Questions: A child pulls a wagon at a constant velocity along a level sidewalk. The child does this by applying a 22-newton force at 35° to the horizontal, as shown below. What is the magnitude of the force of friction on the wagon? A. 11 N B. 13 N C. 18 N D. 22 N

A child pulls a wagon at a constant velocity along a level sidewalk. The child does this by applying a 22-newton force at 35° to the horizontal, as shown below. What is the magnitude of the force of friction on the wagon? A. 11 N B. 13 N C. 18 N D. 22 N
Transcript text: A child pulls a wagon at a constant velocity along a level sidewalk. The child does this by applying a 22-newton force at 35° to the horizontal, as shown below. What is the magnitude of the force of friction on the wagon? A. 11 N B. 13 N C. 18 N D. 22 N
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Solution

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Solution Steps

Step 1: Understanding the Problem

The child is pulling the wagon at a constant velocity, which implies that the net force acting on the wagon is zero. This means that the horizontal component of the pulling force must be equal to the force of friction opposing the motion.

Step 2: Calculate the Horizontal Component of the Pulling Force

The force applied by the child is 22 N at an angle of 35° to the horizontal. To find the horizontal component of this force, we use the cosine function:

\[ F_{\text{horizontal}} = F \cdot \cos(\theta) = 22 \, \text{N} \cdot \cos(35^\circ) \]

Step 3: Compute the Value

Using a calculator, we find:

\[ F_{\text{horizontal}} = 22 \, \text{N} \cdot 0.8192 \approx 18.0224 \, \text{N} \]

Since the wagon is moving at a constant velocity, the force of friction must be equal to the horizontal component of the pulling force.

Final Answer

The magnitude of the force of friction on the wagon is approximately 18 N. Therefore, the correct answer is:

\[ \boxed{18 \, \text{N}} \]

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