QuestionApril 25, 2025

A block is pulled by two horizontal forces. The first force is 115 N at an angle of 75.0^circ and the second is 213 N at an angle of 295^circ What is the y-component of the total force acting on the block? overrightarrow (F_(y))=[?]N

A block is pulled by two horizontal forces. The first force is 115 N at an angle of 75.0^circ and the second is 213 N at an angle of 295^circ What is the y-component of the total force acting on the block? overrightarrow (F_(y))=[?]N
A block is pulled by two horizontal forces.
The first force is 115 N at an angle of 75.0^circ 
and the second is 213 N at an angle of 295^circ 
What is the y-component of the
total force acting on the block?
overrightarrow (F_(y))=[?]N

Solution
4.3(200 votes)

Answer

F_y = 111.02\, \text{N} - 55.12\, \text{N} = 55.90\, \text{N} Explanation 1. Calculate the y-component of the first force Use F_{y1} = F_1 \cdot \sin(\theta_1) where F_1 = 115\, \text{N} and \theta_1 = 75.0^{\circ}. Thus, F_{y1} = 115 \cdot \sin(75.0^{\circ}). 2. Calculate the y-component of the second force Use F_{y2} = F_2 \cdot \sin(\theta_2) where F_2 = 213\, \text{N} and \theta_2 = 295^{\circ}. Thus, F_{y2} = 213 \cdot \sin(295^{\circ}). 3. Sum the y-components Total y-component F_y = F_{y1} + F_{y2}.

Explanation

1. Calculate the y-component of the first force<br /> Use $F_{y1} = F_1 \cdot \sin(\theta_1)$ where $F_1 = 115\, \text{N}$ and $\theta_1 = 75.0^{\circ}$. Thus, $F_{y1} = 115 \cdot \sin(75.0^{\circ})$.<br />2. Calculate the y-component of the second force<br /> Use $F_{y2} = F_2 \cdot \sin(\theta_2)$ where $F_2 = 213\, \text{N}$ and $\theta_2 = 295^{\circ}$. Thus, $F_{y2} = 213 \cdot \sin(295^{\circ})$.<br />3. Sum the y-components<br /> Total y-component $F_y = F_{y1} + F_{y2}$.
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