AP Physics Hoework pg 155: 1, 5, 13, 14, 15, 48, and 55
1. A light string can support a stationary hanging load of 25.0kg before breaking. A 3.00kg object attached to the string rotates on a horizontal, frictionless table in a circle of radius 0.800, and the other end of the string is held fixed. What range of speeds can the object have before the string breaks? 2
#1 Tax = Weight = g = ( 25Kg) ( 9.8 N ) = 245N Kg T = F c = v 2 TR = v = R 0 < v < 8.08 245N ( )( 0.8) 3Kg = 8.08 3
5. A coin placed 30.0 c fro the center of a rotating c horizontal turntable slips when its speed is 50.0. a) What force causes the centripetal acceleration when the coin is stationary relative to the turntable? b) What is the coefficient of static friction between the coin and turntable? 4
#5 F c = f = µg = v 2 R µ = v 2 Rg = ( 0.5 ) 2 ( 0.3) 9.8 ( ) = µ = 0.085 2 5
13. A 40.0kg child swings in a swing supported by two chains, each 3.00 long. The tension in each chain at the lowest point is 350N. Find: a) the child s speed at the lowest point and b) the force exerted by the seat on the child at the lowest point. (Ignore the ass of the seat.) 6
T g = 40kg, R = 3, T = 700N F c = T g v 2 R v = v = = T g R T g ( ) 3 v = 4.81 ( )( 700N 392N) 40kg 7
b) the force exerted by the seat on the child at the lowest point. (Ignore the ass of the seat.) N g F c = N g v 2 R = N g N = v 2 R + g N = v 2 R + g = 40kg N = 700N ( 4.8 ) 2 3 + 9.8 2 8
14. A roller-coaster car (Fig. P6.14) has a ass of 500 kg when fully loaded with passengers. (a) If the vehicle has a speed of 20.0 at point A, what is the force exerted by the track on the car at this point? (b) What is the axiu speed the vehicle can have at point B and still reain on the track? 9
15. Tarzan (85.0kg) tries to cross a river by swinging on a vine. The vine is 10.0 long, and his speed at the botto of the swing (as he just clears the water) will be 8.00 Tarzan doesn t know that the vine has a breaking strength of 1000N. Does he ake it across the river safely?
17. A pail of water is rotated in a vertical circle of radius 1.00. What is the pail s iniu speed at the top of the circle if no water is to spill out? v in = Rg = 1 v in = 3.13 ( ) ( ) 9.8 2 11
21. A 0.500-kg object is suspended fro the ceiling of an accelerating boxcar as shown in Figure 6.12. Taking a = 3.00, find (a) the angle that the string akes 2 with the vertical and (b) the tension in the string. T θ a g tanθ = a g θ = tan 1 a g 3 θ = tan 1 9.8 θ =17 cos17 = g T T = g cos17 ( ) 9.8 T = 0.5kg cos17 T = 5.12N ( ) 2
33. A 9.00kg object, starting fro rest, falls through a viscous ediu and experiences a resistive force R = -bv, where v is the velocity of the object. The object reaches one-half of its terinal speed in 5.54 onds. Deterine: a. The terinal speed. b. the tie the speed of the object is three-fourths of the terinal speed. c. the distance the object travels during the first 5.54 onds.
#33 g bv = a g bv = dv dt g b v = dv dt dv dt = 0 v T = g b
g b v = dv dt = dv g bv 1 dt = 1 dt = dt dv g bv dv g bv u = g bv, du = b dv 1 dt = 1 b du u b t = ln g bv ( ) lnc v = 1 g Ce bt b initial conditions t = 0 & v = 0 C = g v = g b 1 e bt v = v T 1 e bt
At t = 5.54 0.5v T = v t 1 e 0.5 = 1 e 0.5 = e b( 5.54 ) 9kg b( 5.54 ) 9kg ln0.5 = 0.693 = b = 0.693 9kg ( ) 5.54 b( 5.54 ) 9kg b 5.54 ( ) 9kg = 1.13 kg
33a. The terinal speed. v T = g b = 9kg ( ) ( ) 9.8 2 1.13 kg = 78.3
0.75v T = v t 1 e 0.25 = e ln0.25 = 1.39 = 1.13 kg t 9kg 1.13 kg t 9kg 1.13 kg t 9kg 1.13 kg t 9kg b. the tie the speed of the object is threefourths of the terinal speed. 1.39( 9) 1.13 = t 11.1 = t
v = v T 1 e bt dx dt = g b dx = g b x dx = x o 1 e bt 1 e bt t o x x o = gt b g b dt 1 e bt + 2 g b 2 e bt c. the distance the object travels during the first 5.54 onds. dt t 0 = gt b + 2 g b 2 e bt 1
x = gt b x = + 2 g b 2 e bt 9kg 9.8 2 1 ( ) 5.54 1.13 kg ( ) x = 434 + 626 0.5 ( ) x = 121 + 9kg ( ) ( ) 2 9.8 2 ( 1.13 kg ) 2 e 0.693 1 ( )
55. An auseent park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away. the Coefficient of static friction between the person and wall is µs, and the radius of the cylinder is R. a. Show the axiu period of revolution necessary to keep the person f fro falling is b. Obtain a nuerical value for T if R = 4.00 and µs = 0.400. What is the frequiency of the cylinder? c. If the rate of revolution (ƒ) is larger, what happens to the forces? N d. If the rate of revolution is saller, what happens to the forces? g
#55a f N = v 2 R f = µn = g v = NR N = g µ N T = 2πR v = 2πR NR = 4π 2 R 2 NR g T = 4π2 R 2 = g µ R 4π 2 Rµ g
#55b T = 4π 2 4 g f = 1 T = f = 1 T = ( )( 0.4) = 2.54 1rev 2.54 = 0.394Hz 1rev 60 = 23.6 rev 2.54 in in