Deck 14: Statics and Elasticity

Question 1

The maximum number of independent equations that must be satisfied for static equilibrium for a rigid body is

A) 2.
B) 3.
C) 4.
D) 6.

Answer 1

6.

Question 2

A general mathematical similarity between equations involving elongation, shear, and compression occurs when the deformation is related to the appropriate dimension as a

A) sum.
B) difference.
C) product.
D) quotient.

Answer 2

quotient.

Question 3

In SI units, the dimensions of the various sorts of modulus are

A) Newton-meters².
B) Newton-meters.
C) Newtons/meter.
D) Newtons/meter².

Answer 3

Newtons/meter².

Question 4

All of the following properties of a body have the same dimensions except

A) Young's modulus.
B) elastic limit.
C) ultimate strength.
D) shear modulus.

Question 5

A dimensionless quantity is

A) strain.
B) mechanical advantage.
C) Both of the first two answers are valid.
D) Neither of the first two answers is valid.

Question 6

Stress has dimensions of

A) force multiplied by area.
B) force divided by area.
C) force divided by length.
D) none of the above.

Question 7

In general, liquids are characterized by a nonzero

A) shear modulus.
B) bulk modulus.
C) Young's modulus.
D) none of the above.

Question 8

The proper relation between stress and strain is

A) stress = strain.
B) stress = l/strain.
C) Stress ? strain.
D) Stress ? l/strain.

Question 9

The relevant area associated with shear is oriented with the plane of its surface

A) parallel to the applied force.
B) perpendicular to the applied force.
C) making an angle with respect to the applied force that depends on specific conditions.
D) none of the above.

Question 10

The density of a material must change when the material is subjected to

A) shear forces.
B) elongation forces.
C) compression forces.
D) none of the above.

Question 11

A material with a relatively large bulk modulus

A) requires relatively large forces to produce a specified density change.
B) requires relatively small forces to produce a specified density change.
C) is a material that has a relatively small value of density.
D) is a material that has a relatively large value of density.

Question 12

If a rigid body is in rotational equilibrium, all of the following statements are valid except

A) the body will experience no angular accelerations about the center-of-mass axis.
B) the body will experience no angular accelerations about any axis.
C) the body will experience no torques about any axis.
D) none of the above.

Question 13

The shape of a body must change for each of the following forces except

A) shear forces.
B) elongation forces.
C) compression forces.
D) none of the above.

Question 14

The sign of the change in the relevant strain parameter is positive for an increased applied force except when the force is

A) shear.
B) elongation.
C) compression.
D) none of the above.

Question 15

Consider a truss designed to support some maximum weight W on a frictionless, horizontal surface. The truss has three straight members joined as in the letter "A," and all members of the truss are weightless. W is placed at the apex of the truss. A single modification that would permit stable support of a weight heavier than W would include any of the following except

A) decreasing the angle between the two legs.
B) strengthening the horizontal cross member.
C) introducing friction at the (bottom) surface of contact with the truss legs.
D) none of the above.

Question 16

Consider a truss designed to support some maximum weight W on a frictionless, horizontal surface. The truss has three straight members joined as in the letter "A," and all members of the truss are weightless. W is placed at the apex of the truss. A single modification that would permit stable support of a weight heavier than W for a given strength of the horizontal cross member is to

A) move the horizontal cross member toward the apex of the truss.
B) move the horizontal cross member toward the floor.
C) move the horizontal cross member to the exact midpoint of the distance from apex to floor.
D) none of the above.

Question 17

Consider a truss designed to support some maximum weight W on a frictionless, horizontal surface. The truss has three straight members joined as in the letter "A," and all members of the truss are weightless. W is placed at the apex of the truss. The force(s) at the center of the horizontal cross member is (are)

A) compressional.
B) tensional.
C) either of the above, depending on the vertical location of the horizontal cross member.
D) none of the above.

Question 18

If the mechanical advantage of a system is > 1, then

A) the applied force is > the delivered force.
B) the applied force is = the delivered force.
C) the applied force is < the delivered force.
D) none of the above.

Question 19

Neglecting dissipative forces, levers and pulleys are devices for which

A) applied distance = delivered distance.
B) applied force = delivered force.
C) applied work = delivered work.
D) none of the above.

Question 20

When hysteresis is manifest in a system, at some previous time

A) the elastic limit for the system was exceeded.
B) the ultimate strength of the system was reached.
C) catastrophic breakage of the system occurred.
D) none of the above.

Question 21

For a suspension bridge, where the total weight is distributed uniformly over the length of the bridge, the cables hang in the approximate shape of a

A) circle.
B) ellipse.
C) hyperbola.
D) parabola.

Question 22

The bottom end of a ladder rests on a floor with friction. The ladder leans against a frictionless vertical wall, the length of the ladder making an angle $\theta$ with the wall. A boy is perched on the ladder at such a point that equilibrium of the system is barely maintained. The ladder will slip under any of the following independent changes except

A) if the boy's distance from the top is decreased.
B) if the boy's mass is decreased.
C) if µ is decreased.
D) If $\theta$ is increased.

