What is the value of the frictional force when the joint is arthritic? (μ = 0.03)
Understand the Problem
The question is asking to calculate the value of the frictional force at a joint given certain parameters such as the normal force and the coefficient of friction. We will need to apply the formula for frictional force, which is the product of the normal force and the coefficient of friction.
Answer
The frictional force for an arthritic joint is $9 \, N$.
Answer for screen readers
The value of the frictional force for an arthritic joint is $9 , N$.
Steps to Solve
- Identify Given Values
We have the following values from the problem statement:
- Normal force ($F_n$) = 300 N
- Coefficient of friction ($\mu$) for normal joint = 0.9
- Coefficient of friction ($\mu$) for arthritic joint = 0.03
- Calculate Frictional Force for a Normal Joint
The frictional force ($F_f$) can be calculated using the formula:
$$ F_f = \mu \times F_n $$
For the normal joint:
$$ F_f = 0.9 \times 300 , N $$
- Calculate Frictional Force for an Arthritic Joint
Now, calculate the frictional force for an arthritic joint using the lower coefficient:
$$ F_f = \mu \times F_n $$
For the arthritic joint:
$$ F_f = 0.03 \times 300 , N $$
- Compute the Values
Now, let's compute the frictional forces:
For the normal joint:
$$ F_f = 0.9 \times 300 = 270 , N $$
For the arthritic joint:
$$ F_f = 0.03 \times 300 = 9 , N $$
The value of the frictional force for an arthritic joint is $9 , N$.
More Information
Frictional force is critical in understanding joint function. The significant difference between the frictional forces in normal and arthritic joints highlights how joint conditions can impact movement and stability.
Tips
- Confusing the coefficients: Ensure that the correct coefficient is used for each type of joint (normal vs. arthritic).
- Forgetting to multiply with the normal force: Always remember to multiply the coefficient of friction by the normal force in order to find the frictional force.
