Question 1

A block of mass $$m = 260\ \mathrm{g} is $$suspended by two strings at angles $$\$$theta_1$$ = 24^\circ$$ and $$\$$theta_2$$ = 37^\circ$$ from the horizontal. What is the magnitude of the gravitational force acting on the block? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.548\ \mathrm{N}$$

Question 2

Given the block in equilibrium suspended by two strings, which equation correctly represents the sum of forces in the vertical ($$y) $$direction?

Accepted Answer

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

Question 3

If the tension in string 1 is $$T_1$$ and in string 2 is $$T_2$$, which equation correctly represents the sum of forces in the horizontal ($$x) $$direction for equilibrium?

Accepted Answer

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

Question 4

A student calculates the tension in string 1 as $$T_1$$ = \frac{mg \sin \$$theta_2$$}{\sin(\$$theta_1$$ + \$$theta_2$$)}$$. What is the value of T_1$ for m = 0.26$$\ \mathrm{kg}$$, $$\$$theta_1 = 24$$^\circ$$, $$\$$theta_2 = 37$$^\circ$$, and g = 9.8$$\ \mathrm{$$m/s^2$$}$$?

Accepted Answer

$$2.55\ \mathrm{N}$$

Question 5

Which of the following best describes the condition for equilibrium in the system shown?

Accepted Answer

The vector sum of all forces acting on the block is zero.

Question 6

If the angle $$\$$theta_1$$ is increased while keeping $$\$$theta_2$$ constant, what happens to the tension $$T_1 in $$string 1?

Accepted Answer

It decreases.

Question 7

Which equation would you use to solve for $$T_2 in $$terms of $$mg$$, $$\$$theta_1$$, and $$\$$theta_2$$?

Accepted Answer

$$T_2$$ = \frac{mg \sin \$$theta_1$$}{\sin(\$$theta_1$$ + \$$theta_2$$)}$$

Question 8

A block is suspended by two strings at angles $$\$$theta_1$$ and $$\$$theta_2. If $$the mass of the block is doubled, what happens to the tensions $$T_1$$ and $$T_2$$?

Accepted Answer

Both $$T_1$$ and $$T_2$$ double.

Question 9

In the free-body diagram for the suspended block, which direction does the gravitational force act?

Accepted Answer

Vertically downward

Question 10

If the sum of the $$x-$$components of the tensions is not zero, what will happen to the block?

Accepted Answer

It will accelerate horizontally.

Question 11

A block is suspended by two strings. If one string is cut, what will be the immediate effect on the block?

Accepted Answer

It will accelerate downward.

Question 12

Which of the following is a correct statement about the forces acting on the block in equilibrium?

Accepted Answer

The net force on the block is zero.

Question 13

If the angles $$\$$theta_1$$ and $$\$$theta_2$$ are both increased, what happens to the vertical components of the tensions?

Accepted Answer

They decrease.

Question 14

Which of the following best describes the role of the tension forces in the strings?

Accepted Answer

They balance both the weight of the block and each other’s horizontal components.

Question 15

If the mass of the block is $$0.26\ \mathrm{kg}$$ and the acceleration due to gravity is $$9.8\ \mathrm{m/s^2$}$$, what is the weight of the block in Newtons?

Accepted Answer

$$2.548\ \mathrm{N}$$

Question 16

In the context of the suspended block, what does the equation $$\sum F = ma$$ simplify to for equilibrium?

Accepted Answer

$$\sum F = 0$$

Question 17

If the block is in equilibrium and the tensions are $$T_1$$ and $$T_2$$, which of the following must be true?

Accepted Answer

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

Statics: Equilibrium of Forces in Two Dimensions

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