Physics Fundamentals
Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 5, Problem 32P

(a)

To determine

The center of mass of the pole vaulter for the given mass distribution of the athlete at a particular instant.

(a)

Expert Solution
Check Mark

Answer to Problem 32P

The x and y co-ordinates of center of mass of the pole vaulter are xcm=8.8125cm and ycm=9.4375cm respectively.

Explanation of Solution

Given:

A pole vaulter’s distribution of mass with the coordinates. Seven mass points are given. Mass m1 is 11 kg located at (25, -70) cm, m2 is 18 kg located at (25, -20) cm, m3 is 14 kg at (25, 12.25) cm, mass m4 is 20 kg (0, 15) cm, mass m5 is 6 kg locatedat (-25, 17.25) cm, m6 is at 6 kg (- 20,0) cm, m7 is 5 kg at (-20, -40) cm.

Formula used:

The x and y coordinates of the center of mass is given as below:

  xcm=m1x1+m2x2+....................mnxnm1+m2+....................mn

  ycm=m1y1+m2y2+....................mnynm1+m2+....................mn

Calculation:

The x coordinate of the center of mass of the pole-vaulter is given as below:

  xcm=m1x1+m2x2+mx33+mx44+m5x5+mx66+mx77m1+m2+m3+m4+m5+m6+m7

Putting the values of masses and their coordinates we can write as below:

  xcm=(11×25)+(18×25)+(14×25)+(20×0)+6×(25)+6×(20)+5×(20)11+18+14+20+6+6+5

  xcm=275+450+350+015012010080=70580

  xcm=8.8125cm

The y coordinate of the center of mass of the pole-vaulter is given as below:

  ycm=m1y1+m2y2+my33+my44+m5y5+my66+my77m1+m2+m3+m4+m5+m6+m7

Mass m1 is 11 kg located at (25, -70) cm, m2 is 18 kg located at (25, -20) cm, m3 is 14 kg at (25, 12.25) cm, mass m4 is 20 kg (0, 15) cm, mass m5 is 6 kg located at (-25, 17.25) cm, m6 is at 6 kg (- 20, 0) cm, m7 is 5 kg at (-20, -40) cm.

  ycm=(11×( 70))+(18×( 20))+(14×12.25)+(20×15)+(6×17.25)+(5×( 40))80

  ycm=9.4375cm

It is observed that the center of mass of the pole-vaulter lies below the bar at -9.4375 cm.

Conclusion:

The coordinates of the center of mass of the pole-vaulter are xcm=8.8125cm and. ycm=9.4375cm

(b)

To determine

The height of the bar for the given height of the center of mass.

(b)

Expert Solution
Check Mark

Answer to Problem 32P

The height of the bar 6.1 m.

Explanation of Solution

Introduction:

Let say, the center of mass of the pole-vaulter while standing on the ground is 1 meter. As discussed in previous section that the height of the center of mass of the vaulter lies below the bar. Pole vaulter runs with a speed vand hence the Kinetic energy is K.E=12mv2 where mis the mass and thevis the velocity of theVaulter. After reaching up in the air, kinetic energy transforms into potential energy.

  12mv2=mgh

The height of the center of mass of the pole-vaulter is 5.1 m. The height of center of mass while standing on the ground is 1m. Hence, the height of the bar will be (5.1+1) m=6.1m

Conclusion:

The height of the bar 6.1 m.

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