Question

1. A physical therapy patient contracts her biceps muscle, andexerts a horizontal force of 180 N on the spring shown in thefigure at right. Assume the forearm rotates at the elbow. a) Drawan extended force diagram of the forearm (everything from the elbowto the tip of the fingers) showing the pivot point and all of theforces acting on the forearm where they actually are applied. Youwon’t know the magnitudes (or even the directions) of these forcesuntil you finish the whole problem but just draw reasonable vectorsfor now.
b) Now draw a force diagram with the forearm as a dot. c) Use thefact that the forearm is perfectly stationary at all times to findthe horizontal force that her biceps exerts on her forearm AND theforce exerted by the bone of the upper arm (shown below the biceps)on the forearm (weight = 30N). Note that muscles can only PULL inthe direction along the muscle, but that ligaments (like the onesin the elbow that connect the upper arm with the forearm) can exertforces in any direction. d) Briefly explain in complete Englishsentences (i.e., not just equations) why the bone of the upper armexerts such a large force on the forearm. e) What is the advantageof having the point where the biceps is attached to the forearm soclose to the elbow? What is the disadvantage of having it attachedso close?

2. You are trying to roll your bicycle wheel (of mass m andradius R) over a curb (of height h). To do this, you apply ahorizontal force F in the direction of desired motion. What is theminimum magnitude of the force that will successfully raise thewheel onto the curb when the force is applied (a) at the center ofthe wheel, and (b) at the top of the wheel? (c) In which case isthe magnitude of the force the least?

3. A hay bale is being dragged along a horizontal surface withconstant speed by a force F. The hay bale is 0.6 m high, 0.3m wide,and 0.9 m long (the side the force is applied to, perpendicular tothe direction of motion). The coefficient of kinetic friction is0.33. (a) Find the magnitude of the force, F. (b) Find the height,h, at which the bale will begin to tip over if the force is appliedat that height.