Problem 5: A box m = 71 kg is being pulled by a constant force F = 150 N at an angle of 0 = 29 degrees. The initial speed of the box is zero. y F M

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Chapter1: Units, Trigonometry. And Vectors
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**Problem 5:**

A box with mass \( m = 71 \, \text{kg} \) is being pulled by a constant force \( F = 150 \, \text{N} \) at an angle of \( \theta = 29 \, \text{degrees} \). The initial speed of the box is zero.

*Diagram Description:*

The diagram depicts a box labeled \( M \) on a flat surface. A force \( F \) is applied at an angle \( \theta \) to the horizontal axis \( x \).

**Part (a):** 

*Write an expression for the work done by force \( F \) as the block moves a horizontal distance \( d \).*

**Expression:**

\[ W = \text{_______________________________________________} \]

Select from the variables below to write your expression. Note that all variables may not be required.

\[ \cos(\alpha), \cos(\varphi), \cos(\theta), \sin(\alpha), \sin(\varphi), \sin(\theta), \alpha, \beta, \theta, d, F, g, h, j, m, P, t, \tan(\alpha), \tan(\varphi), \tan(\theta) \]

**Part (b):**

*How much work, in joules, was done in moving the block 5.6 m?*

**Numeric:**

A numeric value is expected and not an expression.

\[ W = \text{_______________________________________________} \]

**Part (c):**

*What is the speed of the box at \( d = 5.6 \, \text{m} \) if the surface is frictionless?*

**Numeric:**

A numeric value is expected and not an expression.

\[ v_d = \text{______________________________________________} \]
Transcribed Image Text:**Problem 5:** A box with mass \( m = 71 \, \text{kg} \) is being pulled by a constant force \( F = 150 \, \text{N} \) at an angle of \( \theta = 29 \, \text{degrees} \). The initial speed of the box is zero. *Diagram Description:* The diagram depicts a box labeled \( M \) on a flat surface. A force \( F \) is applied at an angle \( \theta \) to the horizontal axis \( x \). **Part (a):** *Write an expression for the work done by force \( F \) as the block moves a horizontal distance \( d \).* **Expression:** \[ W = \text{_______________________________________________} \] Select from the variables below to write your expression. Note that all variables may not be required. \[ \cos(\alpha), \cos(\varphi), \cos(\theta), \sin(\alpha), \sin(\varphi), \sin(\theta), \alpha, \beta, \theta, d, F, g, h, j, m, P, t, \tan(\alpha), \tan(\varphi), \tan(\theta) \] **Part (b):** *How much work, in joules, was done in moving the block 5.6 m?* **Numeric:** A numeric value is expected and not an expression. \[ W = \text{_______________________________________________} \] **Part (c):** *What is the speed of the box at \( d = 5.6 \, \text{m} \) if the surface is frictionless?* **Numeric:** A numeric value is expected and not an expression. \[ v_d = \text{______________________________________________} \]
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