last testttt :)

a beam with a pivot on its left end is suspended from a rope. in which direction is the force of the pivot of the beam? a. right b. up c. diagonal right d. down

ANSWER: b

a car manufacturer claims that you can drive its new vehicle across a hill with a 46° slope before the vehicle starts to tip. If the vehicle is 2.1 m wide, how high is its center of gravity?

ANSWER: 1.014 WORK: (d/2) / tan(theta) (2.1/2) / tan(46) = 1.014

You're carrying a 3.0-m-long, 27 kg pole to a construction site when you decide to stop for a rest. You place one end of the pole on a fence post and hold the other end of the pole 36 cm from its tip. How much force must you exert to keep the pole motionless in a horizontal position?

ANSWER: 150.34 WORK: F = (mg(L/2)) / (L-d) F= (27 x 9.8(3/2)) / (3-.36) F= 150.34

the tune-up specifications of a car call for the spark plugs to be tightened to a torque of 35.7 Nm. you plan to tighten the plugs by pulling on the end of a 24.8-cm-long wrench. because of the cramped space under the hood, you'll need to pull at an angle of 113 degrees with respect to the wrench shaft. with what force must you pull?

ANSWER: 156.38 WORK: F = torque / Lsin(theta) F = 35.7 / .248sin(113) = 156.38

A uniform beam of length L=1.5 m and mass 14.2 kg is attached to a wall by a cable at the angle θ=21°, as shown in the figure below. The beam is free to pivot at the point where it attaches to the wall. What is the tension in the cable?

ANSWER: 194.16 WORK: T=(mg/sin(theta))/2 T= ((10.6 x 9.8)/sin(21))/2 T= 194.16

consider a 3 kg, uniform, horizontal rod with a length of 1 m. what is the magnitude of the gravitational torque about a point located 41 cm from the left-most edge?

ANSWER: 2.65 WORK: find force... 3 x 9.8 = 29.4 find distance... .5 -.41 = .09 find magnitude... 29.4 x .09 = 2.65

a typical jar has been tightened to a reasonable degree requires 1.99 Nm to open. if you grab a 7.1-cm-diameter jar lid with one hand so that your thumb and fingers exert equal magnitude forces on opposite sides of the lid, what is the magnitude of each of the forces?

ANSWER: 28.03 WORK: 199/7.1 = 28.03

A 64 kg student stands on a very light, rigid board that rests on a bathroom scale at each end, as shown in the figure below. If the values of d and L in the figure are d=1.2 m and L=2.3 m, what weight does the leftmost scale read?

ANSWER: 299.97 WORK: W= mg((L-d)/L) W= 64 x 9.8((2.3-1.2)/2.3) W= 299.97

A force stretches a wire by 1.4 mm. A second wire of the same material has the same cross section and is 2.15 times longer. How far will it be stretched by the same force?

ANSWER: 3.01 WORK: 1.4 x 2.15 3.01

Force F2 acts half as far from the pivot as F1. if F1 = 27 n and the angle is 53 degrees, what magnitude of F2 causes the net torque on the rod to be zero?

ANSWER: 43.13 WORK: F1 x sin(theta) x 2 27 x sin(53) x 2 =43.13

A 27 kg student stands on a 65 kg rigid board that rests on a bathroom scale at each end, as shown in the figure below. If the values of d and L in the figure are d=1.0 m and L=2.3 m, what weight does the leftmost scale read?

ANSWER: 468.06 WORK: F= (mass of board(g)/2) + (mass of student x g) x (L-d / L) F = ((65 x 9.8)/2) + 27x9.8((2.3-1)/2.3) F= 468.06

A glass optical fiber in a communications system has a diameter of 13.6 μm and a Young's Modulus of 7.3x10^10 N/m2. If the glass has a tensile strength of 52.3x10^6 N/m2, by how many mm can a 9.2-m-long fiber be stretched before it snaps?

ANSWER: 6.59 WORK: LT/y (9.2(52.3 x 10^6)) / (7.3 x 10^10) = .00659 =6.59

A glass optical fiber in a communications system has a diameter of 13.1 μm. If the glass has a tensile strength of 55.7x 10^6 N/m2, what maximum tension in mN could this fiber support without breaking?

