Physics 15 Torque (17 of 25) Body Mechanics: Ex. 5, F=? Leg Lifting Weights

Michel van Biezen
24 Jan 201608:51
EducationalLearning
32 Likes 10 Comments

TLDRThe video script explores the mechanics of how the human body, specifically the lower leg and thigh muscle, can lift a significant weight. It uses the example of a 100-pound weight being lifted by the lower leg, with the muscle force exerted through a tendon at an angle. The script explains the concept of torque and equilibrium, leading to a calculation of the force required by the thigh muscle to hold the weight stationary. It concludes with the surprising result that the muscle must exert a force of 799 pounds to lift or hold the weight, emphasizing the incredible strength of human muscles. This educational content provides insight into the physics of human movement and the powerful forces at work in our bodies.

Takeaways
  • 📐 The lower leg is lifted by the action of the calf muscles, which are connected to the leg bone via a tendon.
  • 🔵 The tendon exerts a force on the leg bone to hold up the weight of the lower leg and any additional weight attached to the foot.
  • 📏 The angle of the lower leg (4 degrees) and the angle of the tendon relative to the bone (25 degrees) are crucial in calculating the force exerted.
  • ⚖️ The problem is approached by considering the equilibrium of torques around the knee joint, which must sum up to zero.
  • 🧮 The weight of the lower leg is assumed to be at its midpoint, and the perpendicular distance from the force line of action is calculated.
  • 📐 The perpendicular distance from the tendon's line of action to the pivot point is found using trigonometric relationships.
  • 🔢 The force exerted by the tendon is calculated by balancing the torques, taking into account the angles and distances involved.
  • 🤸‍♂️ The actual weight of the lower leg is corrected to a more reasonable 10 pounds, instead of an unrealistic 100 pounds.
  • 📉 The weight of the additional load (100 pounds) and the force exerted by the tendon are used to calculate the required force (799 pounds).
  • 💪 The human body's muscles are incredibly strong, capable of exerting substantial forces to perform various motions and maintain postures.
  • 🏋️‍♀️ Regular gym users can develop the strength to exert such forces, demonstrating the power of human musculature.
Q & A

  • What is the primary focus of the lecture?

    -The lecture focuses on demonstrating how the mechanics of the human body, specifically the lower leg and the tendons, work to lift and support weight.

  • What is the angle formed by the lower leg in this example?

    -The angle formed by the lower leg in this example is four degrees.

  • What is the role of the tendon in this scenario?

    -The tendon is connected to the leg bone and is responsible for pulling on the bone to suspend the weight of the lower leg and any additional weight connected to the foot.

  • What is the approximate distance of the attachment point of the tendon from the total length of the leg bone?

    -The tendon is attached at a distance of 1/5 the total length of the leg bone.

  • What is the approximate angle between the direction of the tendon and the direction of the bone?

    -The angle is approximately 25 degrees.

  • What is the assumption made about the center of mass of the lower leg?

    -The center of mass of the lower leg is assumed to be at about the halfway point of the leg.

  • What is the force exerted by the tendon in terms of the perpendicular distance from the line of action to the pivot point?

    -The force exerted by the tendon is calculated using the perpendicular distance from its line of action to the pivot point, taking into account the angle of the tendon and the cosine of that angle.

  • What is the significance of the angle theta in the calculation?

    -Theta is the angle between the perpendicular to the bone and the direction of the force exerted by the tendon. It is crucial for calculating the torque produced by the tendon.

  • What is the calculated force required by the thigh muscle to hold up a 100-pound weight at a 40-degree angle?

    -The calculated force required by the thigh muscle is 799 pounds.

  • Why is it important to consider the torque in the equilibrium of the system?

    -Considering the torque is important because it ensures that the sum of all the torques about a point is equal to zero, which is a condition for mechanical equilibrium.

  • How does the lecture illustrate the strength of human muscles?

    -The lecture illustrates the strength of human muscles by calculating the force required to hold a certain weight at a specific angle, demonstrating the enormous strength needed for such a task.

  • What is the practical application of understanding the mechanics of muscle force in daily life or exercise?

    -Understanding the mechanics of muscle force helps in designing effective exercises and physical training programs that target specific muscle groups and improve overall physical performance.

Outlines
00:00
🔍 Mechanics of Lifting Weight with the Lower Leg

This paragraph explains the biomechanics of lifting a heavy weight using the lower leg. It discusses how the angle of the lower leg, the force exerted by the muscle through the tendon, and the weight of the lower leg itself contribute to the ability to lift a weight. The paragraph explores the concept of torque and equilibrium around the knee joint, using the weight of the lower leg and an additional hundred pounds as examples. It also calculates the force required on the tendon to maintain equilibrium, taking into account the angle of the tendon's pull and its distance from the pivot point.

