

To determine

The distance between you and the end of the pier when you are at the front of the raft.

(c)

Expert Solution

Answer to Problem 138P

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Explanation of Solution

Formula used:

$xcm$ after you’ve walked to the front of the raft is given by

$xcm=myd+mr(d+xr_cm)my+mr$ $(5)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm$ is the center of mass of the raft

$d$ is the distance of the raft from the pier after you have walked to the front of the raft

Calculation:

Substituting numerical values in equation in equation $(5)$ ,

$xcm=(60 kg)(2.5 m)+(120 kg)(2.5 m+3 m)60 kg+120 kg$

$= 4.5 m$

Conclusion:

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

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Answer 5

Chapter 5, Problem 138P

(a)

To determine

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

(a)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Explanation of Solution

Given:

Length and mass of the raft are $6 m$ and $120 kg$ respectively.

Your mass is $60 kg$ .

Formula used:

The edge of the pier is taken as the origin and the right side of the pier is taken as positive $X−$ direction, as shown in the Figure $1$ .

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 1

Figure: $1$

In the figure $2$ , $d$ is the distance of the end of the raft from the pier after you have walked to its front.

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 2

Figure: $2$

The center of mass of the you-raft system ( $xcm$ ) before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(1)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

Calculation:

By substituting numerical values in equation $(1)$ ,

$xcm=(60 kg)(7.5 m)+(120 kg)(4.5 m)60 kg+120 kg$

$= 5.5 m$ .

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

(b)

To determine

The center of mass of the you-raft system from the end of the pier when you are at front

(b)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Explanation of Solution

Formula used:

$xcm$ before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(2)$

$xcm$ after you have walked to the front of the raft is given by

$xcm=myxy,f+mrxr_cm,fmy+mr$ $(3)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

$xy,f$ is your final position

$xr_cm,f$ is the final position of the center of mass of the raft, that is after you have walked to the front of the raft

Calculation:

The distance of the raft from the pier after you have walked to the front of the raft is,

$d=0.50 m+xy,f$ $(4)$

Because $Fext,net=0$ , the center of mass remains fixed and hence one can equate the expressions $(2)$ and $(3)$ , that is

$myxy,i+mrxr_cm,i=myxy,f+mrxr_cm,f$

$xy,f=xy,i−mrmy(xr_cm,f−xr_cm,i)$

Since, $xr_cm,f−xr_cm,i$ = $xy,f$

Substituting $xy,f$ for $xr_cm,f−xr_cm,i$ in the above equation,

$xy,f=myxy,imy+mr$

By substituting the numerical values in the above equation,

$xy,f=(60 kg)(6 m)60 kg+120 kg$ = $2 m$

Substituting this value in equation (4),

$d=2 m+0.5 m=2.5 m$

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

(c)

To determine

The distance between you and the end of the pier when you are at the front of the raft.

(c)

Expert Solution

Answer to Problem 138P

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Explanation of Solution

Formula used:

$xcm$ after you’ve walked to the front of the raft is given by

$xcm=myd+mr(d+xr_cm)my+mr$ $(5)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm$ is the center of mass of the raft

$d$ is the distance of the raft from the pier after you have walked to the front of the raft

Calculation:

Substituting numerical values in equation in equation $(5)$ ,

$xcm=(60 kg)(2.5 m)+(120 kg)(2.5 m+3 m)60 kg+120 kg$

$= 4.5 m$

Conclusion:

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Answer 6

Chapter 5, Problem 138P

(a)

To determine

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

(a)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Explanation of Solution

Given:

Length and mass of the raft are $6 m$ and $120 kg$ respectively.

Your mass is $60 kg$ .

Formula used:

The edge of the pier is taken as the origin and the right side of the pier is taken as positive $X−$ direction, as shown in the Figure $1$ .

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 1

Figure: $1$

In the figure $2$ , $d$ is the distance of the end of the raft from the pier after you have walked to its front.

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 2

Figure: $2$

The center of mass of the you-raft system ( $xcm$ ) before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(1)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

Calculation:

By substituting numerical values in equation $(1)$ ,

$xcm=(60 kg)(7.5 m)+(120 kg)(4.5 m)60 kg+120 kg$

$= 5.5 m$ .

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Answer 7

Chapter 5, Problem 138P

(a)

To determine

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

Answer 8

(a)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

Length and mass of the raft are $6 m$ and $120 kg$ respectively.

Your mass is $60 kg$ .

Formula used:

The edge of the pier is taken as the origin and the right side of the pier is taken as positive $X−$ direction, as shown in the Figure $1$ .

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 1

Figure: $1$

In the figure $2$ , $d$ is the distance of the end of the raft from the pier after you have walked to its front.

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS, Chapter 5, Problem 138P , additional homework tip 2

Figure: $2$

The center of mass of the you-raft system ( $xcm$ ) before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(1)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

Calculation:

By substituting numerical values in equation $(1)$ ,

$xcm=(60 kg)(7.5 m)+(120 kg)(4.5 m)60 kg+120 kg$

$= 5.5 m$ .

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at the very rear is at $5.5 m$ .

