1 of 4The figure shows the system of three particles with masses M, 2M, and 3M.

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1 of 4The figure shows the system of three particles with masses M, 2M, and 3M. They are located along one line separated by a distance L from each other.

Imagine throwing a rock upward and away from you. With negligible air resistance, the rock will follow a parabolic path before hitting the ground. Now imagine throwing a stick (or any other extended object). The stick will tend to rotate as it travels through the air, and the motion of each point of the stick (taken individually) will be fairly complex. However, there will be one point that will follow a simple parabolic path: the point about which the stick rotates. No matter how the stick is thrown, this special point will always be located at the same position within the stick. The motion of the entire stick can then be described as a combination of the translation of that single point (as if the entire mass of the stick were concentrated there) and the rotation of the stick about that point. Such a point, it turns out, exists for every rigid object or system of massive particles. It is called the center of mass.

To calculate the center of mass for a system of massive point particles that have coordinates (xi,yi) and masses mi, the following equations are used:

xcm=m1x1+m2x2+m3x3+m1+m2+m3+,

ycm=m1y1+m2y2+m3y3+m1+m2+m3+.

In this problem, you will practice locating the center of mass for various systems of point particles.

Find the x coordinate xcm of the center of mass of the system of particles shown in the figure.

(Figure 4)

Express your answer in meters to two significant figures.

0.56 comma 0.400.56,0.40

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Imagine throwing a rock upward and away from you. With negligible air resistance, the rock will follow a parabolic path before hitting the ground. Now imagine throwing a stick (or any other extended object). The stick will tend to rotate as it travels through the air, and the motion of each point of the stick (taken individually) will be fairly complex. However, there will be one point that will follow a simple parabolic path: the point about which the stick rotates. No matter how the stick is thrown, this special point will always be located at the same position within the stick. The motion of the entire stick can then be described as a combination of the translation of that single point (as if the entire mass of the stick were concentrated there) and the rotation of the stick about that point. Such a point, it turns out, exists for every rigid object or system of massive particles. It is called the center of mass.

To calculate the center of mass for a system of massive point particles that have coordinates (xi,yi) and masses mi, the following equations are used:

xcm=m1x1+m2x2+m3x3+m1+m2+m3+,

ycm=m1y1+m2y2+m3y3+m1+m2+m3+.

In this problem, you will practice locating the center of mass for various systems of point particles.

Find the x coordinate xcm of the center of mass of the system of particles shown in the figure.

(Figure 4)

Express your answer in meters to two significant figures.

0.56 comma 0.400.56,0.40

SubmitPrevious AnswersRequest Answe

Explanation / Answer

consider mass M at the origin

M1 = M

x1 = 0

M2 = 2M

x2 = L

M3 = 3M

x3 = 2L

Coordinate of center of mass is given as

Xcm = (M1 x1 + M2 x2 + M3 x3)/(M1 + M2 + M3)

Xcm = (M (0 ) + (2M) L + (3M) (2L))/(M + 2 M + 3 M)

Xcm = 8ML/(6M)

Xcm = 1.33 L

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