Page 115-116: Questions # 1 to 5 inclusive  [answers in bold print]
 

1.    Define torque, and draw a force diagram of torque, being applied to an object to cause it to rotate.  How could you increase the torque without increasing the magnitude of the applied force.

Torque is equal to an applied force times the perpendicular distance from the line of action of the force to the axis of rotation of the body to be turned.  Torque is increased by applying the force at a greater perpendicular distance from the axis.

2.    Draw a force diagram of two teachers on a teetertotter in a balanced position.  Insert magnitudes for each person's weight (force) and the distance that each force is from the axis (fulcrum).  How much torque is being applied to the teeter-totter by each person?  According to the numbers you selected, is the teeter-totter balanced?  If not, what could be changed to make it balance.

When the clockwise torque is equal to the counter clockwise torque, the teeter-totter will balance.  For example, 650N x 2m - 1300Nm of clockwise torque can be balanced by 433N x 3m - 1300Nm of counterclockwise torque.  Any change in distance of either person's center of gravity from the axis would result in more or less torque being applied.  Leaning forward or backward would create such a shift of the center of gravity.

3.    For each of the illustrations shown in Figure E.8, calculate whether the torques shown are motive torques or resistive torques, and calculate the direction of motion of the system.

Most students will need to calculate the torques for each of the two forces in each of the three systems.  However, the advanced student should be able to determine the answers by observing the relative magnitudes and directions of the forces and force arms within each system.

        System a:       F1 resistive
                               F2 motive
                               System moves clockwise

        System b:      F1 motive
                              F2 resistive
                              System moves counter clockwise

        System c:      F1 is stabilizing or neutralizing
                              F2 is stabilizing or neutralizing
                              System is static

4.    In Figure E.9 a-d, use dashes to indicate the lines of action of each force.  Draw the force arms for each of the forces in each system.  Then answer these questions:
        a.    Compare the force arms and directions of Force 1 (F1) in each of the four systems.  What generalization can be made about the relationship between the direction of the forces and the magnitudes of their force arms?  (F1 is equal in magnitude in all systems.)
        b.    If all the forces are of equal magnitude in all the systems, compare the torque-producing capabilities of each, and then state a principle about the direction of pull of the force and the magnituded of the torque that a force can produce.
        c.    Using the convention of a plus sign for ccw and a minus sign for cs, indicate for each torque whether is is a ccw- or cw-producing torque by blacing a plus or minus sign by the vector.
        d.    Using a scale of 1cm = 10N of force, and 1 cm = 1cm of force-arm distance, calculate each of the torque magnitudes for each of the systems.  Place the appropriate sign in front of each torque, and sum the torques acting on each system.

a. and b.    If forces are equal in magnitude, the close the direction of the force is to 90 degrees to the lever, the greater the torque it will produce; therefore, the F1 in system d would have the potential for the greatest torque.  (It should be noted that the distance that the point of application is from the axis of rotation will also affect the force arm length; however, given that the point of application distance is equal, the above relationship will always be true.)

        c.    System: F1, F2, F3, F4
                a:    +, -, -, 0
                b:    -, +, +, -
                c:    +, -, 0, 0
                d:    +, -, -, 0

        d.    The student will measure the magnitude of the force and the length of the force arm according to the scale given, apply the appropriate sign before each system.  The instructor may want to ditto an answer sheet or chart for the students' convenience.  In addition, the student could be asked to determine from the sign of the sums in which direction the system will be moving, and of those systems moving in the same direction, the students could be asked which of the systems will be accelerating the most.  These questions will enable the student to see the relationship between the sum of the torques (magnitudes) and accelerations.

5.    In Figure E.9e, identify the four properties of the muscle force and its force arm.

Refer to Figure C-1 for the four properties of a force.  The perpendicular distance from the force's line of action to the joint axis of rotation is the force arm.

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Page 123: Questions # 1 to 5 inclusive [answers in bold print]

1.    What is the approximate location of your body's CG when you assume an upright (standing) position?  How is your body's CG location changed when you assume the following positions: (a) raise both arms out to the side to a horizontal position? (b) raise both arms forward to a horizontal position? (c) raise only one arm as indicated in a and b?  Select other positions and track the changing locations of your body's CG.

Depending on body proportions the center of gravity is located somewhere near the pelvic region of someone standing in an upright position.  This location is changed in proportion to segmental mass displacements:
 
a.    Upward only; the lateral change of one extremity is balanced by the lateral change of the other.

b.    Forward and upward.

c.    Upward and toward the right if only the right arm is raised to the side; upward and toward the left if only the left arm is raised to the side.  If each arm is raised upward and forward individually, the center of gravity shifts upward and forward only half as much as in question b.
 
Other segmental mass shifts will lead to a change in the body's center of gravity location which reflects the amount of mass, the direction it shifts, and the magnitude of displacement.

2.    Figure E.17 shows several blocks of various weights placed on a board supported at each end.  A scale is located under the knife edge on the left-hand side of the system.  Determine the position of the CG for each of the two block arrangements shown.  Discuss why and how the CG changes when the arrangements are changed.

        a.    net T=0
                -18.5(40)+42(d)=0
                42(d)=629 torque units    d=629/42    d=17.61 distance units

        b.    net T=0
                -22(40)+42(d)=0
                42(d)=880 torque units     d=990/42    d=20.95 units

        The location of the center of gravity of the total system of blocks will change in accordance with the mass shifts.  The change in the location of the center of gravity of the system will result in a change in the reaction force at each end of the board.

3.    When a person moves a body segment or segments, the CG location changes.  How far and in what direction the total body CG changes depends on two factors.  What are these factors?

How far and in what direction the body's center of gravity will change depends on the relative masses of the segments and the magniturde of their displacements.

4.    If a person measuring 64cm and a person measuring 74 cm each has a CG height of 56 percent of standing height, what does that tell you about their relative body statures?

Both the short and tall individuals have about the same body proportions.

5.    Three people, all the same height, have differnet CG locations: 52 percent, 55 percent, and 58 percent of standing height.  What can you say about their relative body builds?

The person whose center of gravity location is 52 percent of the body height has more body mass distributed lower in the body; for example, narrow or small thorax and arms with more weight in the legs and/or hip region.  The one whose center of gravity is 55 percent has the weight distributed higher in the body, but not as high as the individual whose center of gravity is 58 percent of standing height.  The latter individual has more weight toward the shoulders than toward the hips.

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Page 128: Questions # 1 to 4 inclusive [answers in bold print]

1.    Describe what is meant by center of buoyancy (CB).

The center of buoyancy is that point through which water's buoyant force is applied upward.  It is the center of gravity of the volume of displaced water.

2.    What is the axis of roation for a floater whose lower body rotates downward?

The axis of rotation for a rotating floater is the center of buoyancy.

3.    In which directions do the forces of gravity and buoyancy act on an immersed body?  What are the points of application of these two forces?

Gravity acts downward at the CG; buoyancy acts upward at the CB of an immersed body.

4.    Describe the relative locations of the CG and CB for a person whose legs drop when attempting to float in a horizontal position on the back.  Describe these locations for a person floating horizontally.

If an immersed body rotates, the CG and CB are not in the same vertical line; there is a force arm from the CG weight force to the CB axis.  If a person floats horizontally, the CG and CB are in the same spot or they fall on the same vertical line.