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

$$\sum F_x = 0$$, $$\sum F_y = 0$$, and $$\sum \tau = 0$$

Question 1

A uniform beam of mass $$m is $$supported horizontally by two sawhorses, as shown in the image. If the beam is 4 m long and the sawhorses are placed 1 m from each end, what is the normal force exerted by the left sawhorse?

Accepted Answer

$$F_1$$ = \frac{3}{4}mg$$

Question 2

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

Accepted Answer

$$\sum F_x = 0$$, $$\sum F_y = 0$$, and $$\sum 	au = 0$$

Question 3

A 2 kg mass is attached to a spring with a spring constant $$k = 100 N/m. If $$the spring is stretched by 0.1 m, what is the restoring force according to Hooke's Law?

Accepted Answer

$$F = -10 N$$

Question 4

Given the equation for the center of gravity $$x_{cg} = \frac{x_1$ m_1$ + x_2$ m_2$}{m_1$ + m_2$}$$, what happens to $$x_{cg} if$$ $$m_2 is $$doubled while $$x_1$$, $$x_2$$, and $$m_1$$ remain constant?

Accepted Answer

$$x_{cg}$$ shifts closer to $$x_2$$

Question 5

A ladder of length $$L = 3 m $$rests against a wall at an angle of $$60^\circ$$ with the floor. What is the minimum coefficient of static friction $$\mu_s$$ required to prevent slipping?

Accepted Answer

$$\mu_s = \frac{1}{\sqrt{3}}$$

Question 6

Which of the following objects is in static equilibrium based on the image with four boxes and arrows?

Accepted Answer

Box C

Question 7

A beam with a pivot on its left end is suspended from a rope. In which direction is the force of the pivot on the beam?

Accepted Answer

Direction A (right)

Question 8

A 1.0 kg weight stretches a spring by 5.0 cm. How much will the spring stretch if a 3.0 kg weight is used instead?

Accepted Answer

15.0 cm

Question 9

Which equation best describes the relationship between tensile stress $$s$$, Young's modulus $$Y$$, and strain $$e$$?

Accepted Answer

$$s = Y e$$

Question 10

A rod of length $$L_0$$ and cross-sectional area $$A is $$subjected to a force $$F. If $$the rod is made of a material with Young's modulus $$Y$$, what is the elongation $$\Delta L$$?

Accepted Answer

$$\Delta L = \frac{F L_0$}{A Y}$$

Question 11

Which regime is characterized by a material returning to its original shape after the force is removed?

Accepted Answer

Elastic regime

Question 12

If a spring is compressed by $$\Delta x$$, what is the direction of the restoring force?

Accepted Answer

Opposite to $$\Delta x$$

Question 13

A material is stretched beyond its elastic limit. What happens?

Accepted Answer

It undergoes permanent deformation

Question 14

Which of the following best describes the units of Young's modulus?

Accepted Answer

N/m$$^2 (Pa)$$

Question 15

A spring obeys Hooke's Law. If the spring constant is $$k$$ and the displacement is $$x$$, what is the potential energy stored in the spring?

Accepted Answer

$$PE = \frac{1}{2} k x^2$

Question 16

A bone experiences a compressive force. Which property determines how much it deforms?

Accepted Answer

Young's modulus

Question 17

If a rod is subjected to a shear force, which modulus describes its resistance to deformation?

Accepted Answer

Shear modulus

Question 18

Which of the following is NOT a type of stress that can act on a solid?

Accepted Answer

Rotational stress

Question 19

A blood vessel behaves elastically under normal conditions. What happens if the stress exceeds the elastic limit?

Accepted Answer

The vessel is permanently deformed

Equilibrium and Elasticity: Study Notes

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