Question

a girl tries to pull her large 9.33 kg wooden sled home along flat snowy ground. she manages to just get it moving by pulling it with a horizontal force of 46.8 n. what is the coefficient of static friction between the snow and the sled?

0.512
0.566
0.621
0.652

Explanation:

Identify the given physical parameters

We are given:

• Mass of the wooden sled, \(m = 9.33\text{ kg}\)
• Applied horizontal force to just start motion, \(F_{\text{pull}} = 46.8\text{ N}\)
• Acceleration due to gravity, \(g \approx 9.81\text{ m/s}^2\)

Determine the normal force

Using the Static Equilibrium knowledge point

$$
LATEXBLOCK0
$$

Relate pulling force to maximum static friction

Using the Static Equilibrium knowledge point

$$
LATEXBLOCK1
$$

Calculate the coefficient of static friction

The maximum static friction force is related to the normal force by:

$$ f_{s,\text{max}} = \mu_s F_N $$

Solving for the coefficient of static friction \(\mu_s\):

$$ \mu_s = \frac{f_{s,\text{max}}}{F_N} = \frac{46.8\text{ N}}{91.5273\text{ N}} \approx 0.5113 $$

Rounding to three decimal places, we get approximately \(0.512\).

Answer:

• (A) 0.512 (Correct answer)
• (B) 0.566
• (C) 0.621
• (D) 0.652