Q: A tendon in the human body is stretched by a force of 1000 N. If its cross-sectional area is $$A = 0.001\ \text{m}^2$$, length $$L = 0.1\ \text{m}$$, and Young’s modulus $$Y = 1.5 \times 10^8$\ \text{N/m}^2$$, what is the change in length $$\Delta L$$?

$$\Delta L = 0.00067\ \text{m}$$

Question 1

Which of the following conditions must be satisfied for an extended object to be in static equilibrium?

Accepted Answer

The net force and the net torque must both be zero.

Question 2

A 910 kg bucket is suspended 0.85 m from a pivot, and a person lifts the beam at its end, 3.6 m from the pivot. If the bucket's weight is $$F_b = 8900\ 	ext{N}$$, what force must the person apply to keep the beam in equilibrium?

Accepted Answer

$$F_m = 2100\ 	ext{N}$$

Question 3

For a ladder leaning against a wall at $$60^\circ$$ with respect to the floor, what is the minimum coefficient of static friction $$\mu_s$$ required to prevent slipping, assuming friction at the wall is negligible?

Accepted Answer

$$\mu_s = 0.29$$

Question 4

A 5.0-m ladder of mass $$12.0\ 	ext{kg}$$ leans against a frictionless wall, touching the wall 4.0 m above the floor. What is the horizontal force exerted by the floor?

Accepted Answer

$$F_{Cx} = 44.1\ 	ext{N}$$

Question 5

Which scenario describes an object in unstable equilibrium?

Accepted Answer

The forces tend to move the object away from its equilibrium point.

Question 6

A car will tip over when its center of gravity moves outside its base of support. The critical angle $$	heta_c is $$given by $$	an	heta_c = \frac{t}{2h}$$, where $$t is $$track width and $$h is $$height of the center of gravity. If $$t = 1.5\ 	ext{m}$$ and $$h = 0.75\ 	ext{m}$$, what is $$	heta_c$$?

Accepted Answer

$$	heta_c = 60^\circ$$

Question 7

A 2-m board weighing 50 N extends over a table with 40% of its length off the edge. How far can a 25-N cat walk beyond the table edge before the board tilts?

Accepted Answer

0.6 m

Question 8

Which of the following increases the stability of an object?

Accepted Answer

A lower center of gravity and a wider base

Question 9

According to Hooke’s law, what is the force exerted by a spring with spring constant $$k = 250\ 	ext{N/m}$$ when stretched by $$x = 0.02\ 	ext{m}$$?

Accepted Answer

$$F = 5\ 	ext{N}$$

Question 10

A spring stretches from 20 cm to 22 cm when pulled with a force of 100 N. What is the spring constant $$k$$?

Accepted Answer

$$k = 500\ 	ext{N/m}$$

Question 11

A steel cable of length $$L = 6.0\ 	ext{m}$$ and diameter $$d = 2.5\ 	ext{mm}$$ supports a 120 kg ball. Young’s modulus for steel is $$Y = 2.0 	imes 10$$^{11}$$\ 	ext{N/m}^2. $$How much does the cable stretch?

Accepted Answer

7.2 mm

Question 12

Which material has the highest Young’s modulus among the following?

Accepted Answer

Steel

Question 13

If a rod is stretched beyond its elastic limit, what happens?

Accepted Answer

It permanently deforms and may eventually break.

Question 14

A tendon in the human body is stretched by a force of 1000 N. If its cross-sectional area is $$A = 0.001\ 	ext{m}^2$$, length $$L = 0.1\ 	ext{m}$$, and Young’s modulus $$Y = 1.5 	imes 10^8$\ 	ext{N/m}^2$$, what is the change in length $$\Delta L$$?

Accepted Answer

$$\Delta L = 0.00067\ 	ext{m}$$

Question 15

Which statement about mechanical advantage is correct?

Accepted Answer

Mechanical advantage allows a small force applied far from the pivot to produce a large force.

Question 16

A 61 kg woman stands on tiptoe, and the upward force from the floor acts 0.15 m from the ankle pivot. The Achilles tendon acts 0.05 m from the pivot. If the upward force from the floor is 600 N, what is the tension in the tendon?

Accepted Answer

1800 N

Question 17

Which of the following best describes the relationship between stress and strain in a material obeying Hooke’s law?

Accepted Answer

Stress is proportional to strain.

Question 18

A spring with $$k = 125\ 	ext{N/m}$$ pulls a 25 N block horizontally across a table. If the coefficient of friction is $$\mu = 0.2$$, by how much does the spring stretch?

Accepted Answer

$$0.04\ 	ext{m}$$

Question 19

Which biological material has the highest tensile strength?

Accepted Answer

Spider silk

Chapter 8: Equilibrium and Elasticity – Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드