05:00
📐 Correcting the Weight and Calculating Muscle Force

The second paragraph corrects the weight of the lower leg from an unrealistic hundred pounds to a more reasonable ten pounds, and continues the biomechanical analysis. It outlines the process of calculating the force exerted by the thigh muscle (F) that is transmitted through the tendon to lift or hold a weight. The calculation involves finding the torque created by the weight and the muscle force, and solving for F using trigonometric relationships. The final calculation reveals that a force of 799 pounds is required by the thigh muscle to hold the weight stationary, illustrating the significant strength of human muscles.

Mindmap
Keywords
💡Mechanics
Mechanics refers to the branch of physics that deals with the properties of and forces acting upon objects in motion. In the video, it is central to understanding how the body uses muscle force to lift weights. The script discusses the mechanics of lifting a 100-pound weight using the lower leg as an example.
💡Torque
Torque is the rotational equivalent of linear force. It is the measure of the force that can cause an object to rotate around an axis. In the context of the video, torque is used to describe the forces acting on the leg bone and how they contribute to lifting a weight.
💡Equilibrium
Equilibrium in physics means a state in which all forces acting on an object cancel each other out, resulting in no net force. The script uses the concept of equilibrium to set up the problem of finding the force required to hold up the weight without moving.
💡Tendon
A tendon is a tough, inelastic band of connective tissue that attaches muscle to bone. In the video, the tendon's role is emphasized as it connects the thigh muscle to the leg bone and is responsible for transmitting the force that lifts the weight.
💡Angle of Force
The angle of force refers to the direction in which a force is applied relative to an object or axis. The script discusses the angle between the tendon and the leg bone, which is crucial in calculating the effective force exerted by the muscle.
💡Cosine of Angle
The cosine of an angle is a trigonometric function that describes the ratio of the adjacent side to the hypotenuse in a right-angled triangle. In the context of the video, cosine is used to calculate the component of the tendon's force that contributes to the torque.
💡Sine of Angle
The sine of an angle is another trigonometric function that describes the ratio of the opposite side to the hypotenuse in a right-angled triangle. It is used in the script to calculate the perpendicular distances that are necessary for determining torques.
💡Center of Mass
The center of mass is the point at which the mass of an object is concentrated for the purpose of calculating gravitational forces. In the video, it is assumed that the center of mass of the lower leg is at its halfway point for simplicity in calculations.
💡Perpendicular Distance
The perpendicular distance is the shortest distance between a point and a line, measured at a right angle to the line. The script uses this concept to determine the effective distances from the pivot point to the lines of action of the forces.
💡Thigh Muscle
The thigh muscle, specifically the quadriceps, is a group of four muscles at the front of the thigh responsible for extending the leg. In the video, the force exerted by the thigh muscle through the tendon is calculated to understand its role in lifting the weight.
💡Strength of Muscles
The strength of muscles refers to their capacity to exert force. The video concludes by emphasizing the significant strength required by muscles to perform various motions, such as lifting weights, and how the calculations help understand the underlying mechanics.
Highlights

The lecture discusses how the human body uses mechanics to lift heavy weights, providing insight into the force exerted by muscles.

A 100-pound weight is used as an example to illustrate the mechanics of lifting with the lower leg.

The current angle of the lower leg is noted to be four degrees, which is significant for the force calculation.

The time muscle is identified as the key muscle involved in lifting the leg, connected via a tendon to the leg bone.

The tendon's force is calculated based on its distance from the leg bone, which is one-fifth of the total leg bone length.

The angle between the tendon and the bone is approximately 25 degrees, affecting the torque calculation.

The concept of equilibrium is introduced, stating that the sum of torques about the knee equals zero.

The weight of the lower leg is considered, with the center of mass assumed to be at the halfway point.

The perpendicular distance from the line of action of the force to the pivot point is identified as a key factor in the calculation.

The angle theta is defined as the angle between the perpendicular to the bone and the direction of the force.

The torque caused by the tendon is calculated using the length of the leg bone and the cosine of the angle theta.

The force exerted by the tendon is found by solving a system of equations representing the torques.

The weight of the lower leg is corrected to 10 pounds for a more realistic calculation.

The force required by the thigh muscle to hold the weight is calculated to be 799 pounds.

The strength of the human muscles is highlighted, emphasizing the body's ability to perform various motions.

The lecture concludes by emphasizing the importance of understanding muscle strength and force in human motion.

Transcripts

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Related Tags
Muscle MechanicsBiomechanicsThigh MuscleLower LegWeight LiftingForce CalculationEquilibriumTorque AnalysisPhysical StrengthHealth ScienceHuman Body