Answer 13

(b)

To determine

The center of mass of the you-raft system from the end of the pier when you are at front

(b)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Explanation of Solution

Formula used:

$xcm$ before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(2)$

$xcm$ after you have walked to the front of the raft is given by

$xcm=myxy,f+mrxr_cm,fmy+mr$ $(3)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

$xy,f$ is your final position

$xr_cm,f$ is the final position of the center of mass of the raft, that is after you have walked to the front of the raft

Calculation:

The distance of the raft from the pier after you have walked to the front of the raft is,

$d=0.50 m+xy,f$ $(4)$

Because $Fext,net=0$ , the center of mass remains fixed and hence one can equate the expressions $(2)$ and $(3)$ , that is

$myxy,i+mrxr_cm,i=myxy,f+mrxr_cm,f$

$xy,f=xy,i−mrmy(xr_cm,f−xr_cm,i)$

Since, $xr_cm,f−xr_cm,i$ = $xy,f$

Substituting $xy,f$ for $xr_cm,f−xr_cm,i$ in the above equation,

$xy,f=myxy,imy+mr$

By substituting the numerical values in the above equation,

$xy,f=(60 kg)(6 m)60 kg+120 kg$ = $2 m$

Substituting this value in equation (4),

$d=2 m+0.5 m=2.5 m$

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Answer 14

(b)

To determine

The center of mass of the you-raft system from the end of the pier when you are at front

Answer 15

(b)

Expert Solution

Answer to Problem 138P

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Formula used:

$xcm$ before you walk to the front of the raft is given by

$xcm=myxy,i+mrxr_cm,imy+mr$ $(2)$

$xcm$ after you have walked to the front of the raft is given by

$xcm=myxy,f+mrxr_cm,fmy+mr$ $(3)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm,i$ is the initial position of the center of mass of the raft, that is before you have walked to the front of the raft

$xy,f$ is your final position

$xr_cm,f$ is the final position of the center of mass of the raft, that is after you have walked to the front of the raft

Calculation:

The distance of the raft from the pier after you have walked to the front of the raft is,

$d=0.50 m+xy,f$ $(4)$

Because $Fext,net=0$ , the center of mass remains fixed and hence one can equate the expressions $(2)$ and $(3)$ , that is

$myxy,i+mrxr_cm,i=myxy,f+mrxr_cm,f$

$xy,f=xy,i−mrmy(xr_cm,f−xr_cm,i)$

Since, $xr_cm,f−xr_cm,i$ = $xy,f$

Substituting $xy,f$ for $xr_cm,f−xr_cm,i$ in the above equation,

$xy,f=myxy,imy+mr$

By substituting the numerical values in the above equation,

$xy,f=(60 kg)(6 m)60 kg+120 kg$ = $2 m$

Substituting this value in equation (4),

$d=2 m+0.5 m=2.5 m$

Conclusion:

The center of mass of the you-raft system from the end of the pier when you are at front is at $2.5 m$ .

Answer 20

(c)

To determine

The distance between you and the end of the pier when you are at the front of the raft.

(c)

Expert Solution

Answer to Problem 138P

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Explanation of Solution

Formula used:

$xcm$ after you’ve walked to the front of the raft is given by

$xcm=myd+mr(d+xr_cm)my+mr$ $(5)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm$ is the center of mass of the raft

$d$ is the distance of the raft from the pier after you have walked to the front of the raft

Calculation:

Substituting numerical values in equation in equation $(5)$ ,

$xcm=(60 kg)(2.5 m)+(120 kg)(2.5 m+3 m)60 kg+120 kg$

$= 4.5 m$

Conclusion:

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Answer 21

(c)

To determine

The distance between you and the end of the pier when you are at the front of the raft.

Answer 22

(c)

Expert Solution

Answer to Problem 138P

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Formula used:

$xcm$ after you’ve walked to the front of the raft is given by

$xcm=myd+mr(d+xr_cm)my+mr$ $(5)$

Where, $my$ is your mass

$mr$ is mass of the raft

$xy,i$ is your initial position

$xr_cm$ is the center of mass of the raft

$d$ is the distance of the raft from the pier after you have walked to the front of the raft

Calculation:

Substituting numerical values in equation in equation $(5)$ ,

$xcm=(60 kg)(2.5 m)+(120 kg)(2.5 m+3 m)60 kg+120 kg$

$= 4.5 m$

Conclusion:

The distance between you and the end of the pier when you are at the front of the raft is at $4.5 m$ .

Answer 27

Ch. 5 - Prob. 1P Ch. 5 - Prob. 2P Ch. 5 - Prob. 3P Ch. 5 - Prob. 4P Ch. 5 - Prob. 5P Ch. 5 - Prob. 6P Ch. 5 - Prob. 7P Ch. 5 - Prob. 8P Ch. 5 - Prob. 9P Ch. 5 - Prob. 10P

The center of mass of the you-raft system from the end of the pier when you are at the very rear.

Concept explainers

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The center of mass of the you-raft system from the end of the pier when you are at the very rear.

Answer to Problem 138P

Explanation of Solution

The center of mass of the you-raft system from the end of the pier when you are at front

Answer to Problem 138P

Explanation of Solution

The distance between you and the end of the pier when you are at the front of the raft.

Answer to Problem 138P

Explanation of Solution

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