Physics 15 Torque (4 of 27) Bar Held Up by Friction

Michel van Biezen
12 Jan 201614:42
EducationalLearning
32 Likes 10 Comments

TLDRThe video script presents a physics problem involving a beam held up by friction between it and a post, and a cable making a 20-degree angle with the horizontal. The beam supports another mass, M, at a distance, X, from the post. The challenge is to determine the minimum distance, X, required to prevent the beam from slipping. The solution involves calculating the tension in the cable, the normal force, and the friction force using trigonometric functions and the torque method. By setting the sum of torques to zero around a pivot point, the tension in the cable is expressed in terms of X. Finally, the friction force is calculated, and an equation is solved to find the critical distance, X, ensuring the beam does not slip. The process concludes with a numerical example, assuming specific values for the mass and length of the beam, leading to the minimum distance X in centimeters.

Takeaways
  • ๐Ÿ” A beam is held up by friction against a vertical post and a cable at a 20-degree angle, supporting a suspended mass.
  • ๐Ÿ“ The horizontal component of the cable's tension creates the normal force that results in friction between the beam and the post.
  • ๐Ÿงฎ The friction force can be calculated using the normal force times the coefficient of friction (ฮผ).
  • ๐Ÿ“ The normal force is equal to the horizontal component of the tension (T_x), which is T times the cosine of the angle.
  • โš–๏ธ The torque method is used to find the tension in the cable by considering the sum of all torques about a pivot point to be zero.
  • ๐Ÿ“ The distance from the line of action of the force to the pivot point (d1 and d2) is crucial for calculating torques.
  • ๐Ÿ”ข The length of the beam (L) and the distance of the suspended mass from the post (X) are used to calculate the tension in the cable.
  • ๐Ÿค” The minimum distance (X) at which the beam will not slip is found by balancing the torques caused by the weight of the beam, the suspended mass, and the friction force.
  • ๐Ÿ“‰ As the suspended mass is moved closer to the post, the likelihood of the beam slipping increases due to the increased force pulling it down.
  • ๐Ÿ“š The coefficient of friction (ฮผ) is a key factor in determining the friction force and thus the stability of the beam.
  • ๐Ÿ“ The sine and cosine of the angle (20 degrees) are used in the equations to find the components of the tension and the friction force.
Q & A

  • What is the main problem being discussed in the script?

    -The script discusses a problem involving a beam supported by friction against a post and a cable at an angle. The challenge is to find the minimum distance, denoted as X, that a suspended mass can be from the post without causing the beam to slip.

  • What force prevents the beam from slipping down?

    -The force that prevents the beam from slipping down is the frictional force between the beam and the post, which is generated by the horizontal component of the tension in the cable.

  • How is the friction force calculated in this scenario?

    -The friction force is calculated as the product of the normal force (which is equal to T sub X, the horizontal component of the tension in the string) and the coefficient of friction (mu).

  • What is the role of the torque method in solving this problem?

    -The torque method is used to find the tension in the cable. By setting the sum of all torques around a pivot point to zero, one can solve for the unknown tension, which is necessary to calculate the friction force.

  • How is the tension in the cable related to the angle made by the cable with the horizontal?

    -The tension in the cable can be found using trigonometry. Specifically, the horizontal component of the tension (T sub X) is found using the cosine of the angle (20 degrees in this case), and the vertical component (T sub Y) is found using the sine of the angle.

  • What is the significance of the mass M being moved back and forth?

    -Moving the mass M back and forth changes the force acting on the beam. The farther the mass is from the post, the less the force pulling down on the beam, which reduces the likelihood of slipping. Conversely, moving the mass closer increases the force and the likelihood of slipping.

  • What is the formula for calculating the friction force in terms of the tension in the cable?

    -The friction force is calculated as the tension times the cosine of the angle (20 degrees) times the coefficient of friction (mu).

  • How is the minimum distance X found?

    -The minimum distance X is found by setting up an equation where the sum of all torques about a certain pivot point equals zero, and solving for X, which represents the distance from the post at which the beam will not slip.

  • What are the units of the final answer for the minimum distance X?

    -The final answer for the minimum distance X is given in meters, and then converted to centimeters for a more precise measurement.

  • What is the value of the coefficient of friction (mu) used in the script?

    -The coefficient of friction (mu) used in the script is 0.5.

  • What is the length of the beam (L) used in the numerical example?

    -In the numerical example, the length of the beam (L) is initially considered to be 10 meters but is later simplified to 1 meter for ease of calculation.

  • What is the weight of the beam and the suspended mass, denoted as mg, in the numerical example?

    -In the numerical example, the weight of the beam and the suspended mass (mg) is given as 100 Newtons.

Outlines
00:00
๐Ÿ” Introduction to the Beam and Friction Problem

The video begins with an introduction to a physics problem involving a beam supported by friction against a post and a cable at a 20-degree angle. The beam has mass M and supports another mass M at a distance X from the post. The goal is to determine the minimum distance X that prevents the beam from slipping. The frictional force is explained as being caused by the horizontal component of the tension in the cable, which is then broken down into components and related to the normal force. The video outlines the need to calculate the tension in the cable using the torque method, with the pivot point chosen to balance the torques from the forces acting on the system.

05:04
๐Ÿ“ Calculating Tension and Friction Force

The second paragraph delves into the calculation of the tension in the cable and the subsequent friction force. It explains that the tension can be found using the torque about a pivot point and that the friction force is the product of the normal force and the coefficient of friction. The normal force is identified as the horizontal component of the tension (T sub X), which is then used to calculate the friction force using the cosine of the 20-degree angle. The tension in the cable is expressed in terms of X, and the relationship between the forces and distances involved is developed into an equation that will be used to solve for X.

