# University of Wisconsin Green Bay

You are designing a lamp for the interior of a special executive express elevator in a new office building. The lamp has two sections that hang one directly below the other. The bottom section is attached to the top one by a single thin wire and the upper section is attached to the ceiling by another single thin wire. Because the idea is to make each section appear to be floating without support, you want to use the thinnest (and thus weakest) wire possible. You decide to calculate the force each wire must exert on the lamp sections in case of an emergency stop. The elevator has all the latest safety features and will stop with an acceleration of g/3 in any emergency. Each section of the lamp weighs 7.0 N.
This problem was used with permission of Dr. Ken Heller of the University of Minnesota Physics Education Research Group.

• In this problem, you are asked to relate motion (the acceleration of the lamp) to force (tension, or strength of the wire). Force and motion of an object are always related through Newton's Second Law, so this is a force or 2ndLaw problem.

In this case, you are asked not only about the tension in the top wire but also the tension in the wire between the two parts of the lamp, so this is a two object problem. If you don't see the need for two objects at this stage, it will become apparent when you draw the picture.

• The key equation for any problem that relates forces and motion is Newton's Second Law. The left side of the equation takes into account the forces that act on the object, and the right side shows the effect of those forces. Regardless of what quantity you are asked to find, begin with the Second Law. If additional information is needed, it will become apparent as you proceed.

• The upper wire must be able to exert a force of at least 19 N. The lower wire must be able to exert a force of at least 9.3 N.

• In this problem, the wires on and within the lamp need to be strong enough to support the pieces of the lamp against gravity and to provide an additional maximum upward acceleration equal to 1/3 the weight of the lamp. The values of tension make sense--they are about 1.33 the weight of the pieces that each wire must support.

Because you were asked for the strength of the wire linking the two portions of the lamp, you were not able to treat the lamp as a single system. Whether you initially broke it into two pieces or whether you first treated it as a single system, you must examine one piece of the lamp separately in order to solve for the tension required in the lower wire.