Question 1

A force of $30 \mathrm {~N}$ stretches a very light ideal spring $0.73 \mathrm {~m}$ from equilibrium. What is the force constant (spring constant)of the spring?

Accepted Answer

A) 41 N/m 
B) 22 N/m 
C) 34 N/m 
D) 46 N/m 
A) 41 N/m 
B) 22 N/m 
C) 34 N/m 
D) 46 N/m A

Question 2

A 3.0-kg brick rests on a perfectly smooth ramp inclined at 34° above the horizontal. The brick is kept from sliding down the plane by an ideal spring that is aligned with the surface and attached to a wall above the brick. The spring has a spring constant (force constant)of 120 N/m. By how much does the spring stretch with the brick attached?

Accepted Answer

A) 360 cm 
B) 240 cm 
C) 14 cm 
D) 24 cm 
E) 36 cm 
A) 360 cm 
B) 240 cm 
C) 14 cm 
D) 24 cm 
E) 36 cm C

Question 3

A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it.
(a)What is Young's modulus for the material from this wire is made?
(b)What is the effective spring constant for the stretching wire?

Accepted Answer

(a)1.0 × 10¹¹ Pa (b)2.2 × 10⁴ N/m

Question 4

A 320-g ball and a 400-g ball are attached to the two ends of a string that goes over a pulley with a radius of 8.7 cm. Because of friction in its axle, the pulley does not begin to rotate. What is the magnitude of the frictional torque at the axle of the pulley if the system remains at rest when the balls are released?

Accepted Answer

A) 0.068 N ∙ m 
B) 0.61 N ∙ m 
C) 0.079 N ∙ m 
D) 0.063 N ∙ m 
E) 0.00070 N ∙ m 
A) 0.068 N ∙ m 
B) 0.61 N ∙ m 
C) 0.079 N ∙ m 
D) 0.063 N ∙ m 
E) 0.00070 N ∙ m

Question 5

Two wires are made out of the same metal, but one wire is twice as long as the other wire. Which wire will have the greatest elastic modulus?

Accepted Answer

A) the shorter wire 
B) the longer wire 
C) It will be the same for both wires. 
A) the shorter wire 
B) the longer wire 
C) It will be the same for both wires.

Question 6

A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 2.0 × 1011 N/m2. By what distance does the column shrink when a 5000-kg truck is supported by it?

Accepted Answer

A) 8.0 × 10-7 m 
B) 3.2 × 10-6 m 
C) 7.8 × 10-6 m 
D) 3.1 × 10-5 m 
A) 8.0 × 10-7 m 
B) 3.2 × 10-6 m 
C) 7.8 × 10-6 m 
D) 3.1 × 10-5 m

Question 7

A light board that is 10 m long is supported by two sawhorses, one at one end of the board and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m from the end and 2.0 m from the center. What magnitude forces do the sawhorses exert on the board?

Accepted Answer

16 N at th

Question 8

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest distance?

Accepted Answer

A) the 1.00-m wire 
B) the 2.00-m wire 
C) the 3.00-m wire 
D) They will all stretch by the same distance. 
A) the 1.00-m wire 
B) the 2.00-m wire 
C) the 3.00-m wire 
D) They will all stretch by the same distance.

Question 9

A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is 2.0 × 1011 Pa. The mass of the load is closest to

Accepted Answer

A) 12 kg. 
B) 16 kg. 
C) 20 kg. 
D) 24 kg. 
E) 28 kg. 
A) 12 kg. 
B) 16 kg. 
C) 20 kg. 
D) 24 kg. 
E) 28 kg.

Question 10

If the sum of the external torques on an object is zero, then the sum of the external forces on it must also be zero.

Accepted Answer

A) True 
 B)False

Question 11

A 50-kg load is suspended from a steel wire of diameter 1.0 mm and length 11.2 m. By what distance will the wire stretch? Young's modulus for steel is 2.0 × 1011 Pa.

Accepted Answer

A) 1.5 cm 
B) 2.5 cm 
C) 3.5 cm 
D) 4.5 cm 
A) 1.5 cm 
B) 2.5 cm 
C) 3.5 cm 
D) 4.5 cm

Question 12

A 5.00-m-long uniform ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.20 m away from the wall. The coefficient of static friction between the ladder and the floor is 0.200. How far up the ladder, measured along the ladder, can a 600-N person climb before the ladder begins to slip?

Accepted Answer

A) 1.50 m 
B) 1.26 m 
C) 1.05 m 
D) 3.95 m 
E) 4.56 m 
A) 1.50 m 
B) 1.26 m 
C) 1.05 m 
D) 3.95 m 
E) 4.56 m

Question 13

A stepladder consists of two halves that are hinged at the top and connected by a tie rod which keeps the two halves from spreading apart. In this particular instance, the two halves are 2.5 m long, the tie rod is connected to the center of each half and is 70 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. The ladder is light enough that we can neglect its weight, and it rests on an extremely smooth floor. What is the tension in the tie rod? (Note: To solve this problem, it is helpful to imagine cutting the ladder in half vertically and consider the forces and torques acting on each half of the ladder.)

Accepted Answer

A) 140 N 
B) 240 N 
C) 280 N 
D) 360 N 
E) 560 N 
A) 140 N 
B) 240 N 
C) 280 N 
D) 360 N 
E) 560 N

Question 14

When a 125-kg piece of equipment is hung from a steel wire of length 75 cm, it stretches the wire by 4.00 mm. If instead the wire had a length of 150 cm, but all else were the same, by what distance would the same equipment stretch the wire?

