Q: A car has a track width $$t$$ and a center-of-gravity height $$h. $$The critical angle $$\theta_c at $$which it will tip is given by:

$$\theta_c = \tan$$^{-1}$$ \left( \frac{t}{2h} \right)$$

Q: The stress in a rod of cross-sectional area $$A$$ and length $$L$$ stretched by a force $$F is$$:

$$\text{Stress} = \frac{F}{A}$$

Question 1

A cyclist balances on the back tire of a bicycle, as shown in the image. Which of the following statements best describes the conditions for static equilibrium in this scenario?

Accepted Answer

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

Question 2

A wrench of length $$r is $$used to apply a force $$\vec{F} at an $$angle $$\phi to $$the wrench, as shown. What is the magnitude of the torque $$	au$$ about the pivot?

Accepted Answer

$$	au = r F \sin \phi$$

Question 3

Which of the following is a necessary condition for a particle to be in static equilibrium?

Accepted Answer

The net force on the particle is zero.

Question 4

An extended object is in static equilibrium if:

Accepted Answer

The net force is zero and the net torque is zero.

Question 5

A strongman lifts a beam with a 910 kg bucket hanging 0.85 m from the pivot. He lifts at the end, 3.6 m from the pivot. What force must he apply? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2100\ \mathrm{N}$$

Question 6

Which of the following will increase the stability of an object?

Accepted Answer

Lowering the center of gravity and widening the base of support.

Question 7

A car has a track width $$t$$ and a center-of-gravity height $$h. $$The critical angle $$	heta_c at $$which it will tip is given by:

Accepted Answer

$$	heta_c = 	an$$^{-1}$$ \left( \frac{t}{2h} ight)$$

Question 8

A seesaw of length $$L = 4.00\ \mathrm{m} is $$pivoted in the middle. A woman of mass $$m = 55.0\ \mathrm{kg}$$ sits at one end. Where should a man of mass $$M = 75.0\ \mathrm{kg}$$ sit to balance the seesaw?

Accepted Answer

$$x = 1.47\ \mathrm{m}$$\quad$$ (from the pivot on the opposite side)

Question 9

A uniform ladder 10.0 m long and weighing 50.0 N rests against a frictionless wall at a $$50.0^\circ$$ angle. If it is on the verge of slipping, what is the coefficient of static friction $$\mu_s$$ between the ladder and the ground?

Accepted Answer

$$\mu_s = 0.42$$

Question 10

Which of the following best describes Hooke’s Law for a spring?

Accepted Answer

$$F_s = -k x$$

Question 11

A spring is stretched by 0.10 m by a force of 13 N. What is the spring constant $$k$$?

Accepted Answer

$$k = 130\ \mathrm{N/m}$$

Question 12

For a mass-spring system in simple harmonic motion, the period $$T is $$given by:

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 13

A 0.350-kg object attached to a spring with $$k = 1.30 	imes 10^2$\ \mathrm{N/m} is $$released from $$x = 0.100\ \mathrm{m}. $$What is its acceleration at $$x = 0.100\ \mathrm{m}$$?

Accepted Answer

$$a = -37\ \mathrm{m/s^2$}$$

Question 14

A steel cable of length $$L_0 = 6.0$$\ \mathrm{m}$$ and diameter 2.5$$\ \mathrm{mm}$$ supports a 120 kg mass. Young’s modulus for steel is Y = 2.0$$ 	imes $$10^{11}$$\ \mathrm{$$N/m^2$$}$$. By how much does the cable stretch?

Accepted Answer

$$\Delta L = 7.2\ \mathrm{mm}$$

Question 15

The stress in a rod of cross-sectional area $$A$$ and length $$L$$ stretched by a force $$F is$$:

Accepted Answer

$$	ext{Stress} = \frac{F}{A}$$

Question 16

A rod of length $$L$$ and area $$A is $$stretched by a force $$F$$, resulting in a change in length $$\Delta L. $$Young’s modulus $$Y is $$given by:

Accepted Answer

$$Y = \frac{F L}{A \Delta L}$$

Question 17

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

Accepted Answer

It will not return to its original length when the force is removed.

Question 18

The ultimate tensile strength of a material is defined as:

Accepted Answer

The largest stress the material can sustain before breaking.

Question 19

The shear modulus $$S of a $$material is defined by the equation:

Accepted Answer

$$\frac{F}{A} = S \frac{\Delta x}{h}$$

Question 20

The bulk modulus $$B$$ relates a change in pressure $$\Delta P to a $$change in volume $$\Delta V by$$:

Accepted Answer

$$\Delta P = -B \frac{\Delta V}{V}$$

Chapter 8: Equilibrium and Elasticity – Structured Study Notes

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