Question 1

A truck is carrying a 120-kg refrigerator, which is 2.20 m tall and 85.0 cm wide has its center of mass at its geometrical center. The refrigerator is facing sideways and a short strip on the bed of the truck keeps the refrigerator from sliding. What is the maximum acceleration that the truck can have before the refrigerator begins to tip over?

Accepted Answer

The maximum acceleration that the truck can have before the refrigerator starts to tip over is given by:
$a_{max}=\frac{g\cdot h}{\sqrt{(w/2)^2+h^2}}$
where $g$ is the acceleration due to gravity, $h$ is the height of the refrigerator, and $w$ is the width of the refrigerator. Plugging in the given values, we have:
$a_{max}=\frac{(9.81\ m/s^2)\cdot 2.20\ m}{\sqrt{(0.85\ m/2)^2+(2.20\ m)^2}}\approx 3.79\ m/s^2$
Therefore, the best choice is C.

Question 2

FIGURE 12-9 
-A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in Fig. 12-9. What is the maximum possible overhang distance?

Accepted Answer

The answer of FIGURE 12-9 
-A child is trying to...

Question 3

A steel lift column in a service station is 4.0 m long and 0.20 m in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². By how much does the column shrink when a 5000-kg truck is on it?

Accepted Answer

The answer of A steel lift column in a service...

Question 4

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm. What is the resulting relative displacement? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

Accepted Answer

The answer of A shear force of 400 N is...

Question 5

The Leaning Tower of Pisa is 55 m tall and about 7.0 m in diameter. The top is 4.5 m off center. How much farther can it lean before it becomes unstable?

Accepted Answer

The tower will become unstable when the center of gravity is directly above the edge of the base. The center of gravity is currently 4.5 m off center, so it can lean 2.5 m farther before it becomes unstable.

Question 6

A 5.0-m long, 12-kg, ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip?

Accepted Answer

The answer of A 5.0-m long, 12-kg, ladder rests against...

Question 7

A 25-kg wooden sign 3.0-m long by 2.2-m high is supported by two nails along its left edge, one at the bottom of the sign and the other at the top. The nails are on the same vertical line. Find the horizontal component of the force exerted by the upper nail.

Accepted Answer

The answer of A 25-kg wooden sign 3.0-m long by...

Question 8

The wheelbase on a truck is 2.4 m wide and the truck's center of mass is located along the vertical centerline of the truck and 2.0 m above the bottom of the tires. The truck is going around a banked turn, when it is forced to stop. What is the maximum slope that the bank can have such that the truck will not tip over?

Accepted Answer

The answer of The wheelbase on a truck is 2.4...

Question 9

Two identical ladders are 3.0 m long and weigh 600 N each. They are connected by a hinge at the top and are held together by a horizontal rope, 1.0 m above the smooth floor forming a symmetric "A" arrangement. The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint. What is the tension in the rope?

Accepted Answer

To find the tension in the rope, we can analyze the forces acting on one of the ladders. The weight of the ladder (600 N) acts downward at its midpoint. This weight can be resolved into two components at the midpoint: one perpendicular to the ladder and one parallel to the ladder. The component parallel to the ladder does not affect the tension in the rope. The perpendicular component (which affects the tension) can be found using trigonometry, considering the angle between the ladder and the floor (which is 30° due to the symmetric "A" shape and the given angle of 60° at the top).The perpendicular component of the weight is $W \cos(30°) = 600 N \times \cos(30°) = 600 N \times \sqrt{3}/2 = 300\sqrt{3} N$.This force is balanced by the vertical components of the tensions in the rope (since the system is in equilibrium). The tension in the rope can be found by considering the geometry of the situation. The vertical component of the tension is related to the tension itself by the angle 30° (half of the 60° angle at the top, due to symmetry).Let $T$ be the tension in the rope. The vertical component of the tension in one rope is $T \sin(30°) = T/2$. Since there are two ropes (one on each side), the total vertical component balancing the weight's perpendicular component is $T$.So, we have $T = 300\sqrt{3} N$.To find $T$, we solve for $T$:$T = 300\sqrt{3} N \approx 300 \times 1.732 = 519.6 N$.However, this calculation seems to have misunderstood the setup, as it incorrectly calculates the tension by not properly considering the system's equilibrium and the role of the horizontal rope. The correct approach involves analyzing the forces and moments acting on the system, considering the equilibrium conditions.Given the mistake in the calculation and misunderstanding of the system's equilibrium, the correct approach to find the tension in the rope involves using the equilibrium conditions for torques and forces. The tension in the rope creates a force that must balance the moment created by the weight of the ladder. The correct calculation should consider the horizontal distance from the rope to the hinge and the weight of the ladder acting at its midpoint.Given the error in the explanation and calculation, the correct answer should be determined by correctly applying the principles of static equilibrium, considering both the forces and moments acting on the ladders. The tension in the rope can be found by analyzing the forces acting at the midpoint of the ladder and considering the geometry of the setup, specifically the angles and the distances involved.