Question 23

If only two forces act on a body, all of the following are possible except

A) translational and rotational equilibrium of the body.
B) translational but no rotational equilibrium of the body.
C) rotational but no translational equilibrium of the body.
D) none of the above.

Question 24

A 10-meter-long steel rod (Young's modulus of $2 \times 10 ^ { 11 }$ Pa) having a 0.8-cm radius is supporting a 500-kg mass. The change in the length of the rod is

A) 2.3 mm.
B) 4.5 mm.
C) 1.2 mm.
D) 0.5 mm.

Question 25

A 0.75-m-long piano wire (radius of 0.5 mm) has one end fixed and the other end attached to a rotatable tuning peg (having a radius of 2 mm). The tuning peg is rotated so that the wire is just taut, and then the peg is given three full turns (tightening the wire). If the Young's modulus is $2 \times 10 ^ { 11 }$ Pa, the tension in the piano wire is

A) 7900 N.
B) 6600 N.
C) 5600 N.
D) 4400 N.

Question 26

A pressure of 1,100 Pa is applied to the ends of a long cylindrical mass (mass = 512 kg). The change in the length of the cylinder is $- 1 / 100$ the original length. The Young's modulus of the cylinder is

A) $2.2 \times 10 ^ { 5 }$ N/m $2$
B) $0.5 \times 10 ^ { 5 }$ N/m $2$
C) $4.4 \times 10 ^ { 5 }$ N/m $2$
D) $1.1 \times 10 ^ { 5 }$ N/m $2$

Question 27

A metal sphere (bulk modulus of $1 \times 10 ^ { 11 }$ Pa) is put under a hydraulic pressure of $10 ^ { 10 }$ Pa. If the original volume of the sphere was 1 cm $3$ , the new volume of the sphere is

A) 1.2 cm $3$
B) 1.1 cm $3$
C) 0.8 cm $3$
D) 0.9 cm $3$

Question 28

A metal cube, 5 cm on edge, undergoes a shearing force of 14,000 N (on opposing ends). If the shear modulus is $9 \times 10 ^ { 10 }$ Pa, the distance that the cube is sheared is

A) $7.5 \mu$ m.
B) $4.4 \mu$ m.
C) $3.1 \mu$ m.
D) $5.6 \mu$ m.

Question 29

Water has a bulk modulus of $0.2 \times 10 ^ { 10 }$ Pa. The pressure required to compress a volume of liquid water by 1% is

A) 20 MPa.
B) 10 KPa.
C) 10 MPa.
D) 20 KPa.

Question 30

A 4-m-long I-beam (of uniform shape) having a mass of 48 kg is held at a 35º angle above the floor by a bracket attached to its end. The bracket is securely bolted to the floor. The torque that the bracket must provide to hold the I-beam in place is

A) 540 Nm.
B) 770 Nm.
C) 610 Nm.
D) 660 Nm.

Question 31

A 4-m-long I-beam (of uniform shape) having a mass of 48 kg is held at a 35º angle above the floor by a bracket attached to its end. The bracket is securely bolted to the floor. The upward force that the floor must supply to support the bracket is

A) 240 N.
B) 0 N.
C) 390 N.
D) 470 N.

Question 32

A 5-m-long steel cable is horizontally attached (just tautly) between two large trees. A 40-kg child hangs from the middle, and in doing so lowers the cable 6 cm from its original position. The tension in the cable is

A) 400 N.
B) 4400 N.
C) 8200 N.
D) 800 N.

Question 33

A 5-m-long steel cable is horizontally attached (just tautly) between two large trees. A 40-kg child hangs from the middle, and in doing so lowers the cable 6 cm from its original position. If the Young's modulus of the steel cable is $1 \times 10 ^ { 11 }$ Pa and the cross-sectional area is 0.7 cm $2$ , the distance that the steel cable is stretched is

A) 6 mm.
B) 6 m.
C) 6 cm.
D) 0.6 m.

Question 34

A 530-kg I-beam that is 4.6 m long has one end attached to a vertical wall. The I-beam is allowed to pivot up and down about the attachment location. A long cable is then attached to the other end of the I-beam and hoisted vertically so the I-beam is exactly parallel with the ground. The tension in the cable is

A) 5300 N.
B) 0 N.
C) 2600 N.
D) 4500 N.

Question 35

A 530-kg I-beam that is 4.6 m long has one end attached to a vertical wall. The I-beam is allowed to pivot up and down about the attachment location. A long cable is then attached to the other end of the I-beam and hoisted vertically so the I-beam is exactly parallel with the ground. The vertical pin force at the pivot is

A) 5300 N.
B) 0 N.
C) 2600 N.
D) 4500 N.

Question 36

A 530-kg I-beam that is 4.6 m long has one end attached to a vertical wall. The I-beam is allowed to pivot up and down about the attachment location. A long cable is then attached to the other end of the I-beam and hoisted vertically so the I-beam is exactly parallel with the ground. The horizontal pin force at the pivot is

A) 5300 N.
B) 0 N.
C) 2600 N.
D) 4500 N.