ANSWER: 7.51 WORK: TA = tension (55.7 x 10^6) x 3.14((13.1/2) x 10^-6)^2

a 3-m-long, 406 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. a 96 kg construction worker stands at the far end of the beam. what is the magnitude of the torque about the point where the beam is bolted into place?

ANSWER: 8790.6 WORK: ((L/2) x 406 x 9.8) + (96 x 9.8 x 3) = 8790.6

A 7-m-long beam with mass 1039 kg is attached to a wall on its left side by a freely rotating pivot. It is supported on the right side by a cable at an angle of θ=35°. If a 75 kg worker sits 1 m from the right side of the beam to eat his lunch, what force must the cable be capable of supporting in order for the worker to be safe?

ANSWER: 8988.14 WORK: F= (mass of board x g(L/2) + mass of worker x g(L-d)) / Lsin(theta) F= (1039 x 9.8(7/2) + 75 x 9.8 (7-1)) / 7sin(35) F= 8988.14

A vendor hangs an 5.4 kg sign in front of his shop with a cable held away from the building by a lightweight pole. The pole is free to pivot about the end where it touches the wall, as shown in the figure below. If the angle of the cable is θ=54°, what is the tension in the cable?

ANSWER: 90.03 WORK: T= mg/cos(theta) T= (5.4 x 9.8) / cos(54) T= 90.03

A glass optical fiber in a communication system has a diameter of 27 μm and a young's modulus of 8 x 10^10 n/m^2. if the glass has a tensile strength of 33 x 10^6 n/m^2, by how many mm can a 44-m-long fiber be stretched before it snaps? a. 18 mm b. 16 mm c. 20 mm d. 17 mm e. 11 mm

ANSWER: a WORK: deltaL = lf / ay deltaL = 44 x (33 x 10^6) / (8 x 10^10) = .0182 m deltaL = 18.15 mm

A store's sign has a mass of 41 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end. what is the tension in the wire? angle=25 degrees a. 200 n b. 460 n c. 120 n d. 300 n e. 230 n

ANSWER: b WORK: T x 3 x sin(25) = 41 x 9.8 x (3/2) T = 475.37

a 13 m-long beam with mass 777 kg is attached to a wall on its left side by a freely rotating pivot. it is supported on the right side by a cable at a angle of 22 degrees. if a 55 kg worker sits 10.3 from the left side of the beam to eat her lunch, what force must the cable be capable of supporting in order for the worker to be safe? a. 7000 n b. 11000 n c. 13000 n d. 21000 n e. 9000 n

ANSWER: b WORK: wB x L / 2 + wW x LW = L x T x sin(theta) 777 x 9.8 x 6.5 + 55 x 9.8 * 10.3 = T x 13 x sin(22) T= (49495 + 5552) / 4.87 = 11303

as shown in the figure a 10 m long bar is attached by a frictionless hinge to a wall and held horizontally by a light rope that makes an angle of 36 degrees with the bar. the bar is uniform and light. what distance of x from the hinge should a 44 kg mass be suspended for the tension in the rope to be 587 n? a. 10 m b. 8 m c. 6 m d. 4 m e. 2 m

ANSWER: b WORK: 587 x 10 x sin(36) = 44 x 9.8(x) x = 8.0016

a 10 m long bar is attached by a frictionless hinge to a wall and held horizontally by a light rope that makes an angle of 36 degrees with the bar. the bar is uniform and light. what distance x from the hinge should a 44 kg mass be suspended for the tension in the rope to be 587 n? a. 10 m b. 8 m c. 6 m d. 4 m e. 2 m

ANSWER: b WORK: 587 x 10 x sin(36) = 44 x 9.8x x = 8.0016

in the figure, force f2 acts half as far from the pivot as F1. What magnitude of f2 causes the net torque on the rod to be zero? a. 14 n b. 28 n c. 40 n d. 20 n e. 33 n

