https://file.aiquickdraw.com/mathbot/file/17282704155727hh1gjfr.jpg

Let's solve both parts (a) and (b) from the image you've uploaded.

### Part (a):
The person supports **65.0 kg** on their knee. To find the maximum frictional force in the knee joint, we first need to calculate the force due to gravity acting on that mass, which is given by:

\[
F_{\text{gravity}} = m \cdot g
\]

where:
- \(m = 65.0 \, \text{kg}\) is the mass,
- \(g = 9.81 \, \text{m/s}^2\) is the acceleration due to gravity.

Now, let's compute:

\[
F_{\text{gravity}} = 65.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 637.65 \, \text{N}
\]

Thus, the maximum frictional force in the knee joint is **637.65 N**.

---

### Part (b):
In strenuous exercise, forces up to **10 times** greater than the weight being supported can be exerted on the joints. Therefore, the maximum frictional force under these conditions is:

\[
F_{\text{max}} = 10 \times F_{\text{gravity}} = 10 \times 637.65 \, \text{N} = 6376.5 \, \text{N}
\]

Thus, the maximum frictional force in this scenario is **6376.5 N**.

---

Do you want more details on any of these calculations? Let me know!

### Here are 5 related questions you might consider:
1. How would the frictional force change if the person weighed 80 kg instead of 65 kg?
2. What happens to the frictional force if the acceleration due to gravity changes, say, on another planet?
3. How can knee injuries affect the frictional force in the joint?
4. Is the frictional force always proportional to the weight supported, or could other factors influence it?
5. How does joint lubrication affect the friction in knee joints?

**Tip:** When calculating forces related to body mass, always ensure you're using the correct unit for gravity, \(9.81 \, \text{m/s}^2\), unless specified otherwise (like on other planets).

What is the maximum frictional force in the knee joint of a person who supports 65.0 kg of her mass on that knee? During strenuous exercise, forces up to 10 times greater than the weight can be exerted on the joints. What is the maximum frictional force under such conditions?

Find out how to calculate the maximum frictional force in a knee joint supporting 65 kg of mass. This problem applies Newton's Second Law, taking into account forces during strenuous exercise, which can reach up to 10 times the normal force.

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