7.5 Equilibrium (2.1) F = k Dx t = r X F
· How can Ms. Tevlin overpower two students in a tug of war with just one finger?
· A spring scale is set between two pulleys supporting two 1-kg masses. What does the scale read?
· You have 3 masses and 3 elastic bands. What is the stretch like if all three are side-by-side and if they are one after the other?
· A uniform ladder is safely leaning against a wall. What diagram represents the forces acting on it?
1) Justin Trudeau is hanging from the middle of a clothesline. The rope is attached at equal heights 24 units apart and the centre point sags 1 unit below them. What is the tension if he has a mass of 20 kg?
2) Frank and Ernest have constructed a hoist using three pulleys and two pieces of rope.
One piece passes over pulley A and supports pulleys B and C. the other piece is
attached to the ceiling and goes under B and over C. How hard must they pull down
on the end of the second rope to pull up a trunk of 2400 N attached to pulley B?
(Assume that the ropes and pulleys are ideal and the ropes hang vertically.)
3) Huey, Louis and Dewey are three ducks, each with a mass of 3 kg. They are standing on the end of a uniform board of length 10 m and mass 5 kg. The board is on a table with 6 m sticking beyond the edge. Huey slowly walks toward the other end. How far does he get before the board starts to tip?
4) A uniform bar is supported by a spring and stretches 3 inches. The bar and spring are cut into three equal parts and suspended one after the other. What is the total increase in spring length in the second case?
5) Snoopy is flying his plane north in a straight level flight at constant speed. What is the direction of the total force acting on the aircraft?
6) An overweight acrobat weighing 115 kg wants to perform a single handstand. He cheats by resting one foot against a smooth frictionless vertical wall. The wall exerts a horizontal force of 130 N. What is the magnitude of the force exerted by the floor in his hand?
7) A 2.0 kg chicken rests at a point C on a slack clothesline ACB. CA and CB slope up from horizontal at 30o and 45o. What minimum strength must the line have to ensure that the rope doesn’t break? (p. 119)
8) Robin Hood pulled back on his bow. It broke when the tension in the string was equal to the pull by Robin’s fingers. What was the angle between the two halves of the string?
9) Batman has hung a uniform bar 10 m long from the ceiling using two springs with the same unstretched length. One will stretch three times as far as the other when equal forces are applied. Robin has a mass 5 times that of the bar and is hanging from the bar so that the bar is level. Where is he hanging?
10) A light spring with a force constant of 50 N/m has three 5 kg masses attached at the 1, 2 and 3 m points. If it is hung up by the loose end, by how much will the entire spring be stretched?