Free-Body Diagrams and Equilibrium - 5 Steps to a 5 500 AP Physics Questions to Know by Test Day

5 Steps to a 5 500 AP Physics Questions to Know by Test Day (2012)

Chapter 2. Free-Body Diagrams and Equilibrium

31. Which of Newton’s laws describes equilibrium?

(A) The first, which mathematically states that Σ F = 0.

(B) The second, which mathematically states that Σ F = ma.

(C) The third, which mathematically states that F = -F.

(D) The fourth, which mathematically states that F = Gm1m2/r2.

(E) The fifth, which mathematically states that dx/dt = v.

32. A book is resting on a table. What forces are acting on the book?

(A) The weight of the book

(B) The weight of the book and the acceleration of gravity

(C) The supporting force of the table on the book

(D) The weight of the book and the pushback force of the table

(E) The weight of the book and the force of the table

33. When is the normal force not equal to the weight of an object?

(A) In space where there is no gravity

(B) When the object is being accelerated upward

(C) When the object is on an inclined plane

(D) When the object is supported by a string

(E) When it is moving along a flat surface

34. Why can a string hung from two opposite points never be made perfectly straight?

(A) A free-body diagram (FBD) of the string shows that the string tension must be infinite to balance the weight of the string.

(B) An FBD of the string shows that an angle must exist between the string and a perfectly straight line to balance the weight of the string.

(C) An FBD of the string shows that an angle must exist between the string and a perfectly straight line to allow vertical forces to balance the weight of the string.

(D) If the string were perfectly straight, it would break.

(E) Strings, ropes, and cable always hang in the shape of a helix.

35. A more general statement of Newton’s first law is:

(A) Σ F = 0

(B) Σ Fx = 0, Σ Fy = 0, and Σ Fz = 0

(C) All the forces and moments must be zero

(D) All the forces added together must be zero

(E) Σ Fx = 0, Σ Fy = 0, Σ Fz = 0, Σ Mx = 0, Σ My = 0, and Σ Mz = 0

36. A torque is:

(A) A force applied at a distance

(B) A moment

(C) A force applied to a body that causes the body to rotate

(D) A pair of forces

(E) A force multiplied by a distance

37. Can a compressive force be carried by a rope?

(A) Only if the rope is very stiff

(B) No

(C) Yes

(D) If a rope is pushed, it tends to wriggle

(E) Generally, no

38. What is a friction force and how does it act?

(A) It is a force that acts along the plane.

(B) It is a force that opposes motion.

(C) It is a force that is proportional to the normal force that acts in opposition to the direction of motion.

(D) It is a force that is proportional to the normal force that acts in the direction of motion.

(E) It is a force that is proportional to a body’s weight that acts in the direction of motion.

39. What is a Free Body Diagram (FBD)?

(A) An FBD shows the forces acting on a body.

(B) An FBD shows the forces and their locations on a body.

(C) An FBD shows the forces and accelerations and their locations acting on a body.

(D) An FBD shows the forces and torques and their locations acting on a body.

(E) An FBD shows the forces and velocities and their locations acting on a body.

40. What defines a lever arm?

(A) The distance parallel to the line of action of the force

(B) The distance parallel to the line of action of the force from the pivot point

(C) The distance perpendicular to the line of action of the force

(D) The distance perpendicular to the line of action of the force from the pivot point

(E) F = |F| cos(θ)x

41. A pulley is supporting a 200-pound box. What is the tension in the rope?

(A) 100 pounds

(B) 200 pounds

(C) 50 pounds

(D) It depends on the angle that the rope makes with the pulley

(E) It depends on where the rope is placed on the box

42. A rope is strung between two cliffs. A mountain climber weighing 100 kg is halfway across the rope when the rope forms an angle of 10° with the horizontal. What is the tension in the rope?

(A) 980 N

(B) 498 N

(C) 980 kg

(D) 100 N

(E) 497 N

43. A 300-kg piano is being lifted into an upper-story window. Two pulleys are being used. At one point in the lift, one pulley rope on the left forms a 33° angle with the horizontal and forms a 63° angle with the horizontal on the right. What are the tensions in the two ropes?

(A) Tright = 1,610 N and Tleft = 2,633 N

(B) Tright = 1,610.0 N and Tleft = 2,633.3 N

(C) Tright = 1,610.96 N and Tleft = 2,633.92 N

(D) Tright = 1,610 N and Tleft = 2,630 N

(E) Tright = 1,600 N and Tleft = 2,600 N

44. A 1-m pry bar is used to open a crate. It is forced 2 cm between the crate lid and the crate and is horizontal. If the pry bar tip is the fulcrum of the lever, and the end of the bar is pressed down with a 20-N force, what force is applied on the crate lid?

(A) 1 N

(B) 100 N

(C) 10 N

(D) 1,000 N

(E) 10,000 N

45. A 100-kg box is sitting on a 10° incline with a coefficient of friction of 0.5. How much must the incline be raised to make the box slide down?

(A) 30°

(B) 33°

(C) 26°

(D) 24°

(E) 15°

46. An astronaut floating in space uses an ordinary wrench to loosen a bolt on a massive satellite. What happens?

(A) He loosens the bolt.

(B) The satellite rotates around the bolt.

(C) The astronaut rotates around the bolt.