ANSWER: b WORK: F2 = 20 sin(45) x 2 F2= 28.28

as an audio cd plays, the frequency at which the disk spins changes. at 210 rpm, the speed of a point on the outside edge of the disk is 1.3 m/s. at 420 rpm, the speed of a point on the outside edge is... a. 1.3 m/s b. 2.6 m/s c. 3.9 m/s d. 5.2 m/s

ANSWER: b WORK: the speed is proportional to the frequency, so doubling the frequency means doubling the speed.

the end of a spring is pulled to the right by 4 cm; the restoring force is 8 N to the left. if the spring is returned to equilibrium and then pushed to the left by 2 cm, the restoring force is... a. 4 n to the left b. 4 n to the right c. 8 n to the left d. 8 n to the right e. 16 n to the left f. 16 n to the right

ANSWER: b WORK: the spring is now compressed, so the restoring force will be to the right, the end of the spring is displaced by half of what it was in the earlier case, so the restoring force will be half of what it is as well.

two children hold opposite ends of a lightweight, 2.6-m-long horizontal pole with a water bucket hanging from it. The older child supports twice as much weight as the younger child. how far is the bucket from the older child? a. .3 m b. .6 m c. .9 m d. 1.2 m e. .5 m

ANSWER: c WORK: 3x = 2.6 x = .867

a nut needs to be tightened with a wrench. Which force shown in the figure will apply the greatest torque to the nut? a. downwards in the middle b. straight-on c. downwards at the end d. diagonal

ANSWER: c WORK: c and a have the biggest angles, which eliminated b and d. torque increases with distance away from pivot point, and c is the farthest away, so c is the answer.

a 66 kg student stands on a very light, rigid board that rests on a bathroom scale at each end. if the values of d and L are d = 7.5 m and L = 12 m, what weight dies the rightmost scale read? a. 450 n b. 500 n c. 400 n d. 550 n e. 350 n

ANSWER: c WORK: d x m x g = L x N N = 7.5 x 66 x 9.8 / 12 = 404.25

specifications require the oil filter for your car to be tightened with a torque of 55 n m. you are using an 18-cm-long oil filter wrench, and you apply a force at the very end of the wrench in the direction that produces maximum torque. how much force should you apply? a. 2000 n b. 400 n c. 300 n d. 30 n e. 1000 n

ANSWER: c WORK: t = rf 55 = .18f f = 305.55

a 1 kg weight is suspended from a spring, stretching it by 5 cm. how much does the spring stretch if the 1 kg weight is replaced by a 3 kg weight? a. 5 cm b. 10 cm c. 15 cm d. 20 cm

ANSWER: c WORK: the restoring force of the spring is proportional to the stretch. increasing the restoring force by a factor of 3 requires increasing the stretch by a factor of 3.

a light board supports two children weighing 777 n and 333 n. if the support is at the center of the board and the 777-n child is 2 m from its center, how far is the 333-n child from the center? a. 1.5 m b. 2.5 m c. 3.5 m d. 4.5 m e. 5.5 m

ANSWER: d WORK: 777 x 2 = 333(x) x = 4.67

a uniform beam of length L = 13 m and 88 kg is attached to a wall by a cable at the angle 22 degrees. the beam is free to pivot at the point where it attaches to the wall. what is the tension in the cable? a. 1400 n b. 500 n c. 1600 n d. 1200 n e. 700 n

ANSWER: d WORK: T = m x g / (2sin(theta)) T = 88 x 9.8 / (2sin(22)) T = 1151

one end of a 44 cm-long spring is attached to the ceiling. when a 3.3 kg mass is hung from the other end, the spring stretches to a length of 60 cm. what is the spring constant? a. 600 N/m b. 700 N/m c. 100 N/m d. 200 N/m e. 300 N/m

ANSWER: d WORK: mg = k(deltaX) k = 3.3 x 9.8 / (.6-.44) k = 202

a student lies on a very light, rigid board with a scale under each end. her feet are directly over one scale, and her body is in a straight position. the two scales read 65 n and 100 n, what is the student's weight? a. 65 n b. 75 n c. 100 n d. 165 n e. 225 n

