By LearningExpress Editors
Updated on Aug 12, 2011
Answers
 a. Every foot block A is lowered will raise block B by the same amount. To equalize the 10foot difference, block A must be lowered 10 feet ÷ 2 = 5 feet.
 d. Gear 2 turning counterclockwise will lead all gears it touches to turn clockwise.
 d. When George leaves, Lenny will have already traveled 8 mph × 0.5 hours = 4 miles. George runs 2 mph faster than Lenny. Since Lenny got a 4mile head start, it will take George 4 miles ÷ 2 mph = 2 hours to catch Lenny. Since George left at 6:30 A.M., he will catch Lenny at 8:30 A.M.
 b. Mechanical advantage (MA) is the factor by which a simple machine multiplies for the force put into it. In this case, 60 pounds of force is used to move a 240pound block, so MA = 240 ÷ 60 = 4. The MA of a ramp is determined by the length of the ramp, l, divided by the height gained, h. In this case, MA = 3 = = l8 feet. Solving for l tells us the ramp is 32 feet long.
 d. The weight of the load is spread over 4 cables, so the mechanical advantage is 4.
 c. w_{1} × d_{1} = w_{2} × d_{2}. w_{1} × 8 feet = 200 pounds × 12 feet. Solving for w_{1} gives 300 pounds.
 a. Each block will have a different size and weight, but, since each is made from the same material, they will all have the same density. Since an object's density determines whether it will float or sink in water, all three objects will either float or sink.
 c. If 8 pounds of force will move a spring 4 inches, it has a force constant of 8 pounds ÷ 4 inches = 2 pounds per inch. Moving the spring 12 inches will require 12 inches × 2 pounds per inch = 24 pounds of force.
 d. There are 7 threads per inch. To move the nut 3 inches will require 7 × 3 = 21 turns. d. Oil is a lubricant used to decrease the amount of friction between the many moving parts in an engine.
 c. The mechanical advantage of this pulley system is 2. The force required to lift the 80pound load is 80 pounds ÷ 1 = 80 pounds.
 b. A single fixed pulley has the advantage of being able to change the direction of force. Thus, a flag can be raised up a flagpole without having to climb and lift it.
 d. Gear 2 turning clockwise will cause the neighboring gears to turn counterclockwise, so no other gears will turn clockwise.
 b. w_{1} × d_{1} = w_{2} × d_{2}. Andre is 24 feet away from the pivot point. 126 pounds × 12 feet = 12 feet × w_{2}. Solving for w_{2} gives 63 pounds.
 a. 500 pounds ÷ 2.5 inches = 200 pounds per inch.
 b. Valves 2, 3, and 5 are all directly connected to the break and so must remain closed. 1 and 4 may be opened to successfully route the flow from A to B.
 d. Each full turn of the pedals will turn the rear wheel 48 ÷ 12 = 4 revolutions. If the pedals are turning at 90 rpm, the rear wheel will move at 4 × 90 rpm = 360 rpm.
 d. Frictional forces point in the opposite direction of motion (arrow B).
 a. Of the materials listed, metal objects are the best at conducting heat and therefore will warm the fastest. Plastic, glass, and ceramic are all good insulators and thus will take a long time to absorb heat.
 c. A pulley system of this type has a mechanical advantage of 2. So, to lift a 300pound weight will require 300 pounds ÷ 2 = 150 pounds.
 b. A screw is a special type of inclined plane where the ramp is wrapped around a cylindrical object.
 a. w_{1} × d_{1} = w_{2} × d_{2}. 57 pounds × 6 feet = 76 pounds × d_{2}. Solving for d_{2} gives 4.5 feet.
 c. While ramp B offers a greater mechanical advantage, the amount of work is determined by the overall change in height of the barrel. Since the barrel is raised the same height regardless of which ramp is used, the amount of work done is the same.
 a. Since A and B are identical in size, they will rotate at the same rate. The belt connects the two, so A and B also rotate in the same direction.
 a. The mechanical advantage (MA) of a ramp is determined by the length of the ramp, l, divided by the height gained, h. In this case, MA = = 36 feet ÷ 4 feet = 9. The force required to pull a 270pound block up a ramp is 270 pounds ÷ 9 = 30 pounds.
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