Question 37

An I-beam having a mass of 810 kg and length of 5.1 m has one end attached to a vertical wall.The I-beam is allowed to pivot up and down about the attachment location. A cable is then attached from the vertical wall to the other end of the I-beam. The cable makes an angle of 31º with the I-beam, and the I-beam is horizontal (parallel with the ground). The tension in the cable is

A) 7700 N.
B) 4600 N.
C) 6600 N.
D) 2700 N.

Question 38

An I-beam having a mass of 810 kg and length of 5.1 m has one end attached to a vertical wall, the I-beam is allowed to pivot up and down about the attachment location. A cable is then attached from the vertical wall to the other end of the I-beam. The cable makes an angle of 31º with the I-beam, and the I-beam is horizontal (parallel with the ground). The vertical pin force at the pivot is

A) 8100 N.
B) 4000 N.
C) 6000 N.
D) 3000 N.

Question 39

An I-beam having a mass of 810 kg and length of 5.1 m has one end attached to a vertical wall. The I-beam is allowed to pivot up and down about the attachment location. A cable is then attached from the vertical wall to the other end of the I-beam. The cable makes an angle of 31º with the I-beam, and the I-beam is horizontal (parallel with the ground). The horizontal pin force at the pivot is

A) 8100 N.
B) 4200 N.
C) 6600 N.
D) 3800 N.

Question 40

A 4-m-long ladder (mass $= 56 \mathrm {~kg}$ ) leans against a frictionless wall. The base of the ladder makes an angle $\theta$ with the rough floor $\left( \mu _ { s } \right)$ . If $\mu _ { s } = 0.5$ , the minimum value of $\theta$ , such that the ladder will not slip, is

A) 45º.
B) 56º.
C) 61º.
D) 72º.

Question 41

A ladder of length $l$ and mass $= m$ leans against a frictionless wall. The base of the ladder makes an angle $\theta$ with the rough floor, $\mu _ { s }$ . Providing that the ladder is in static equilibrium, the relation between $\theta$ and $\mu _ { s }$ is

A) $2 \mu \tan \theta = 1$
B) $2 \mu = m g \cos \theta$
C) $\mu = 2 \theta$
D) $\tan \theta = \mu$

Question 42

A 4-m-long ladder (mass = 56 kg) leans against a frictionless wall. The base of the ladder makes an angle of 55º with the rough floor, having $\mu _ { s } = 0.5$ . The frictional force (which is not the maximum frictional force) exerted by the floor that acts on the ladder is

A) 270 N.
B) 240 N.
C) 210 N.
D) 190 N.

Question 43

A 4-m-long ladder (mass = 56 kg) leans against a frictionless wall. The base of the ladder makes an angle of 55(which is not the maximum frictional force) with the rough floor, having $\mu _ { s } = 0.5$ . The horizontal force exerted by the frictionless wall that acts on the ladder is

A) 270 N.
B) 0 N.
C) 210 N.
D) 190 N.

Question 44

A 4-m-long ladder (mass = 56 kg) leans against a frictionless wall. The base of the ladder makes an angle of 55(which is not the maximum frictional force) with the rough floor, having $\mu _ { s } = 0.5$ . The upward vertical force exerted by the floor that acts on the ladder is

A) 270 N.
B) 550 N.
C) 230 N.
D) 190 N.

Question 45

A tightrope walker weighing 950 N stands in the middle of a tightrope that is 10 m long. The tension in the tightrope so that the walker has deflected the tightrope downward by only 1 cm is

A) 240,000 N.
B) 18,000 N.
C) 9500 N.
D) 51,000 N.

Question 46

A nonlinear spring generates a force $f = \beta x ^ { 2 }$ , where $\beta$ is a constant and $x$ is the distance that the spring is compressed or stretched. The spring hangs from the ceiling, and a mass $m$ is attached to the other end of the spring. The distance that the spring is stretched is

A) $\beta / ( m g )$
B) $\sqrt { m g / \beta }$
C) $\beta \sqrt { m g }$
D) $\sqrt { \beta / m / g }$

Question 47

Five cubes (each edge of a cube is 5 cm) are stacked vertically on a table. If each cube weighs 5 N, the pressure exerted on the table is

A) 1 Pa.
B) 20 Pa.
C) 10 kPa.
D) 100 Pa.

Question 48

Five cubes (each edge of a cube is 5 cm) are stacked vertically on a table. If each cube weighs 5 N, the net force exerted on the table is

A) 5 N.
B) 25 N.
C) 10 N.
D) 50 N.

Question 49

Five cubes (each edge of a cube is 5 cm) are each laid on the top of a table (cubes are not stacked). If each cube weighs 5 N, the pressure exerted on the table is

A) 1 Pa.
B) 2000 Pa.
C) 10 kPa.
D) 200 Pa.

Question 50

Five cubes (each edge of a cube is 5 cm) are each laid on the top of a table (the cubes are not stacked). If each cube weighs 5 N, the net force exerted on the table is

A) 5 N.
B) 25 N.
C) 10 N.
D) 50 N.