Accepted Answer

A) 16.0 mm 
B) 8.00 mm 
C) 4.00 mm 
D) 2.00 mm 
E) 1.00 mm 
A) 16.0 mm 
B) 8.00 mm 
C) 4.00 mm 
D) 2.00 mm 
E) 1.00 mm

Question 15

Which of the following are SI units of Young's modulus? (There could be more than one correct choice.)

Accepted Answer

A) N/m ∙ s2 
B) kg/m2 
C) kg ∙ m/s2 
D) kg/m ∙ s2 
E) kg ∙ m2/s2 
A) N/m ∙ s2 
B) kg/m2 
C) kg ∙ m/s2 
D) kg/m ∙ s2 
E) kg ∙ m2/s2

Question 16

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s2 by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is 2.0 × 1011 N/m2. What is the change in length of the cable caused by lifting the car?

Accepted Answer

A) 8.4 mm 
B) 8.4 cm 
C) 4.9 mm 
D) 4.9 cm 
E) 4.9 m 
A) 8.4 mm 
B) 8.4 cm 
C) 4.9 mm 
D) 4.9 cm 
E) 4.9 m

Question 17

An aluminum wire and a steel wire, each of length 2.0 m, are hung from the ceiling. A 5.0-kg mass is suspended from the lower end of each wire. The aluminum wire has a diameter of 2.2 mm. What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire, so that the two wires maintain equal lengths after the masses are attached? Young's modulus for aluminum is 0.70 × 1011 Pa and for steel it is 2.0 × 1011 Pa.

Accepted Answer

Question 18

A uniform rod weighs 40 N and is 1.0 m long. It is hinged to a wall at the left end, and held in a horizontal position at the right end by a vertical string of negligible weight, as shown in the figure. What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.

Accepted Answer

A) 40 N ∙ m 
B) 10 N ∙ m 
C) 5.0 N ∙ m 
D) 20 N ∙ m 
E) 30 N ∙ m 
A) 40 N ∙ m 
B) 10 N ∙ m 
C) 5.0 N ∙ m 
D) 20 N ∙ m 
E) 30 N ∙ m

Question 19

In the figure, a uniform ladder of weight 200 N and length 10 m leans against a perfectly smooth wall. A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of static friction between the ladder and the floor is 0.50. What is the maximum value of x for which the ladder will not slip?

Accepted Answer

A) 3.9 m 
B) 5.0 m 
C) 6.0 m 
D) 6.3 m 
E) 8.4 m 
A) 3.9 m 
B) 5.0 m 
C) 6.0 m 
D) 6.3 m 
E) 8.4 m

Question 20

A brass wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. By what distance did this fixture stretch the wire? Young's modulus for brass is 10 × 1010 N/m2.

Accepted Answer

A) 0.11 mm 
B) 0.22 mm 
C) 0.33 mm 
D) 0.62 mm 
A) 0.11 mm 
B) 0.22 mm 
C) 0.33 mm 
D) 0.62 mm

Exam 8: Equilibrium Ad Elasticity

A force of 30 N30 \mathrm {~N}30 N stretches a very light ideal spring 0.73 m0.73 \mathrm {~m}0.73 m from equilibrium. What is the force constant (spring constant)of the spring?

A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it. (a)What is Young's modulus for the material from this wire is made? (b)What is the effective spring constant for the stretching wire?

Two wires are made out of the same metal, but one wire is twice as long as the other wire. Which wire will have the greatest elastic modulus?

A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 2.0 × 1011 N/m2. By what distance does the column shrink when a 5000-kg truck is supported by it?

A light board that is 10 m long is supported by two sawhorses, one at one end of the board and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m from the end and 2.0 m from the center. What magnitude forces do the sawhorses exert on the board?

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest distance?

A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is 2.0 × 1011 Pa. The mass of the load is closest to

If the sum of the external torques on an object is zero, then the sum of the external forces on it must also be zero.

A 50-kg load is suspended from a steel wire of diameter 1.0 mm and length 11.2 m. By what distance will the wire stretch? Young's modulus for steel is 2.0 × 1011 Pa.

When a 125-kg piece of equipment is hung from a steel wire of length 75 cm, it stretches the wire by 4.00 mm. If instead the wire had a length of 150 cm, but all else were the same, by what distance would the same equipment stretch the wire?

Which of the following are SI units of Young's modulus? (There could be more than one correct choice.)

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s2 by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is 2.0 × 1011 N/m2. What is the change in length of the cable caused by lifting the car?

A brass wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. By what distance did this fixture stretch the wire? Young's modulus for brass is 10 × 1010 N/m2.

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A force of $30 \mathrm {~N}$ stretches a very light ideal spring $0.73 \mathrm {~m}$ from equilibrium. What is the force constant (spring constant)of the spring?

A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 2.0 × 10¹¹ N/m². By what distance does the column shrink when a 5000-kg truck is supported by it?

A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is 2.0 × 10¹¹ Pa. The mass of the load is closest to

A 50-kg load is suspended from a steel wire of diameter 1.0 mm and length 11.2 m. By what distance will the wire stretch? Young's modulus for steel is 2.0 × 10¹¹ Pa.

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s² by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is 2.0 × 10¹¹ N/m². What is the change in length of the cable caused by lifting the car?

A brass wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. By what distance did this fixture stretch the wire? Young's modulus for brass is 10 × 10¹⁰ N/m².