Question 1

If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors,what is the angle between the two vectors?

Accepted Answer

The answer of If the magnitude of the cross product...

Question 2

If an irregularly shaped object (such as a wrench)is dropped from rest in a classroom and feels no air resistance,it will

Accepted Answer

A)  accelerate but will not spin. 
B)  accelerate and turn until its center of gravity reaches its lowest point. 
C)  accelerate and turn about its center of gravity with uniform angular speed. 
D)  accelerate and turn about its center of gravity with uniform angular acceleration. 
E)  accelerate and spin until its center of gravity reaches its highest point. 
A)  accelerate but will not spin. 
B)  accelerate and turn until its center of gravity reaches its lowest point. 
C)  accelerate and turn about its center of gravity with uniform angular speed. 
D)  accelerate and turn about its center of gravity with uniform angular acceleration. 
E)  accelerate and spin until its center of gravity reaches its highest point.

Question 3

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).You release the hanging blocks simultaneously from rest,and call tL the time taken by the block on the left and tR the time taken by the block on the right to reach the bottom,respectively.The bar,pulley,and rope have negligible mass,the rope does not slip,and there is no friction in the axle of the pulley.Under these conditions

Accepted Answer

A)  tL =   tR. 
B)  tL = tR. 
C)  tL =   tR. 
D)  tL = 2tR. 
E)  tl = 4tR. 
A)  tL =   tR. 
B)  tL = tR. 
C)  tL =   tR. 
D)  tL = 2tR. 
E)  tl = 4tR.

Question 4

In the figure,a uniform ladder 12 meters long rests against a vertical frictionless wall.The ladder weighs 400 N and makes an angle θ of 79° with the floor.A man weighing 790 N climbs slowly up the ladder When he has climbed to a point that is 7.8 m from the base of the ladder,the ladder starts to slip.What is the coefficient of static friction between the floor and the ladder?

Accepted Answer

The answer of In the figure,a uniform ladder 12 meters...

Question 5

Consider a uniform solid sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?

Accepted Answer

A)  Its translational kinetic energy is larger than its rotational kinetic energy. 
B)  Its rotational kinetic energy is larger than its translational kinetic energy. 
C)  Both forms of energy are equal. 
D)  You need to know the speed of the sphere to tell. 
A)  Its translational kinetic energy is larger than its rotational kinetic energy. 
B)  Its rotational kinetic energy is larger than its translational kinetic energy. 
C)  Both forms of energy are equal. 
D)  You need to know the speed of the sphere to tell.

Question 6

A solid uniform brick is placed on a sheet of wood.When one end of the sheet is raised (see figure),you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°.There is enough friction to prevent the brick from sliding.What is the width w of the brick?

Accepted Answer

A)  5.18 cm 
B)  6.09 cm 
C)  6.81 cm 
D)  9.40 cm 
E)  10.5 cm 
A)  5.18 cm 
B)  6.09 cm 
C)  6.81 cm 
D)  9.40 cm 
E)  10.5 cm

Question 7

A 1.10-kg wrench is acting on a nut trying to turn it. The length of the wrench lies directly to the east of the nut. A force 150.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0° north of east. What is the magnitude of the torque about the center of the nut?

Accepted Answer

A)  22.5 N • m 
B)  11.3 N • m 
C)  19.5 N • m 
D)  2250 N • m 
E)  1949 N • m 
A)  22.5 N • m 
B)  11.3 N • m 
C)  19.5 N • m 
D)  2250 N • m 
E)  1949 N • m

Question 8

A torque of 12 N • m is applied to a solid,uniform disk of radius 0.50 m,causing the disk to accelerate at 5.7 rad/s2.What is the mass of the disk?

Accepted Answer

A)  17 kg 
B)  13 kg 
C)  8.5 kg 
D)  4.3 kg 
A)  17 kg 
B)  13 kg 
C)  8.5 kg 
D)  4.3 kg

Question 9

A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp that makes an angle of 30° with the horizontal.How long does it take it to travel the first 3.1 m?

Accepted Answer

A)  1.4 s 
B)  1.1 s 
C)  2.1 s 
D)  1.6 s 
E)  1.8 s 
A)  1.4 s 
B)  1.1 s 
C)  2.1 s 
D)  1.6 s 
E)  1.8 s

Question 10

If two forces of equal magnitude act on an object that is hinged at a pivot,the force acting farther from the pivot must produce the greater torque about the pivot.

Accepted Answer

A)  True 
B)  False 
C)  unable to decide without knowing the shape of the object 
A)  True 
B)  False 
C)  unable to decide without knowing the shape of the object

Question 11

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board,which is supported by two narrow pillars 1.60 m apart,as shown in the figure.Find the magnitude and direction of the force exerted on the diving board
(a)by pillar A.
(b)by pillar B.

Accepted Answer

(a)1.71 kN

Question 12

A 3.00-kg ball rests in a frictionless groove as shown in the figure.   
(a)What is the magnitude of the force that the left side of the groove exerts on the ball?
(b)What is the magnitude of the force that the right side of the groove exerts on the ball?

Accepted Answer

(a)26.4 N

Question 13

If   and  
Are nonzero vectors for which  
•  
= 0,it must follow that

Accepted Answer

A)    ×
  = 0. 
B)    is parallel to
  . 
C)  |   ×
  | = AB. 
D)  |   ×
  | = 1. 
A)    ×
  = 0. 
B)    is parallel to
  . 
C)  |   ×
  | = AB. 
D)  |   ×
  | = 1.

Question 14

A uniform sign is supported against a wall at point P as shown in the figure.If the sign is a square 0.40 m on a side and its mass is 4.0 kg,what is the magnitude of the horizontal force that the wall at P experiences?