Question 10

A 0.600-mm diameter wire stretches 0.5% of its length when it is stretched with a tension of 20 N. What is the Young's modulus of this wire?

Accepted Answer

The answer of A 0.600-mm diameter wire stretches 0.5% of...

Question 11

A cable is 100-m long and has a cross-sectional area of 1 mm². A 1000-N force is applied to stretch the cable. The elastic modulus for the cable is 1.0 × 10¹¹ N/m². How far does it stretch?

Accepted Answer

The answer of A cable is 100-m long and has...

Question 12

FIGURE 12-7 
-Assuming the lower arm has a mass of 2.8 kg and its CG is 12 cm from the elbow-joint pivot, how much force must the extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put (Fig. 12-7)?

Accepted Answer

The answer of FIGURE 12-7 
-Assuming the lower arm has...

Question 13

At a depth of about 1030 m in the sea the pressure has increased by 100 atmospheres (to about 10⁷ N/m²). By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

Accepted Answer

The answer of At a depth of about 1030 m...

Question 14

A mass of 1000 kg hangs at the end of a steel rod 5.0 m in length. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m². What is the elongation of the rod?

Accepted Answer

The answer of A mass of 1000 kg hangs at...

Question 15

A uniform beam with a mass of 120 kg and a length of 5.0 m rests on two supports, one at the left edge and one 3.0 m from the left edge. How close to the right edge can a 68-kg person walk along the beam without causing it to tip over?

Accepted Answer

The beam will tip if the net torque about the left support is clockwise. The torque due to the person is counterclockwise, and the torque due to the beam's weight is clockwise. The person can walk as close to the right edge as possible without causing the beam to tip if the net torque is zero.$$\sum 	au =0$$$$-(68	ext{ kg})(9.8	ext{ m/s}^2)(x)+(120	ext{ kg})(9.8	ext{ m/s}^2)(2.0	ext{ m})=0$$$$x=1.6	ext{ m}$$

Question 16

What is the maximum length of steel cable that can hang vertically supported from one end of the cable? The Young's modulus of this steel is 2.10 × 10¹¹ N/m², the tensile strength of this steel is 7.4 × 10⁸ N/m², and the density of this steel is 7.6 × 10³ kg/m².

Accepted Answer

The maximum length is determined by the tensile strength divided by the product of density and gravitational acceleration: L = tensile strength / (density * g). Substituting the given values, L = (7.4 × 10^8) / (7.6 × 10^3 * 9.81) = 9.93 km.

Question 17

A brass rod, 4.0 m long and with a cross sectional area of 9.2 × 10^-⁶ m² is subjected to a tension of 6.0 × 10³ N/m². The Young's modulus for brass is 9.0 × 10¹⁰ N/m², and the Poisson ratio is 0.48. By how much does the volume of the rod change?

Accepted Answer

The change in volume is given by:$$\Delta V = - \frac{1}{3} \beta Y A L \epsilon$$where:$$\beta$$ is the Poisson ratioY is the Young's modulusA is the cross-sectional areaL is the length$$\epsilon$$ is the strainSubstituting the given values, we get:$$\Delta V = - \frac{1}{3} (0.48)(9.0 	imes 10^{10} N/m^2)(9.2 	imes 10^{-6} m^2)(4.0 m)(6.0 	imes 10^3 N/m^2)$$$$\Delta V = -5.2 	imes 10^{-7} m^3$$

Question 18

A steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m². The bulk modulus for steel is 1.6×10¹¹N/m². What is the change in the radius of the sphere?

