# Homework due 11/2/99

## Chapter 5:

Q9.  Apparent weight:

• Your apparent weight (normal force) will be greatest when the normal force must both balance out your weight and provide the extra force required to accelerate you upward.
• Your apparent weight (normal force) will be smallest when you accelerate down.   Some of your weight provides the force required to accelerate you down and the normal force only needs to balance out the remainder of your weight.
• Your apparent weight (normal force) is the same as your usual weight when no force is required to accelerate you and the normal force exactly balances out your weight.   This happens when you are moving with a constant velocity in the elevator or when the elevator is not moving.

Q12.  You do not sense gravity directly but only through the upward normal force exerted on your feet which balances out the gravitational force.  As long as this force is present you feel that gravity is present.  When you are along the outside of a rotating cylinder, the outer wall exerts a normal force against you to give you the required centripetal acceleration so you will move in a circular path.  This normal force is no different than the one you experience when gravity is present and thus gravity is simulated.  The inside of the outer wall of the rotation cylinder seem just like a floor to you.

1. If you release an object from you hand when you are inside the rotating cylinder, the object no longer experiences the centripetal force exerted by your hand and moves off in a straight line.  You see the object approach the floor as you follow a circular path and it looks as if it is falling under the influence of gravity.  The only problem is that the object will not strike the spot  directly beneath it when it was released although it will strike a spot close by.  In a well designed space ship the difference will be undetectable to the naked eye and this will occur when the radius of the cylinder is much greater than the height of a typical human.
2. You feel an upward force on your feet that is just like the upward force you feel when gravity is present.  In a well designed space ship this will be approximately equal to the normal force you experience when standing stationary on the earth.  This requires the prudent selection of both cylinder radius and rotation speed.
3. Tossing an object to another person as well as catching a tossed object will require some relearning because the trajectory will not be exactly like what you have experienced on earth and will depend on the orientation of the initial velocity with respect to the tangential velocity.  This would also make pouring difficult.  If there were several floors in the structure, the normal force would increase as the radius increased and your apparent weight would rise as you went to lower floors in the structure.

Q16.  No force is required to keep a satellite up in orbit.  A force is required to pull it down so it follows a circular path and doesn't fly off in a straight line.

## Chapter 6:

Q2.  A centripetal force can do work on an object when the radius of the circular path followed by the object is changing (i.e., the object is being pulled in toward the center of the circle or being "let out").

Q3.  The normal force can do work on an object when the surface exerting the normal force is moving.  For example, the nornal force exerted by the floor of an elevator does work on a passenger when the elevator rises and falls.

Q9.  The net work done by external forces on a system equals the change in the kinetic energy of that system.  When you double the work, the change in the kinetic energy is doubled.  Since  the kinetic energy is proportional to the velocity squared, when the velocity equals 1.414 times the initial velocity the kinetic energy will have doubled.  (Note:  1.414 = square root of 2)