Question
7. The force of static friction of your car tires against the driveway is \( 400 . \mathrm{N} \). Your bike has a weight of 750 N. What is the coefficient of static friction?
Ask by Turnbull Peters. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The coefficient of static friction is approximately 0.53.
Solution
To determine the **coefficient of static friction (\( \mu_s \))** between your bike and the driveway, you can use the following formula:
\[
\mu_s = \frac{f_s}{N}
\]
Where:
- \( f_s \) is the force of static friction.
- \( N \) is the normal force (which, in this case, is equal to the weight of the bike).
**Given:**
- Force of static friction, \( f_s = 400 \, \text{N} \)
- Weight of the bike, \( N = 750 \, \text{N} \)
**Calculation:**
\[
\mu_s = \frac{400 \, \text{N}}{750 \, \text{N}} = \frac{400}{750} \approx 0.533
\]
**Rounded to two decimal places:**
\[
\mu_s \approx 0.53
\]
**Conclusion:**
The coefficient of static friction between your bike and the driveway is **approximately 0.53**.
**Answer:** The coefficient of static friction is approximately 0.53.
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Simplify this solution Beyond the Answer
To find the coefficient of static friction \( \mu_s \), you can use the formula: \[ \mu_s = \frac{F_s}{N} \] where \( F_s \) is the force of static friction, and \( N \) is the normal force, which is equal to the weight of the object. In this case, the normal force \( N \) for the bike is 750 N. Given that the static friction force \( F_s \) for the tires is 400 N, we plug the values into the formula: \[ \mu_s = \frac{400 \, \mathrm{N}}{750 \, \mathrm{N}} \approx 0.53 \] So, the coefficient of static friction between the bike and the surface is approximately \( 0.53 \).
