Chapter 8, Problem 85AP

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# Many aspects of a gymnast's motion can be modeled by representing the gymnast b) four segments consisting of arms, torso (including the head), thighs, and lower legs, as in Figure P8.85. Figure P8.85b shows arrows of lengths rcg locating the center of gravity of each segment. Use the data below and the coordinate system shown in Figure P8.85b to locate the center of gravity of the gymnast shown in Figure P8.85a. Masses for the aims, thighs, and legs include both appendages.Figure P8.85

To determine
The centre of gravity of the gymnast for a given segment.

Explanation

Explanation

Given Info:

The mass of the arms is 6.87â€‰kg , the mass of torso is 33.57â€‰kg , the mass of thighs is 14.07â€‰kg , the mass of legs is 7.54â€‰kg

From the table the length of arms is 0.548â€‰m , the length of torso is 0.601â€‰m , the length of thighs is 0.374â€‰m , the length of legs is 0.350â€‰m

From the table the centre of gravity of arms is 0.239â€‰m along y direction, the centre of gravity of torso 0.337â€‰m along x direction, the centre of gravity of thighs isÂ  0.151â€‰m , the centre of gravity of legs is 0.227â€‰m . The angle between thigh and horizontal is 60Â° .

Formula to calculate the position of centre of gravity of gymnast along x-axis is,

x=maxa(cg)+mtxt(cg)+mthxth(cg)+mlxl(cg)ma+mt+mth+ml

• x is the centre of gravity of gymnast along x axis
• ma is the mass of arms
• mt is the mass of torso
• mth is the mass of thighs
• ml is the mass of legs
• xa(cg) is the centre of mass in the x direction of the arms
• xt(cg) is the centre of mass in the x direction of the torso
• xth(cg) is the centre of mass in the x direction of the thighs
• xl(cg) is the centre of mass in the x direction of the legs

Formula to calculate the position of centre of gravity of gymnast along y-axis is,

y=maya(cg)+mtyt(cg)+mthyth(cg)+mlyl(cg)ma+mt+mth+ml

• y is the centre of gravity of gymnast along y axis.
• ya(cg) is the centre of mass in the y direction of the arms
• yt(cg) is the centre of mass in the y direction of the torso
• yth(cg) is the centre of mass in the y direction of the thighs
• yl(cg) is the centre of mass in the y direction of the legs

Formula to calculate the centre of gravity of thighs along x direction is,

xth(cg)=Lt+rcg(th)cosÎ¸

• Lt is the length of the torso
• rcg(th) is the centre of gravity of thighs
• Î¸ is the angle between thighs and horizontal x axis

Substitute 0.601â€‰m for Lt , 0.151â€‰m for rcg(th) , and 60Â° for Î¸ to calculate xth(cg) .

xth(cg)=0.601â€‰m+(0.151â€‰m)cosâ€‰60Â°=0.601â€‰m+(0.151â€‰m)12=0.677â€‰m

Formula to calculate the centre of gravity of thighs along y direction is,

yth(cg)=rcg(th)sinÎ¸

Substitute 0.151â€‰m for rcg(th) and 60Â° for Î¸ to calculate yth(cg)

yth(cg)=(0.151â€‰m)sin60Â°=(0.151â€‰m)32=0.131â€‰m

Formula to calculate the centre of gravity of legs along x direction is,

xl(cg)=Lt+LthcosÎ¸+rcg(l)

• Lt is the length of the torso
• rcg(l) is the centre of gravity of legs
• Lth is the length of thighs.

Substitute 0.601â€‰m for Lt , 0.227â€‰m for rcg(l) , 0.374â€‰m for Lth and 60Â° for Î¸ to calculate xl(cg)

xl(cg)=[0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started