10:05
๐Ÿ”ข Solving for the Minimum Distance X

The final paragraph involves plugging in numerical values to solve for the minimum distance X that keeps the beam from slipping. It assumes the weight of the masses (mg) is 100 Newtons and the length of the beam (L) is 1 meter for simplicity. The forces and torques are analyzed around a second pivot point (point B) to ensure the friction force is sufficient to prevent slipping. The resulting equation is solved for X, which turns out to be 20.7 centimeters. This distance is identified as the closest the second mass can be to the post without the beam slipping, thus completing the problem's solution.

Mindmap
Keywords
๐Ÿ’กFriction
Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact. In the video, friction is critical for preventing the beam from slipping down the post. It is generated by the horizontal component of the tension in the cable acting on the beam, which is essential for the static equilibrium of the system.
๐Ÿ’กTension
Tension refers to the force exerted by a rope, cable, or similar object when it is pulled tight by forces acting from opposite ends. In the context of the video, the tension in the cable holding up the beam at an angle is decomposed into horizontal and vertical components, which are used to calculate the normal force and subsequently the frictional force required to keep the beam stationary.
๐Ÿ’กNormal Force
Normal force is the force exerted by a surface that supports the weight of an object resting on it, acting perpendicular to the surface. In the video, the normal force is the result of the horizontal component of the tension in the cable pushing the beam against the post. It is a key factor in calculating the frictional force that prevents the beam from slipping.
๐Ÿ’กCoefficient of Friction (ฮผ)
The coefficient of friction (ฮผ) is a dimensionless scalar value that describes the ratio of the frictional force between two bodies and the normal force between them. It is used in the video to calculate the frictional force acting on the beam, which is ฮผ times the normal force, and is crucial in determining the minimum distance X that the suspended mass can be without the beam slipping.
๐Ÿ’กTorque
Torque is the rotational equivalent of linear force, a measure of the force that can cause an object to rotate about an axis. In the video, the concept of torque is used to analyze the forces acting on the beam and to ensure that the sum of all torques equals zero for the beam to remain in equilibrium. The torques considered are due to the weight of the suspended mass, the weight of the beam itself, and the tension in the cable.
๐Ÿ’กPivot Point
A pivot point is a point or line around which a body rotates orๆ‰ญ (twists). In the video, the pivot point is used as a reference to calculate the torques acting on the beam. The selection of the pivot point is crucial for simplifying the calculation of torques and determining the conditions for equilibrium.
๐Ÿ’กEquilibrium
Equilibrium refers to a state of balance where the sum of the forces acting on a body is zero, resulting in no acceleration. The video's main theme revolves around finding the conditions (specifically, the minimum distance X) for the beam to be in equilibrium, where it neither slips nor accelerates.
๐Ÿ’กBeam
A beam is a horizontal or sloping load-bearing element in a structure. In the video, the beam is the main subject of the problem, which is held up by friction against a post and a cable at an angle. The beam is subjected to various forces and torques, and the goal is to find the position of the suspended mass that maintains the beam's equilibrium.
๐Ÿ’กSuspended Mass (M)
The suspended mass (M) refers to the weight of the object that is hung from the beam. In the video, the position of this mass can be adjusted along the beam, and the challenge is to find the minimum distance X from the post at which the mass can be placed without causing the beam to slip, considering the forces and torques involved.
๐Ÿ’กDistance X
Distance X is the variable representing the horizontal distance from the post to the point where the suspended mass is attached to the beam. The video aims to find the minimum value of X that prevents the beam from slipping, taking into account the forces acting on the system.
๐Ÿ’กStatic Equilibrium
Static equilibrium occurs when all the forces acting on an object cancel each other out, resulting in no net force and no motion. The problem presented in the video is a classic example of static equilibrium, where the frictional force balances the components of gravitational forces to prevent motion.
Highlights

The problem involves finding the minimum distance X to prevent a beam from slipping down due to friction

The beam is supported by a cable making a 20 degree angle with the horizontal

The beam has mass M and supports another mass M at a distance X from the post

The horizontal component of the cable tension pushes the beam against the post, creating friction

The friction force is the normal force times the coefficient of friction

The normal force is equal to the horizontal component of the cable tension

The horizontal tension component can be found using the cosine of the 20 degree angle

The torque method is used to find the tension in the cable

The sum of all torques about a pivot point equals zero

The torques are caused by the hanging mass, the beam's weight, and the cable tension

The center of mass of the beam is found to be at its halfway point

The perpendicular distance from the cable tension to the pivot point is found using sine

The cable tension is expressed in terms of X using the mass, distance, and angle

The friction force is calculated as the tension times cosine of 20 degrees times the coefficient of friction

A pivot point is chosen on the other side to find the minimum friction force needed to prevent slipping

The sum of torques about the new pivot point equals zero, with terms for the hanging mass, beam weight, and friction force

The equation is solved for the minimum distance X, which is found to be 20.7 cm

If the mass is moved closer than 20.7 cm, the beam will slip; if farther, the friction will hold the beam up

Transcripts

Browse More Related Video

Physics 15 Torque Example 1 (1 of 7) Mass on Rod and Cable

Physics 15 Torque (19 of 25) More Examples: 1 T=? of Cable Holding Fish

Physics 15 Torque (3 of 27) Tension=? in the Cable

Physics 15 Torque Example 6 (6 of 7) The Hungry Bear on a Beam; Tension in the Cable

Physics 15 Torque Fundamentals (8 of 13) How to Calculate a Torque (Basic Example 2)

Physics 15 Torque Example 3 (3 of 7) Mass on Rod and Cable

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Friction ForceTension CalculationBeam BalancePhysics ProblemEngineering ChallengeMechanical StabilityTorque AnalysisCritical ThinkingMathematical SolutionEngineering Physics