Question 1

A block of mass $$0.26\ \mathrm{kg} is $$suspended by two cables as shown in the diagram. If the acceleration due to gravity is $$g = 9.81\ \mathrm{m/s^2$}$$, what is the weight of the block?

Accepted Answer

$$2.554\ \mathrm{N}$$

Question 2

Given a block in equilibrium suspended by two cables at angles $$\$$theta_1$$ and $$\$$theta_2$$ from the horizontal, which of the following equations correctly represents the sum of forces in the $$x-$$direction?

Accepted Answer

$$T_1$$ \cos \$$theta_1$$ - $$T_2$$ \cos \$$theta_2 = 0$

Question 3

If the block is in static equilibrium, which of the following must be true for the sum of the forces in the $$y-$$direction?

Accepted Answer

$$T_1$$ \sin \$$theta_1$$ + $$T_2$$ \sin \$$theta_2 - mg = 0$

Question 4

A $$0.26\ \mathrm{kg}$$ mass is suspended by two cables making angles $$24^\circ$$ and $$37^\circ$$ with the horizontal. What is the tension $$T_1 in $$the cable at $$24^\circ$$? (Use $$g = 9.81\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.85\ \mathrm{N}$$

Question 5

Which of the following best describes the method used to solve for the tensions in the cables supporting a mass in equilibrium?

Accepted Answer

Resolve the forces into $$x$$ and $$y$$ components and set the sum of each to zero.

Question 6

If the angles of the cables are changed so that both are $$45^\circ$$ from the horizontal, what happens to the tension in each cable compared to the original configuration ($$24^\circ$$ and $$37^\circ$$)?

Accepted Answer

The tension in each cable increases.

Question 7

Given the equilibrium equations for the system, which of the following is the correct system of equations to solve for $$T_1$$ and $$T_2$$?

Accepted Answer

$$\begin{cases} T_1$ \cos \$$theta_1$$ = T_2$ \cos \$$theta_2$$ \ T_1$ \sin \$$theta_1$$ + T_2$ \sin \$$theta_2$$ = mg \end{cases}$$

Question 8

A student incorrectly calculates the tension in one cable by using $$T_1 = mg$$ / \sin \$$theta_1. $$What is the error in this approach?

Accepted Answer

It ignores the contribution of the second cable to the equilibrium.

Question 9

If the mass is increased while keeping the angles the same, what happens to the tensions in the cables?

Accepted Answer

Both tensions increase proportionally.

Question 10

In a real-world scenario, why is it important to consider the angles at which cables are attached when suspending a load?

Accepted Answer

Because the tension in the cables increases as the angle with the horizontal decreases, potentially exceeding the cable's strength.

Question 11

A $$0.26\ \mathrm{kg}$$ mass is suspended by two cables at $$24^\circ$$ and $$37^\circ$$ from the horizontal. If the tension in the second cable is $$T_2$$, which equation would you use to solve for $$T_2$$ after finding $$T_1$$?

Accepted Answer

$$T_2$$ = $$T_1$$ \frac{\cos \$$theta_1$$}{\cos \$$theta_2$$}$$

Question 12

If the sum of the forces in the $$x-$$direction is not zero, what does this imply about the system?

Accepted Answer

The system is not in equilibrium and will accelerate horizontally.

Question 13

Which of the following best explains why the sum of the forces in both $$x$$ and $$y$$ directions must be zero for a suspended mass in equilibrium?

Accepted Answer

Because equilibrium requires no net force in any direction.

Question 14

A $$0.26\ \mathrm{kg}$$ mass is suspended by two cables at $$24^\circ$$ and $$37^\circ$$ from the horizontal. If the tension in the first cable is $$2.85\ \mathrm{N}$$, what is the vertical component of this tension?

Accepted Answer

$$2.85 \sin 24^\circ$$

Question 15

If the cables are not massless, how would this affect the calculation of tensions?

Accepted Answer

The weight of the cables would add to the total force each cable must support, increasing the calculated tensions.

Statics: Equilibrium of Forces in Two Dimensions

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