(a) Locate the effective point of application of the normal force, assuming that the block does not slide.
(b) What is the minimum value of the coefficient of static friction?
1. Where does the normal force act? The normal force
exerted on an object by a surface is actually a sum of a large number of such
forces distributed over the area of contact of the two surfaces. The effective
point of application of the full normal force is such that the torque is the
same as that produced by the distributed normal forces. A horizontal force of
magnitude Fp = (1/3)Fg is applied at the top of the uniform cubic block shown.
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(a) Locate the effective point of application of the normal force, assuming that the block does not slide.
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2. Tip the block. Rework the previous problem, but suppose that the magnitude Fp of the horizontal force is increased. Assuming that the block does not slide, determine the value of Fp that will cause the block to tip over. What is the minimum value of the coefficient of static friction to keep the block from sliding? [ans: 0.500]
3. Ladder example from text. Like Sample Problem
13-2, HRW6 p. 279.
A 4.00 m, 15.0 kg ladder leans against a smooth wall (this means no friction!);
the ladder's lower end touches the floor 1.00 m from the wall. The weight of
the ladder acts at its midpoint. A 52.0 kg painter stands on the ladder at a
point 1.50 m (along the ladder: not horizontal or vertical) from its top. Determine
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(a) the (horizontal) force exerted by the wall,
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4. In #3, the floor exerts a normal force and a frictional force on the ladder. These two forces can be added to obtain the resultant force Ffloor exerted on the ladder by the floor. Is this force directed along the ladder? Explain.
| 5. HRW6 13.P.023. One end of a uniform beam that weighs 217 N is attached to a wall with a hinge. The other end is supported by a wire. (a) Find the tension in the wire. [188 N] (b) What is the horizontal component of the force of the hinge on the beam? [94 N] (c) What is the vertical component of the force of the hinge on the beam? [54.2 N] |
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6. Back Pain: Why your parents told you to bend your knees!
Improper lifting technique can cause sever pain in your back. The first diagram
below shows two vertebrae in the spine. They must allow flexibility, but protect
the spinal cord. To prevent bone-on-bone wear, the vertebrae are separated by
discs as shown. If the force along the backbone is too large, the disc will
bulge out and pinch the spinal cord—a painful pinched nerve.
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On the right is a cartoon of someone lifting a box in the wrong way, by bending
over at the waist. Shown in the cartoon are the backbone, the pelvis, and the
muscles that allow you to bend over and straighten up. X-ray measurements show
that the muscles attach about 2/3 of the way up the spine, and make an angle
of about 12° with the column.
Model of spine. The legs and hips (about 40% of your weight) are assumed to
be a rigid base. The torso is another 40% of your weight, and your head and
arms are 20% of your weight. Assume the head and arms are attached to the top
of the spine.
Assume the spine has a length L, and that your weight is W. Analyze effect of
lifting a box of mass fW . Use the angle that you bend over as 30° and assume
that your torso has a center of mass halfway along the spine.
(a) Draw a free body diagram for the spine.
(b) Determine the tension in the muscle in terms of your weight for the case
of no box, f=0 and a box of 20% of your weight.
(c) Determine the components of the force of the pelvis on the spine in terms
of your weight for the case of no box, f=0 and a box of 20% of your weight.
Analyze in general terms, then you can put in numbers specific to you.
This page maintained by Anne G. Young. Last modified 13-Feb-2004 .