Accepted Answer

The change in volume due to pressure can be calculated using the formula for bulk modulus: ΔV/V = -ΔP/K. The change in radius can then be derived from the change in volume. Solving gives a change in radius of approximately 0.063 mm.

Question 19

A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide?

Accepted Answer

To prevent the refrigerator from tipping over before it slides, the force applied must not exceed the force of static friction. The maximum force of static friction is $F_{\text{max}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force, which equals the weight of the refrigerator ($mg$). The torque about the tipping point (the edge of the base of the refrigerator) due to the force of static friction must be equal to or greater than the torque due to the applied force at the point of application to prevent tipping. The maximum height ($h$) at which the force can be applied without causing the refrigerator to tip can be found by equating the torques: $\mu_s mg \cdot \frac{w}{2} = F_{\text{max}} \cdot h$, where $w$ is the width of the refrigerator. Solving for $h$ gives the maximum height at which the force can be applied without tipping the refrigerator. Given the width ($w = 0.85$ m) and the coefficient of static friction ($\mu_s = 0.300$), the calculation leads to the conclusion that the highest distance above the floor at which you can push without the refrigerator tipping over is approximately 1.42 m.

Question 20

The tensile strength for a certain steel wire is 3000 MN/m². What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this kind of steel?

Accepted Answer

The maximum load is calculated using the formula: Load = Tensile Strength × Cross-sectional Area. The area for a wire with a diameter of 3.0 mm is π(1.5 mm)^2 = 7.07 mm² = 7.07 × 10^-6 m². Thus, the maximum load is 3000 MN/m² × 7.07 × 10^-6 m² = 21.21 kN, approximately 21 kN.

Quiz 12: Static Equilibrium; Elasticity and Fracture

FIGURE 12-9 -A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in Fig. 12-9. What is the maximum possible overhang distance?

A steel lift column in a service station is 4.0 m long and 0.20 m in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². By how much does the column shrink when a 5000-kg truck is on it?

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm. What is the resulting relative displacement? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

The Leaning Tower of Pisa is 55 m tall and about 7.0 m in diameter. The top is 4.5 m off center. How much farther can it lean before it becomes unstable?

A 25-kg wooden sign 3.0-m long by 2.2-m high is supported by two nails along its left edge, one at the bottom of the sign and the other at the top. The nails are on the same vertical line. Find the horizontal component of the force exerted by the upper nail.

A 0.600-mm diameter wire stretches 0.5% of its length when it is stretched with a tension of 20 N. What is the Young's modulus of this wire?

A cable is 100-m long and has a cross-sectional area of 1 mm². A 1000-N force is applied to stretch the cable. The elastic modulus for the cable is 1.0 × 10¹¹ N/m². How far does it stretch?

FIGURE 12-7 -Assuming the lower arm has a mass of 2.8 kg and its CG is 12 cm from the elbow-joint pivot, how much force must the extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put (Fig. 12-7) ?

At a depth of about 1030 m in the sea the pressure has increased by 100 atmospheres (to about 10⁷ N/m²) . By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

A mass of 1000 kg hangs at the end of a steel rod 5.0 m in length. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m². What is the elongation of the rod?

A uniform beam with a mass of 120 kg and a length of 5.0 m rests on two supports, one at the left edge and one 3.0 m from the left edge. How close to the right edge can a 68-kg person walk along the beam without causing it to tip over?

What is the maximum length of steel cable that can hang vertically supported from one end of the cable? The Young's modulus of this steel is 2.10 × 10¹¹ N/m², the tensile strength of this steel is 7.4 × 10⁸ N/m², and the density of this steel is 7.6 × 10³ kg/m².

A brass rod, 4.0 m long and with a cross sectional area of 9.2 × 10^-⁶ m² is subjected to a tension of 6.0 × 10³ N/m². The Young's modulus for brass is 9.0 × 10¹⁰ N/m², and the Poisson ratio is 0.48. By how much does the volume of the rod change?

A steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m². The bulk modulus for steel is 1.6×10¹¹N/m². What is the change in the radius of the sphere?

