### Understanding Forces in the Quadriceps and Knee JointThe quadriceps muscle group, located in the upper leg, plays a crucial role in knee extension. This educational module explores the biomechanics of the knee using forces exerted by the quadriceps muscle.#### Muscle Force AnalysisThe quadriceps muscle exerts a force denoted as \( F_q \), which is specified in this scenario to be \( F_q = 1240 \, \text{N} \). This force is transmitted through a tendon over the kneecap (the patella) and is illustrated in the accompanying diagram.#### Diagram DescriptionThe diagram depicts a side view of the knee joint, illustrating the following components:1. **Quadriceps Tendon**: Visible at the top, connecting the quadriceps muscle to the patella.2. **Patella**: The kneecap, acting as a fulcrum for the forces applied.3. **Force Vectors**: - \( F_q \): The force exerted by the quadriceps muscle. - \( F_{t2} \): The force exerted by the tendon post-patella. - \( F_c \): The force exerted by the patella on the femur, directed along the shaft of the femur.The angles in the diagram are measured as follows:- 30° between the quadriceps tendon (\( F_q \)) and the vertical.- 75° between the femur and the tendon (\( F_{t2} \)).#### Problem StatementYour task is to determine the resultant force on the upper leg bone (the femur) caused by these interactions:1. **Magnitude in Newtons**: Calculate the resultant force magnitude.2. **Direction in Degrees**: Measure the direction in degrees counterclockwise from an axis directed to the left.To solve:1. Calculate vector components of \( F_{t2} \) and \( F_c \) relative to known angles.2. Use vector addition principles to find the resultant force vector.3. Determine the angle of this resultant vector counterclockwise from the horizontal axis.Fill in the blanks provided in the exercise for magnitude and direction:- Magnitude: __________ [N]- Direction: __________° counter-clockwise from an axis directed to the leftThis exercise enhances understanding of biomechanical forces and vector analysis, crucial in fields like kinesiology, physical therapy, and biomedical engineering.

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The upper leg muscle (quadriceps) exerts a force of Fg 1240 N, which is caried by a tendon over the kneecap (the patella) at the angles shown in the figure below. 75 Find the magnitude in newtons and direction in degrees counter-clockwise from an axis directed to the left of the force exerted by the kneecap on the upper leg bone (the femur). magnitude • counter-clockwise from an axis directed to the left direction

The upper leg muscle (quadriceps) exerts a force of Fg 1240 N, which is caried by a tendon over the kneecap (the patella) at the angles shown in the figure below. 75 Find the magnitude in newtons and direction in degrees counter-clockwise from an axis directed to the left of the force exerted by the kneecap on the upper leg bone (the femur). magnitude • counter-clockwise from an axis directed to the left direction

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).

Question

### Understanding Forces in the Quadriceps and Knee Joint

The quadriceps muscle group, located in the upper leg, plays a crucial role in knee extension. This educational module explores the biomechanics of the knee using forces exerted by the quadriceps muscle.

#### Muscle Force Analysis

The quadriceps muscle exerts a force denoted as \( F_q \), which is specified in this scenario to be \( F_q = 1240 \, \text{N} \). This force is transmitted through a tendon over the kneecap (the patella) and is illustrated in the accompanying diagram.

#### Diagram Description

The diagram depicts a side view of the knee joint, illustrating the following components:

1. **Quadriceps Tendon**: Visible at the top, connecting the quadriceps muscle to the patella.
2. **Patella**: The kneecap, acting as a fulcrum for the forces applied.
3. **Force Vectors**:
- \( F_q \): The force exerted by the quadriceps muscle.
- \( F_{t2} \): The force exerted by the tendon post-patella.
- \( F_c \): The force exerted by the patella on the femur, directed along the shaft of the femur.

The angles in the diagram are measured as follows:
- 30° between the quadriceps tendon (\( F_q \)) and the vertical.
- 75° between the femur and the tendon (\( F_{t2} \)).

#### Problem Statement

Your task is to determine the resultant force on the upper leg bone (the femur) caused by these interactions:
1. **Magnitude in Newtons**: Calculate the resultant force magnitude.
2. **Direction in Degrees**: Measure the direction in degrees counterclockwise from an axis directed to the left.

To solve:
1. Calculate vector components of \( F_{t2} \) and \( F_c \) relative to known angles.
2. Use vector addition principles to find the resultant force vector.
3. Determine the angle of this resultant vector counterclockwise from the horizontal axis.

Fill in the blanks provided in the exercise for magnitude and direction:
- Magnitude: __________ [N]
- Direction: __________° counter-clockwise from an axis directed to the left

This exercise enhances understanding of biomechanical forces and vector analysis, crucial in fields like kinesiology, physical therapy, and biomedical engineering.

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