Accepted Answer

A)  20 N 
B)  0.00 N 
C)  7.8 N 
D)  98 N 
A)  20 N 
B)  0.00 N 
C)  7.8 N 
D)  98 N

Question 15

A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure.A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor.   
(a)What is the tension in the rope?
(b)What is the magnitude of the force that the floor exerts on the plank?

Accepted Answer

The answer of A 20.0-kg uniform plank is supported by...

Question 16

A very thin uniform rod,2.40 m long and of weight 135 N,has a frictionless hinge at its lower end.It starts out vertically from rest and falls,pivoting about the hinge.Just as it has rotated through an angle of 55.0°,what is the downward acceleration of the end farthest from the hinge?

Accepted Answer

A)  5.02 m/s2 
B)  8.03 m/s2 
C)  9.80 m/s2 
D)  12.0 m/s2 
E)  19.6 m/s2 
A)  5.02 m/s2 
B)  8.03 m/s2 
C)  9.80 m/s2 
D)  12.0 m/s2 
E)  19.6 m/s2

Question 17

A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal force B applied to an axle through the center of the roller,as shown in the figure.The roller has radius 0.65 meters and mass 51 kg and rolls without slipping.What magnitude of the force B is required to give the center of mass of the roller an acceleration of 2.8 m/s2?

Accepted Answer

Question 18

For the vectors shown in the figure,find the magnitude and direction of the vector product   ×  
,assuming that the quantities shown are accurate to two significant figures.

Accepted Answer

A)  16, directed into the plane 
B)  16, directed out of the plane 
C)  45, directed on the plane 
D)  45, directed into the plane 
E)  45, directed out of the plane 
A)  16, directed into the plane 
B)  16, directed out of the plane 
C)  45, directed on the plane 
D)  45, directed into the plane 
E)  45, directed out of the plane

Question 19

A uniform disk,a uniform hoop,and a uniform solid sphere are released at the same time at the top of an inclined ramp.They all roll without slipping.In what order do they reach the bottom of the ramp?

Accepted Answer

A)  disk, hoop, sphere 
B)  hoop, sphere, disk 
C)  sphere, disk, hoop 
D)  sphere, hoop, disk 
E)  hoop, disk, sphere 
A)  disk, hoop, sphere 
B)  hoop, sphere, disk 
C)  sphere, disk, hoop 
D)  sphere, hoop, disk 
E)  hoop, disk, sphere

Question 20

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal.After it has rolled 4.20 m along the ramp,what is the magnitude of the linear acceleration of its center of mass?

Accepted Answer

A)  9.80 m/s2 
B)  4.60 m/s2 
C)  3.29 m/s2 
D)  3.07 m/s2 
E)  2.30 m/s2 
A)  9.80 m/s2 
B)  4.60 m/s2 
C)  3.29 m/s2 
D)  3.07 m/s2 
E)  2.30 m/s2

Exam 12: Torque

If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors,what is the angle between the two vectors?

If an irregularly shaped object (such as a wrench)is dropped from rest in a classroom and feels no air resistance,it will

Consider a uniform solid sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?

A solid uniform brick is placed on a sheet of wood.When one end of the sheet is raised (see figure),you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°.There is enough friction to prevent the brick from sliding.What is the width w of the brick?

A torque of 12 N • m is applied to a solid,uniform disk of radius 0.50 m,causing the disk to accelerate at 5.7 rad/s2.What is the mass of the disk?

A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp that makes an angle of 30° with the horizontal.How long does it take it to travel the first 3.1 m?

If two forces of equal magnitude act on an object that is hinged at a pivot,the force acting farther from the pivot must produce the greater torque about the pivot.

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board,which is supported by two narrow pillars 1.60 m apart,as shown in the figure.Find the magnitude and direction of the force exerted on the diving board (a)by pillar A. (b)by pillar B.

A 3.00-kg ball rests in a frictionless groove as shown in the figure. (a)What is the magnitude of the force that the left side of the groove exerts on the ball? (b)What is the magnitude of the force that the right side of the groove exerts on the ball?

If and Are nonzero vectors for which • = 0,it must follow that

A uniform sign is supported against a wall at point P as shown in the figure.If the sign is a square 0.40 m on a side and its mass is 4.0 kg,what is the magnitude of the horizontal force that the wall at P experiences?

A very thin uniform rod,2.40 m long and of weight 135 N,has a frictionless hinge at its lower end.It starts out vertically from rest and falls,pivoting about the hinge.Just as it has rotated through an angle of 55.0°,what is the downward acceleration of the end farthest from the hinge?

For the vectors shown in the figure,find the magnitude and direction of the vector product × ,assuming that the quantities shown are accurate to two significant figures.

A uniform disk,a uniform hoop,and a uniform solid sphere are released at the same time at the top of an inclined ramp.They all roll without slipping.In what order do they reach the bottom of the ramp?

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal.After it has rolled 4.20 m along the ramp,what is the magnitude of the linear acceleration of its center of mass?

Foundations

A: Foundations

Motion in One Dimension

Acceleration

Momentum

Energy

Principle of Relativity

Interactions

Force

Work

Motion in a Plane

Motion in a Circle

Gravity

Special Relativity

Periodic Motion

Waves in One Dimension

Waves in Two and Three Dimensions

Fluids

Entropy

Energy Transferred Thermally

Degradation of Energy

Electric Interactions

The Electric Field

Gausss Law

Work and Energy in Electrostatics

Charge Separation and Storage

Magnetic Interactions

Magnetic Fields of Charged Particles in Motion

Changing Magnetic Fields

Changing Electric Fields

Electric Circuits

Electronics

Ray Optics

Wave and Particle Optics

Filters

A torque of 12 N • m is applied to a solid,uniform disk of radius 0.50 m,causing the disk to accelerate at 5.7 rad/s².What is the mass of the disk?