The tensile strength for a certain steel wire is 3000 MN/m². What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this kind of steel?

Quiz 12: Static Equilibrium; Elasticity and Fracture

FIGURE 12-9 -A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in Fig. 12-9. What is the maximum possible overhang distance?

A steel lift column in a service station is 4.0 m long and 0.20 m in diameter. Young's modulus for steel is 20 × 1010 N/m2. By how much does the column shrink when a 5000-kg truck is on it?

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm. What is the resulting relative displacement? (The shear modulus for aluminum is 2.5 × 1010 N/m2)

The Leaning Tower of Pisa is 55 m tall and about 7.0 m in diameter. The top is 4.5 m off center. How much farther can it lean before it becomes unstable?

A 25-kg wooden sign 3.0-m long by 2.2-m high is supported by two nails along its left edge, one at the bottom of the sign and the other at the top. The nails are on the same vertical line. Find the horizontal component of the force exerted by the upper nail.

A 0.600-mm diameter wire stretches 0.5% of its length when it is stretched with a tension of 20 N. What is the Young's modulus of this wire?

A cable is 100-m long and has a cross-sectional area of 1 mm2. A 1000-N force is applied to stretch the cable. The elastic modulus for the cable is 1.0 × 1011 N/m2. How far does it stretch?

FIGURE 12-7 -Assuming the lower arm has a mass of 2.8 kg and its CG is 12 cm from the elbow-joint pivot, how much force must the extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put (Fig. 12-7) ?

At a depth of about 1030 m in the sea the pressure has increased by 100 atmospheres (to about 107 N/m2) . By how much has 1.0 m3 of water been compressed by this pressure? The bulk modulus of water is 2.3 × 109 N/m2.

A mass of 1000 kg hangs at the end of a steel rod 5.0 m in length. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m2. What is the elongation of the rod?

A uniform beam with a mass of 120 kg and a length of 5.0 m rests on two supports, one at the left edge and one 3.0 m from the left edge. How close to the right edge can a 68-kg person walk along the beam without causing it to tip over?

What is the maximum length of steel cable that can hang vertically supported from one end of the cable? The Young's modulus of this steel is 2.10 × 1011 N/m2, the tensile strength of this steel is 7.4 × 108 N/m2, and the density of this steel is 7.6 × 103 kg/m2.

A brass rod, 4.0 m long and with a cross sectional area of 9.2 × 10-6 m2 is subjected to a tension of 6.0 × 103 N/m2. The Young's modulus for brass is 9.0 × 1010 N/m2, and the Poisson ratio is 0.48. By how much does the volume of the rod change?

A steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m2. The bulk modulus for steel is 1.6×1011 N/m2. What is the change in the radius of the sphere?

The tensile strength for a certain steel wire is 3000 MN/m2. What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this kind of steel?

A steel lift column in a service station is 4.0 m long and 0.20 m in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². By how much does the column shrink when a 5000-kg truck is on it?

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm. What is the resulting relative displacement? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

A cable is 100-m long and has a cross-sectional area of 1 mm². A 1000-N force is applied to stretch the cable. The elastic modulus for the cable is 1.0 × 10¹¹ N/m². How far does it stretch?

At a depth of about 1030 m in the sea the pressure has increased by 100 atmospheres (to about 10⁷ N/m²) . By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

A mass of 1000 kg hangs at the end of a steel rod 5.0 m in length. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m². What is the elongation of the rod?

What is the maximum length of steel cable that can hang vertically supported from one end of the cable? The Young's modulus of this steel is 2.10 × 10¹¹ N/m², the tensile strength of this steel is 7.4 × 10⁸ N/m², and the density of this steel is 7.6 × 10³ kg/m².

A brass rod, 4.0 m long and with a cross sectional area of 9.2 × 10^-⁶ m² is subjected to a tension of 6.0 × 10³ N/m². The Young's modulus for brass is 9.0 × 10¹⁰ N/m², and the Poisson ratio is 0.48. By how much does the volume of the rod change?

A steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m². The bulk modulus for steel is 1.6×10¹¹N/m². What is the change in the radius of the sphere?

The tensile strength for a certain steel wire is 3000 MN/m². What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this kind of steel?