Problem Solving

• There are problems which do not require much problem solving skills, e.g.

• 2 + 9 = ?• The solution can be found by– Using your addition skills– Counting on your fingers and toes– Using your personal calculator– Using computational software, e.g. Excel

• All of the above methods lead to the solution that– 2 + 9 = 11

• Other types of problems involve text and numbers, e.g.• The bed of a truck is 4’ 2” from the road surface. The

maximum height of the truck with no load is 12’7”. A crate of dimensions 5’6” x 8’5” x 10’10” is to be placed on the bed of the truck and secured using straps. The crate has no warning labels indicating “THIS SIDE UP”. The truck route includes passing under a highway where the maximum clearance is 12’6”. Determine how the crate can be oriented on the bed of the truck to allow it to take this route.

Quick Solution

• There are only three ways the crate can be oriented on the bed of the truck.

• With the 5’6” dimension vertical, 5’6” plus 4’2” = 9’8” That is less than the 12’6” maximum clearance.

• With the 8’5” dimension vertical, 8’8” plus 4’2” = 12’7”. That is greater than the maximum clearance of 12’6”.

• With the 10’10” dimension vertical, 10’10” plus 4’2” = 15’. That is greater than the maximum clearance of 12’6”.

• Therefore the crate must be oriented so that the 5’6” dimension is vertical for the truck to be able to take this route.

•WRONG!

• The truck height is 12’7” and the maximum clearance is 12’6”.

• Therefore the truck cannot get under the bridge even if there were no crate on the truck bed!

• Read the problem completely.• Note what is given.• Note what is asked.• Do not jump into the problem before you have

performed the three steps listed above!• You were given the height of the truck and the

maximum clearance in the text of the problem.

• How could you get the unloaded truck under the bridge?

• If so, how would the crate have to be oriented to get the loaded truck safely under the bridge?

• Let air out of the truck tires so that the maximum height of the truck is less than 12’6”. The unloaded truck can then safely pass under the bridge.

• With the 5’6” vertical, the height of the load would be 9’8”. That would be OK.

• With the 8’5” dimension vertical, the height of the load would be 12’7” and the loaded truck with air let out of its tires could pass under the bridge.

•WRONG!

• The chains running over the top of the crate would hit the bridge!

Another type of problem

• Some problems may have mixed units, i.e. some units may be in the SI (metric) system and some may be in the US system.

• Consider the truck with a bed 4’2” above the road surface and a crate of dimensions 2m x 3m x 4m.

• Now you must decide which system of units you want to keep and convert all others to that system.

• If the rest of the problem were the same as the one we just looked at, then you would be better off staying in US or conventional units.

• You would then convert the crate dimensions from meters to feet and inches.

Another type of problem

• An engineer decides to measure the time it would take for a 2 inch diameter, 5 lb steel ball to fall to the ground from a height of 200 ft neglecting aerodynamic drag, wind, etc. The engineer looks up the acceleration due to gravity in his book and finds that g= 32.2 ft/sec/sec = 9.81 m/sec/sec.

• How long will it take?

• You may be more comfortable in the SI (metric) system and want to use g = 9.81 m/sec/sec. If so, you must convert all other units in your calculations from US to SI.

• Since the units have been stated in US units, you would be better off staying in US units and using g = 32.2 ft/sec/sec.

• For this course, Egr 102, I will state a problem entirely in SI units OR entirely in US units.

• I will expect you to stay in the system in which the problem has been stated.

IMPORTANT HINT

• Do not let your pencil start to write before you have read the complete problem and formulated in your mind your method of attack!