A custod an pulls a vacuum 13.5 m
with a 33.9 N force at a
angle aganst a 141 N friction
force Find the work done by the
custodian
(Unt = J)

Question

A custod an pulls a vacuum 13.5 m with a 33.9 N force at a $$ 550^{\circ} $$ angle aganst a 141 N friction force Find the work done by the custodian (Unt = J)

UpStudy AI · Accepted Answer

To determine the work done by the custodian while pulling the vacuum cleaner, we'll analyze the given information step-by-step.

### **Given:**
- **Applied Force (F):** 33.9 N
- **Angle of Applied Force (θ):** $$ 55.0^{\circ} $$
- **Friction Force (f):** 141 N
- **Distance (d):** 13.5 m

### **Understanding the Problem:**
The custodian applies a force at an angle to the direction of motion. The work done by the custodian is given by the component of the applied force in the direction of motion multiplied by the distance moved.

### **Formula for Work Done:**
$$ W = F \cdot \cos(\theta) \cdot d $$

Where:
- $$ W $$ is the work done.
- $$ F $$ is the magnitude of the applied force.
- $$ \theta $$ is the angle between the force and the direction of motion.
- $$ d $$ is the distance over which the force is applied.

### **Calculations:**
1. **Calculate the Horizontal Component of the Applied Force:**
   $$ F_{\text{horizontal}} = F \cdot \cos(\theta) $$
   $$ F_{\text{horizontal}} = 33.9 \, \text{N} \cdot \cos(55.0^{\circ}) $$
   $$ \cos(55.0^{\circ}) \approx 0.5736 $$
   $$ F_{\text{horizontal}} \approx 33.9 \times 0.5736 \approx 19.43 \, \text{N} $$

2. **Calculate the Work Done by the Custodian:**
   $$ W = F_{\text{horizontal}} \cdot d $$
   $$ W = 19.43 \, \text{N} \cdot 13.5 \, \text{m} $$
   $$ W \approx 262.3 \, \text{J} $$

### **Conclusion:**
The work done by the custodian in pulling the vacuum cleaner is approximately **262 joules**.

**Answer:**  
The custodian does approximately 262 J of work.
The custodian does approximately 262 joules of work.

A custod an pulls a vacuum 13.5 m
with a 33.9 N force at a
angle aganst a 141 N friction
force Find the work done by the
custodian
(Unt = J)

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A custod an pulls a vacuum 13.5 m with a 33.9 N force at a angle aganst a 141 N friction force Find the work done by the custodian (Unt = J)

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Responder

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preguntas relacionadas

Latest Physics Questions

A custod an pulls a vacuum 13.5 m
with a 33.9 N force at a
angle aganst a 141 N friction
force Find the work done by the
custodian
(Unt = J)