ANSWER: d WORK: w = 65 + 100 w = 165

an old-fashioned tire swing exerts a force on the branch and a torque about the point where the branch meets the trunk, this will _____ the force and ____ the torque a. increase, increase b. not change, increase c. not change, not change d. not change, decrease e. decrease, not change f. decrease, decrease

ANSWER: d WORK: the tension in the rope is equal to the weight suspended from it. the force does not change with the position at which the rope is attached. but the torque about the point where the branch meets the trunk depends in both this force and the distance from the pivot point. as the distance decreases, so does the torque

a uniform 777 n piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends. a small but dense 222 n weight is placed on the apparatus 2 m from one end. what are the tensions, a and b, in the two wires? a. a = 5200 n, b = 4800 n b. a = 480 n, b = 520 n c. a = 5000 n, b = 5000 n d. a = 4800 n, b = 5200 n e. a = 520 n, b = 480 n

ANSWER: e WORK: TA + TB = 777 + 222 = 999 more weight is on TA (shown in picture) 520 + 480 = ~999

a wire that is 8 mm in diameter and 13 m long stretches 7 mm when a 33-kg tool is hung from it. what is young's modulus for the material from this wire is made? a. 1 x 10^7 n/m^2 b. 1 x 10^8 n/m^2 c. 1 x 10^9 n/m^2 d. 1 x 10^10 n/m^2 e. 1 x 10^11 n/m^2

ANSWER: e WORK: Y = m x g x L / (A x deltaL) Y = 33 x 9.8 x 13 / ((3.14 x .004^2) x .007) Y = 1.2 x 10^10

a wire that is 8 mm in diameter and 13 m long stretches 7 mm when a 33-kg tool is hung from it. what is young's modulus for the material from this wire is made. a. 1 x 10^7 n/m^2 b. 1 x 10^8 n/m^2 c. 1 x 10^9 n/m^2 d. 1 x 10^11 n/m^2 e. 1 x 10^10 n/m^2

ANSWER: e WORK: Y = m x g x l / (a x deltaL) Y = 33 x 9.8 x 13 / ((3.14 x .0004^2) x .007 Y = 1.2 x 10^10

a wire that is 5.5 mm in diameter and 16 m long stretches 8 mm when a 33-kg tool is hung from it. what is the effective spring constant for the stretching wire? a. 4.1 x 10^2 N/m\ b. 4.1 x 10^3 N/m c. 4.1 x 10^5 N/m d. 4.1 x 10^6 N/m e. 4.1 x 10^4 N/m

ANSWER: e WORK: mg = k(deltaX) k = 33 x 9.8 / .008 k = 40425

a wheel turns freely on an axle at the center. which force will provide the largest positive torque on the wheel? a. 2F up from the left b. 2F right from the midpoint between the center and top c. F right from the center d. F right from the right e. F right from the bottom

ANSWER: e WORK: forces d and c act at or in line with the pivot and provide no torque. of the others, only e tries to rotate the wheel counterclockwise, so it is the only choice that gives a positive nonzero torque.

a 10 kg mass is hung from a 1-m-long cable, causing the cable to stretch by 2 mm. suppose a 10 kg mass is hung from a 2 m length of the same cable. by how much does the cable stretch? a. .5 mm b. 1 mm c. 2 mm d. 3 mm e. 4 mm

ANSWER: e WORK: the cables have the same diameter, and the force is the same, so the stress is the same in both cases. this means that the strain is the same. the 2 m cable will experience twice the change in length of the 1 m cable.

a glass optical fiber in a communications system has a diameter of 22 μm and a young's modulus of 8 x 10^10 n/m^2. if the glass has a tensile strength of 33 x 10^6 n/m^2, what maximum tension could this fiber support without breaking? a. 1 mN b. 2 mN c. 4 mN d. 8 mN e. 12 mN

ANSWER: e WORK: Fmax = tensile strength x area Fmax = 33 x 10^6 x 3.14 x (11 x 10^-6)^2 F = 0.0125 N F = 12.54 mN