(D) Nothing happens.

(E) The astronaut moves in the direction of the force on the wrench.

47. A 5-kg baby carriage that is carrying a baby that weighs 5 kg rolls on all four wheels. The front wheels are 60 cm from the back wheels and 90 cm from the carriage handle. Assuming that the center of gravity for the baby and the carriage’s center is equidistant between the front and back wheels, what force must the mother apply to tip the carriage back to lift the front wheels?

(A) 10 kg

(B) 100 N

(C) 5 kg

(D) 50 N

(E) 100 N.m

48. A six-strand pulley is used to raise a load weighing 1,000 kg. What is the tension on the pulley cables?

(A) 15,000 N

(B) 1,000 N

(C) 1,633 N

(D) 10,000 N

(E) 16,000 N

49. Newton published his laws of motion in what text?

(A) Philosophiæ Naturalis Principia Physica

(B) Philosophiæ Naturalis Principia Mathematica

(C) Philosophiæ Naturalis Principia Il Movo

(D) Principia

(E) Principia Mathematica

50. An object is supported by a spring attached to the ceiling. What are the forces acting on the object?

(A) The mass of the object in the downward direction and the supporting force of the spring in the upward direction

(B) The mass of the object in the downward direction and the supporting force of the spring in the downward direction

(C) The weight of the object in the upward direction and the supporting force of the spring in the downward direction

(D) The weight of the object in the downward direction and the supporting force of the spring in the upward direction

(E) The weight of the object and the supporting force of the spring

51. A box that is resting on an inclined plane has what forces acting on it?

(A) The weight of the box, the box’s component forces perpendicular to and along the plane, and the friction force along the surface of the plane beneath the box

(B) The weight of the box, the box’s component forces perpendicular to and along the plane, the resultant force of the plane on the box, and the friction force along the surface of the plane beneath the box

(C) The weight of the box and the friction force along the surface of the plane beneath the box

(D) The mass of the box and its acceleration along the plane

(E) The weight of the box, the resultant force of the plane on the box, and the friction force along the surface of the plane beneath the box

52. A crane is used to pick up a 50-m-long steel beam to place in a building. The beam is uniform, but the crane cable is placed 2 m off the center of the beam. How much vertical force must be placed on the guide rope to keep the beam level? The beam has a mass of 5 kg/m, and the guide rope is placed on the end of the shorter side of the beam.

(A) 213 N

(B) 213 kg

(C) 21 N

(D) 21 kg

(E) 106 N

53. A large chest is at the bottom of a lake. From its size, it has a buoyancy force of 200 N, but it is known to hold gold bullion with a mass of 200 kg. How much force is required to vertically pull the chest to the surface? How much force is required to pull it out of the water?

(A) 176 kg and 196 kg

(B) 176 N and 196 N

(C) 1,760 N and 1,960 N

(D) 1,960 N and 1,760 N

(E) 196 N and 1,760 N

54. A 2-m-long lever is placed under a 1,000-N rock. A fulcrum is placed at 0.5 m from the end of the rock, placing the lever at 30° above the horizontal. How much vertical force must be applied to the far end of the lever to lift the rock?

(A) 67 N

(B) 667 N

(C) 333 N

(D) 1,000 N

(E) 22 N

55. At what distance from the Earth is the center of mass for the Earth–Moon system? (The center of mass is the point between the bodies at which their masses balance. Assume that the Earth has a mass of 5.97 × 1024 kg, the Moon has a mass of 7.35 × 1022 kg, and they are 3.84 × 108 m apart.)

(A) 5.00 × 107 m from the Earth

(B) 1.92 × 108 m from the Moon

(C) 4.73 × 106 m from the Moon

(D) 4.73 × 106 m from the Earth

(E) 1.92 × 108 m from the Earth

56. A large 2,000-N cement block is pulled up a frictionless 43° incline using a dual-strand pulley that is attached to the block. One end of the rope is tied to the wall at the top of the plane while a man is pulling the other end of the rope. What is the tension in the pull of the rope if the rope is pulled parallel to the plane?

(A) 732 N

(B) 682 N

(C) 1,463 N

(D) 1,364 N

(E) 462 N

57. Three men are trying to position a heavy soda machine into a niche in a wall. Two men are pushing diagonally along the front of the machine. Where should the third man push so that the machine will move straight into the niche?

(A) At the top

(B) Pull from the rear

(C) Along a diagonal

(D) At the front center of the machine

(E) At either side

58. A helicopter is holding a 5,000-N bridge section 100 m over the spot where it is going to be placed, but the helicopter is slightly off. How much force must the spotter on the ground apply to the bridge section to move it 1 m into the proper position?

(A) 500 N

(B) 50 N

(C) 5 N

(D) 490 N

(E) 4.9 N

59. A large 2,000-N cement block is being pulled up a 43° incline with a single-strand pulley attached to the block. What is the tension in the pull rope if the rope is being pulled parallel to the plane? (Assume a coefficient of friction of 0.5 between the block and the plane.)

60. A crane has a 200,000-N counterweight, a 30-m boom, and a 12-strand pulley. The crane body is 4.0 m × 4.0 m, and the boom can be lowered to 5° from the horizontal. Neglecting the weight of the crane and boom, what weight can the crane lift without tipping?